%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU475^1 : TPTP v9.2.1. Bugfixed v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.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 126.27s 126.56s % Output : Proof 126.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU475^1 : TPTP v9.2.1. Bugfixed v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.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 17:36:53 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TH0 % 126.27/126.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 126.27/126.56 --- 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... % 126.27/126.56 --- 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... % 126.27/126.56 % SZS status Theorem % 126.27/126.56 % SZS output start Proof % 126.27/126.56 ( % 126.27/126.56 (declare-sort $$unsorted 0) % 126.27/126.56 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 126.27/126.56 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 126.27/126.56 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 126.27/126.56 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 126.27/126.56 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 126.27/126.56 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 126.27/126.56 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 126.27/126.56 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 126.27/126.56 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 126.27/126.56 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 126.27/126.56 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 126.27/126.56 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 126.27/126.56 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 126.27/126.56 (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))))))))) % 126.27/126.56 (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)))))) % 126.27/126.56 (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)))))) % 126.27/126.56 (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))))) % 126.27/126.56 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 126.27/126.56 (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)))))))) % 126.27/126.56 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 126.27/126.56 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 126.27/126.56 (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)))))))) % 126.27/126.56 (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))))))) % 126.27/126.56 (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)))))))) % 126.27/126.56 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 126.27/126.56 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 126.27/126.56 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 126.27/126.56 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 126.27/126.56 (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)))))))) % 126.27/126.56 (define @t1 () (@var "Z" $$unsorted)) % 126.27/126.56 (define @t2 () (@var "Y" $$unsorted)) % 126.27/126.56 (define @t3 () (= @t2 @t1)) % 126.27/126.56 (define @t4 () (not @t3)) % 126.27/126.56 (define @t5 () (@var "X" $$unsorted)) % 126.27/126.56 (define @t6 () (= @t5 @t1)) % 126.27/126.56 (define @t7 () (not @t6)) % 126.27/126.56 (define @t8 () (= @t5 @t2)) % 126.27/126.56 (define @t9 () (not @t8)) % 126.27/126.56 (define @t10 () (and @t9 @t7 @t4)) % 126.27/126.56 (define @t11 () (@list @t5 @t2 @t1)) % 126.27/126.56 (define @t12 () (exists @t11 @t10)) % 126.27/126.56 (define @t13 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 126.27/126.56 (define @t14 () (_ tptp.tc @t13)) % 126.27/126.56 (define @t15 () (= (_ tptp.sc @t14) (_ tptp.tc (_ tptp.sc @t13)))) % 126.27/126.56 (define @t16 () (@list @t13)) % 126.27/126.56 (define @t17 () (forall @t16 @t15)) % 126.27/126.56 (define @t18 () (not @t17)) % 126.27/126.56 (define @t19 () (not @t18)) % 126.27/126.56 (define @t20 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 126.27/126.56 (define @t21 () (_ (_ @t20 @t5) @t2)) % 126.27/126.56 (define @t22 () (_ @t13 @t5)) % 126.27/126.56 (define @t23 () (_ @t22 @t2)) % 126.27/126.56 (define @t24 () (@list @t5 @t2)) % 126.27/126.56 (define @t25 () (forall @t24 (=> @t23 @t21))) % 126.27/126.56 (define @t26 () (@list @t13 @t20)) % 126.27/126.56 (define @t27 () (lambda @t26 @t25)) % 126.27/126.56 (define @t28 () (_ @t13 @t2)) % 126.27/126.56 (define @t29 () (_ @t28 @t5)) % 126.27/126.56 (define @t30 () (@list @t13 @t5 @t2)) % 126.27/126.56 (define @t31 () (lambda @t30 @t29)) % 126.27/126.56 (define @t32 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 126.27/126.56 (define @t33 () (_ @t32 @t13)) % 126.27/126.56 (define @t34 () (@list @t32)) % 126.27/126.56 (define @t35 () (lambda @t34 (forall @t16 (= (_ @t32 @t33) @t33)))) % 126.27/126.56 (define @t36 () (_ tptp.subrel @t13)) % 126.27/126.56 (define @t37 () (lambda @t34 (forall @t16 (_ @t36 @t33)))) % 126.27/126.56 (define @t38 () (_ @t36 @t20)) % 126.27/126.56 (define @t39 () (lambda @t34 (forall @t26 (=> @t38 (_ (_ tptp.subrel @t33) (_ @t32 @t20)))))) % 126.27/126.56 (define @t40 () (_ @t22 @t5)) % 126.27/126.56 (define @t41 () (@list @t5)) % 126.27/126.56 (define @t42 () (lambda @t16 (forall @t41 @t40))) % 126.27/126.56 (define @t43 () (lambda @t16 (forall @t41 (not @t40)))) % 126.27/126.56 (define @t44 () (lambda @t30 (or @t8 @t23))) % 126.27/126.56 (define @t45 () (lambda @t16 (forall @t24 (=> @t23 @t29)))) % 126.27/126.56 (define @t46 () (lambda @t16 (forall @t24 (=> (and @t23 @t29) @t8)))) % 126.27/126.56 (define @t47 () (lambda @t16 (forall @t24 (=> @t23 (not @t29))))) % 126.27/126.56 (define @t48 () (or @t29 @t23)) % 126.27/126.56 (define @t49 () (lambda @t30 @t48)) % 126.27/126.56 (define @t50 () (_ @t22 @t1)) % 126.27/126.56 (define @t51 () (_ @t28 @t1)) % 126.27/126.56 (define @t52 () (and @t23 @t51)) % 126.27/126.56 (define @t53 () (forall @t11 (=> @t52 @t50))) % 126.27/126.56 (define @t54 () (lambda @t16 @t53)) % 126.27/126.56 (define @t55 () (and (_ tptp.trans @t20) @t38)) % 126.27/126.56 (define @t56 () (=> @t55 @t21)) % 126.27/126.56 (define @t57 () (@list @t20)) % 126.27/126.56 (define @t58 () (forall @t57 @t56)) % 126.27/126.56 (define @t59 () (lambda @t30 @t58)) % 126.27/126.56 (define @t60 () (@var "__flatten_var_1" $$unsorted)) % 126.27/126.56 (define @t61 () (@var "__flatten_var_0" $$unsorted)) % 126.27/126.56 (define @t62 () (_ tptp.rc @t14)) % 126.27/126.56 (define @t63 () (@list @t13 @t61 @t60)) % 126.27/126.56 (define @t64 () (lambda @t63 (_ (_ @t62 @t61) @t60))) % 126.27/126.56 (define @t65 () (lambda @t63 (_ (_ (_ tptp.sc @t62) @t61) @t60))) % 126.27/126.56 (define @t66 () (_ tptp.trans @t13)) % 126.27/126.56 (define @t67 () (lambda @t16 (and (_ tptp.refl @t13) (_ tptp.antisymm @t13) @t66))) % 126.27/126.56 (define @t68 () (lambda @t16 (and (_ tptp.asymm @t13) @t66))) % 126.27/126.56 (define @t69 () (lambda @t16 (forall @t24 (or @t8 @t23 @t29)))) % 126.27/126.56 (define @t70 () (not @t23)) % 126.27/126.56 (define @t71 () (@var "A" (-> $$unsorted Bool))) % 126.27/126.56 (define @t72 () (@list @t2)) % 126.27/126.56 (define @t73 () (_ @t71 @t5)) % 126.27/126.56 (define @t74 () (lambda @t16 (forall (@list @t71) (=> (exists @t41 @t73) (exists @t41 (and @t73 (forall @t72 (=> (_ @t71 @t2) @t70)))))))) % 126.27/126.56 (define @t75 () (@var "P" (-> $$unsorted Bool))) % 126.27/126.56 (define @t76 () (_ @t75 @t5)) % 126.27/126.56 (define @t77 () (lambda @t16 (forall (@list @t75) (=> (forall @t41 (=> (forall @t72 (=> (_ (_ @t14 @t5) @t2) (_ @t75 @t2))) @t76)) (forall @t41 @t76))))) % 126.27/126.56 (define @t78 () (lambda (@list @t13 @t5) (not (exists @t72 @t23)))) % 126.27/126.56 (define @t79 () (_ tptp.trc @t13)) % 126.27/126.56 (define @t80 () (_ @t79 @t2)) % 126.27/126.56 (define @t81 () (lambda @t30 (and (_ @t80 @t5) (_ (_ tptp.innf @t13) @t5)))) % 126.27/126.56 (define @t82 () (lambda @t16 (forall @t41 (exists @t72 (_ (_ (_ tptp.nfof @t13) @t2) @t5))))) % 126.27/126.56 (define @t83 () (_ @t79 @t5)) % 126.27/126.56 (define @t84 () (_ @t83 @t1)) % 126.27/126.56 (define @t85 () (lambda @t30 (exists (@list @t1) (and @t84 (_ @t80 @t1))))) % 126.27/126.56 (define @t86 () (_ tptp.join @t13)) % 126.27/126.56 (define @t87 () (_ (_ @t86 @t1) @t2)) % 126.27/126.56 (define @t88 () (lambda @t16 (forall @t11 (=> (and @t50 @t23) @t87)))) % 126.27/126.56 (define @t89 () (_ @t83 @t2)) % 126.27/126.56 (define @t90 () (lambda @t16 (forall @t11 (=> (and @t50 @t89) @t87)))) % 126.27/126.56 (define @t91 () (lambda @t16 (forall @t11 (=> (and @t84 @t89) @t87)))) % 126.27/126.56 (define @t92 () (lambda @t16 (forall @t24 (=> (_ (_ (_ tptp.trsc @t13) @t5) @t2) (_ (_ @t86 @t5) @t2))))) % 126.27/126.56 (define @t93 () (_ @t20 @t5 @t2)) % 126.27/126.56 (define @t94 () (@var "BOUND_VARIABLE_7746" $$unsorted)) % 126.27/126.56 (define @t95 () (@var "BOUND_VARIABLE_7744" $$unsorted)) % 126.27/126.56 (define @t96 () (_ @t20 @t95 @t94)) % 126.27/126.56 (define @t97 () (_ @t13 @t95 @t94)) % 126.27/126.56 (define @t98 () (_ (_ @t13 @t95) @t94)) % 126.27/126.56 (define @t99 () (not @t98)) % 126.27/126.56 (define @t100 () (_ @t13 @t94 @t95)) % 126.27/126.56 (define @t101 () (_ (_ @t13 @t94) @t95)) % 126.27/126.56 (define @t102 () (not @t101)) % 126.27/126.56 (define @t103 () (and @t102 @t99)) % 126.27/126.56 (define @t104 () (or @t103 @t96)) % 126.27/126.56 (define @t105 () (@list @t95 @t94)) % 126.27/126.56 (define @t106 () (or @t101 @t98)) % 126.27/126.56 (define @t107 () (or (not @t106) @t96)) % 126.27/126.56 (define @t108 () (lambda @t24 @t48)) % 126.27/126.56 (define @t109 () (_ @t108 @t95 @t94)) % 126.27/126.56 (define @t110 () (not @t109)) % 126.27/126.56 (define @t111 () (or @t110 @t96)) % 126.27/126.56 (define @t112 () (forall @t105 @t111)) % 126.27/126.56 (define @t113 () (not @t112)) % 126.27/126.56 (define @t114 () (@var "BOUND_VARIABLE_7755" $$unsorted)) % 126.27/126.56 (define @t115 () (@var "BOUND_VARIABLE_7757" $$unsorted)) % 126.27/126.56 (define @t116 () (@list @t114 @t115 @t1)) % 126.27/126.56 (define @t117 () (not (forall @t116 (or (not (_ @t20 @t114 @t115)) (not (_ @t20 @t115 @t1)) (_ @t20 @t114 @t1))))) % 126.27/126.56 (define @t118 () (or @t117 @t113 @t93)) % 126.27/126.56 (define @t119 () (forall @t57 @t118)) % 126.27/126.56 (define @t120 () (lambda @t24 @t119)) % 126.27/126.56 (define @t121 () (not @t97)) % 126.27/126.56 (define @t122 () (not (forall @t105 (or @t121 @t96)))) % 126.27/126.56 (define @t123 () (forall @t57 (or @t117 @t122 @t93))) % 126.27/126.56 (define @t124 () (lambda @t30 @t123)) % 126.27/126.56 (define @t125 () (_ @t49 @t13)) % 126.27/126.56 (define @t126 () (_ @t13 @t5 @t2)) % 126.27/126.56 (define @t127 () (not @t126)) % 126.27/126.56 (define @t128 () (forall @t24 (or @t127 @t93))) % 126.27/126.56 (define @t129 () (not @t128)) % 126.27/126.56 (define @t130 () (forall @t11 (or (not @t93) (not (_ @t20 @t2 @t1)) (_ @t20 @t5 @t1)))) % 126.27/126.56 (define @t131 () (not @t130)) % 126.27/126.56 (define @t132 () (lambda @t30 (forall @t57 (or @t131 @t129 @t93)))) % 126.27/126.56 (define @t133 () (lambda @t72 @t123)) % 126.27/126.56 (define @t134 () (lambda @t24 @t123)) % 126.27/126.56 (define @t135 () (_ @t134 @t5)) % 126.27/126.56 (define @t136 () (_ @t20 @t2 @t5)) % 126.27/126.56 (define @t137 () (forall @t57 (or @t117 @t122 @t136))) % 126.27/126.56 (define @t138 () (@var "BOUND_VARIABLE_8851" $$unsorted)) % 126.27/126.56 (define @t139 () (lambda (@list @t138) (forall @t57 (or @t117 @t122 (_ @t20 @t2 @t138))))) % 126.27/126.56 (define @t140 () (or (_ (_ @t134 @t2) @t5) (_ @t135 @t2))) % 126.27/126.56 (define @t141 () (lambda @t24 @t140)) % 126.27/126.56 (define @t142 () (= (_ @t49 (_ @t132 @t13)) (_ @t132 @t125))) % 126.27/126.56 (define @t143 () (forall @t16 @t142)) % 126.27/126.56 (define @t144 () (or @t131 @t129 @t21)) % 126.27/126.56 (define @t145 () (and @t130 @t128)) % 126.27/126.56 (define @t146 () (lambda @t57 @t128)) % 126.27/126.56 (define @t147 () (_ (lambda @t26 @t128) @t13)) % 126.27/126.56 (define @t148 () (_ @t13 @t5 @t1)) % 126.27/126.56 (define @t149 () (_ @t13 @t2 @t1)) % 126.27/126.56 (define @t150 () (_ (lambda @t16 (forall @t11 (or @t127 (not @t149) @t148))) @t20)) % 126.27/126.56 (define @t151 () (and @t150 (_ @t147 @t20))) % 126.27/126.56 (define @t152 () (=> @t151 @t21)) % 126.27/126.56 (define @t153 () (or @t70 @t21)) % 126.27/126.56 (define @t154 () (not @t51)) % 126.27/126.56 (define @t155 () (or @t70 @t154 @t50)) % 126.27/126.56 (define @t156 () (forall @t11 (or @t8 @t6 @t3))) % 126.27/126.56 (define @t157 () (@quantifiers_skolemize @t156 1)) % 126.27/126.56 (define @t158 () (_ @t20 @t157 @t94)) % 126.27/126.56 (define @t159 () (@list @t94)) % 126.27/126.56 (define @t160 () (not (forall @t159 @t158))) % 126.27/126.56 (define @t161 () (or (forall @t57 (or @t117 @t160 @t136)) (forall @t57 (or @t117 @t160 @t93)))) % 126.27/126.56 (define @t162 () (lambda @t24 @t161)) % 126.27/126.56 (define @t163 () (@purify @t162)) % 126.27/126.56 (define @t164 () (@var "BOUND_VARIABLE_87222" $$unsorted)) % 126.27/126.56 (define @t165 () (_ @t20 @t157 @t164)) % 126.27/126.56 (define @t166 () (@list @t164)) % 126.27/126.56 (define @t167 () (forall @t166 @t165)) % 126.27/126.56 (define @t168 () (not @t167)) % 126.27/126.56 (define @t169 () (@var "BOUND_VARIABLE_87210" $$unsorted)) % 126.27/126.56 (define @t170 () (_ @t20 @t169 @t157)) % 126.27/126.56 (define @t171 () (@list @t169)) % 126.27/126.56 (define @t172 () (forall @t171 @t170)) % 126.27/126.56 (define @t173 () (not @t172)) % 126.27/126.56 (define @t174 () (or @t117 @t173 @t168 @t93)) % 126.27/126.56 (define @t175 () (forall @t57 @t174)) % 126.27/126.56 (define @t176 () (lambda @t24 @t175)) % 126.27/126.56 (define @t177 () (@purify @t176)) % 126.27/126.56 (define @t178 () (= @t162 @t176)) % 126.27/126.56 (define @t179 () (forall @t16 (= (lambda @t24 (or @t137 @t123)) (lambda @t24 (forall @t57 (or @t117 (not (forall @t105 (or (and (not @t100) @t121) @t96))) @t93)))))) % 126.27/126.56 (define @t180 () (or @t117 (not (and @t172 @t167)) @t93)) % 126.27/126.56 (define @t181 () (= @t157 @t157)) % 126.27/126.56 (define @t182 () (not @t181)) % 126.27/126.56 (define @t183 () (or @t182 @t165)) % 126.27/126.56 (define @t184 () (@var "BOUND_VARIABLE_87220" $$unsorted)) % 126.27/126.56 (define @t185 () (_ @t20 @t184 @t164)) % 126.27/126.56 (define @t186 () (not (= @t157 @t184))) % 126.27/126.56 (define @t187 () (not (= @t184 @t157))) % 126.27/126.56 (define @t188 () (@list @t184)) % 126.27/126.56 (define @t189 () (or @t186 @t186 @t185)) % 126.27/126.56 (define @t190 () (or @t186 @t185)) % 126.27/126.56 (define @t191 () (forall @t188 @t190)) % 126.27/126.56 (define @t192 () (forall @t166 @t191)) % 126.27/126.56 (define @t193 () (forall (@list @t164 @t184) @t190)) % 126.27/126.56 (define @t194 () (@list @t184 @t164)) % 126.27/126.56 (define @t195 () (or @t187 @t185)) % 126.27/126.56 (define @t196 () (forall @t194 @t195)) % 126.27/126.56 (define @t197 () (or @t182 @t170)) % 126.27/126.56 (define @t198 () (@var "BOUND_VARIABLE_87212" $$unsorted)) % 126.27/126.56 (define @t199 () (_ @t20 @t169 @t198)) % 126.27/126.56 (define @t200 () (not (= @t157 @t198))) % 126.27/126.56 (define @t201 () (not (= @t198 @t157))) % 126.27/126.56 (define @t202 () (@list @t198)) % 126.27/126.56 (define @t203 () (or @t200 @t200 @t199)) % 126.27/126.56 (define @t204 () (or @t200 @t199)) % 126.27/126.56 (define @t205 () (forall @t202 @t204)) % 126.27/126.56 (define @t206 () (forall @t171 @t205)) % 126.27/126.56 (define @t207 () (@list @t169 @t198)) % 126.27/126.56 (define @t208 () (or @t201 @t199)) % 126.27/126.56 (define @t209 () (forall @t207 @t208)) % 126.27/126.56 (define @t210 () (= @t95 @t157)) % 126.27/126.56 (define @t211 () (not @t210)) % 126.27/126.56 (define @t212 () (or @t211 @t96)) % 126.27/126.56 (define @t213 () (forall @t105 @t212)) % 126.27/126.56 (define @t214 () (@list @t95 @t94)) % 126.27/126.56 (define @t215 () (= @t94 @t157)) % 126.27/126.56 (define @t216 () (not @t215)) % 126.27/126.56 (define @t217 () (or @t216 @t96)) % 126.27/126.56 (define @t218 () (forall @t105 @t217)) % 126.27/126.56 (define @t219 () (and @t218 @t213)) % 126.27/126.56 (define @t220 () (@var "BOUND_VARIABLE_16031" $$unsorted)) % 126.27/126.56 (define @t221 () (lambda (@list @t220 (@var "BOUND_VARIABLE_16032" $$unsorted)) (= @t220 @t157))) % 126.27/126.56 (define @t222 () (_ @t221 @t95 @t94)) % 126.27/126.56 (define @t223 () (not @t222)) % 126.27/126.56 (define @t224 () (_ @t221 @t94 @t95)) % 126.27/126.56 (define @t225 () (not @t224)) % 126.27/126.56 (define @t226 () (and @t225 @t223)) % 126.27/126.56 (define @t227 () (or @t226 @t96)) % 126.27/126.56 (define @t228 () (forall @t105 @t227)) % 126.27/126.56 (define @t229 () (not @t228)) % 126.27/126.56 (define @t230 () (or @t117 @t229 @t93)) % 126.27/126.56 (define @t231 () (forall @t57 @t230)) % 126.27/126.56 (define @t232 () (lambda @t24 @t231)) % 126.27/126.56 (define @t233 () (or @t182 @t158)) % 126.27/126.56 (define @t234 () (or @t211 @t211 @t96)) % 126.27/126.56 (define @t235 () (@list @t95)) % 126.27/126.56 (define @t236 () (forall @t235 @t212)) % 126.27/126.56 (define @t237 () (forall @t159 @t236)) % 126.27/126.56 (define @t238 () (forall (@list @t94 @t95) @t212)) % 126.27/126.56 (define @t239 () (or @t223 @t96)) % 126.27/126.56 (define @t240 () (forall @t105 @t239)) % 126.27/126.56 (define @t241 () (not @t240)) % 126.27/126.56 (define @t242 () (or @t117 @t241 @t93)) % 126.27/126.56 (define @t243 () (forall @t57 @t242)) % 126.27/126.56 (define @t244 () (or @t117 @t241 @t136)) % 126.27/126.56 (define @t245 () (forall @t57 @t244)) % 126.27/126.56 (define @t246 () (or @t245 @t243)) % 126.27/126.56 (define @t247 () (lambda @t24 @t246)) % 126.27/126.56 (define @t248 () (= @t247 @t232)) % 126.27/126.56 (define @t249 () (= @t177 @t163)) % 126.27/126.56 (define @t250 () (@list false)) % 126.27/126.56 (define @t251 () (forall @t24 (= @t175 @t161))) % 126.27/126.56 (define @t252 () (=> @t249 @t251)) % 126.27/126.56 (define @t253 () (forall @t24 (= @t161 @t175))) % 126.27/126.56 (define @t254 () (@quantifiers_skolemize @t156 2)) % 126.27/126.56 (define @t255 () (_ @t20 @t254 @t254)) % 126.27/126.56 (define @t256 () (forall @t57 (or @t117 @t173 @t168 @t255))) % 126.27/126.56 (define @t257 () (forall @t57 (or @t117 @t160 @t255))) % 126.27/126.56 (define @t258 () (or @t257 @t257)) % 126.27/126.56 (define @t259 () (= @t258 @t256)) % 126.27/126.56 (define @t260 () (= @t257 @t256)) % 126.27/126.56 (define @t261 () (not @t4)) % 126.27/126.56 (define @t262 () (not @t7)) % 126.27/126.56 (define @t263 () (not @t9)) % 126.27/126.56 (define @t264 () (or @t263 @t262 @t261)) % 126.27/126.56 (define @t265 () (forall @t11 (not @t10))) % 126.27/126.56 (define @t266 () (not @t265)) % 126.27/126.56 (define @t267 () (= @t157 @t254)) % 126.27/126.56 (define @t268 () (@quantifiers_skolemize @t156 0)) % 126.27/126.56 (define @t269 () (or (= @t268 @t157) (= @t268 @t254) @t267)) % 126.27/126.56 (define @t270 () (@list true)) % 126.27/126.56 (define @t271 () (@var "BOUND_VARIABLE_244752" $$unsorted)) % 126.27/126.56 (define @t272 () (lambda (@list @t271 (@var "BOUND_VARIABLE_244753" $$unsorted)) (= @t271 @t157))) % 126.27/126.56 (define @t273 () (_ @t272 @t254 @t254)) % 126.27/126.56 (define @t274 () (_ @t272 @t157 @t94)) % 126.27/126.56 (define @t275 () (forall @t159 @t274)) % 126.27/126.56 (define @t276 () (not @t275)) % 126.27/126.56 (define @t277 () (= @t114 @t157)) % 126.27/126.56 (define @t278 () (= @t115 @t157)) % 126.27/126.56 (define @t279 () (not @t278)) % 126.27/126.56 (define @t280 () (_ @t272 @t114 @t1)) % 126.27/126.56 (define @t281 () (_ @t272 @t115 @t1)) % 126.27/126.56 (define @t282 () (not @t281)) % 126.27/126.56 (define @t283 () (_ @t272 @t114 @t115)) % 126.27/126.56 (define @t284 () (not @t283)) % 126.27/126.56 (define @t285 () (or @t284 @t282 @t280)) % 126.27/126.56 (define @t286 () (forall @t116 @t285)) % 126.27/126.56 (define @t287 () (not @t286)) % 126.27/126.56 (define @t288 () (or @t287 @t276 @t273)) % 126.27/126.56 (define @t289 () (not @t257)) % 126.27/126.56 (define @t290 () (not @t256)) % 126.27/126.56 (define @t291 () (@list true false)) % 126.27/126.56 (define @t292 () (@quantifiers_skolemize @t256 0)) % 126.27/126.56 (define @t293 () (_ @t292 @t254 @t254)) % 126.27/126.56 (define @t294 () (forall @t166 (_ @t292 @t157 @t164))) % 126.27/126.56 (define @t295 () (not @t294)) % 126.27/126.56 (define @t296 () (forall @t171 (_ @t292 @t169 @t157))) % 126.27/126.56 (define @t297 () (not @t296)) % 126.27/126.56 (define @t298 () (forall @t116 (or (not (_ @t292 @t114 @t115)) (not (_ @t292 @t115 @t1)) (_ @t292 @t114 @t1)))) % 126.27/126.56 (define @t299 () (not @t298)) % 126.27/126.56 (define @t300 () (or @t299 @t297 @t295 @t293)) % 126.27/126.56 (define @t301 () (not @t300)) % 126.27/126.56 (define @t302 () (@list @t300)) % 126.27/126.56 (define @t303 () (@list @t254)) % 126.27/126.56 (define @t304 () (_ @t292 @t254 @t157)) % 126.27/126.56 (define @t305 () (_ @t292 @t157 @t254)) % 126.27/126.56 (define @t306 () (not @t305)) % 126.27/126.56 (define @t307 () (not @t304)) % 126.27/126.56 (define @t308 () (or @t307 @t306 @t293)) % 126.27/126.56 (define @t309 () (not @t308)) % 126.27/126.56 (assume @p1 @t12) % 126.27/126.56 (assume @p2 @t19) % 126.27/126.56 (assume @p3 true) % 126.27/126.56 (step @p4 (= tptp.subrel @t27) :rule refl :args (@t27)) % 126.27/126.56 (step @p5 (= tptp.inv @t31) :rule refl :args (@t31)) % 126.27/126.56 (step @p6 (= tptp.idem @t35) :rule refl :args (@t35)) % 126.27/126.56 (step @p7 (= tptp.infl @t37) :rule refl :args (@t37)) % 126.27/126.56 (step @p8 (= tptp.mono @t39) :rule refl :args (@t39)) % 126.27/126.56 (step @p9 (= tptp.refl @t42) :rule refl :args (@t42)) % 126.27/126.56 (step @p10 (= tptp.irrefl @t43) :rule refl :args (@t43)) % 126.27/126.56 (step @p11 (= tptp.rc @t44) :rule refl :args (@t44)) % 126.27/126.56 (step @p12 (= tptp.symm @t45) :rule refl :args (@t45)) % 126.27/126.56 (step @p13 (= tptp.antisymm @t46) :rule refl :args (@t46)) % 126.27/126.56 (step @p14 (= tptp.asymm @t47) :rule refl :args (@t47)) % 126.27/126.56 (step @p15 (= tptp.sc @t49) :rule refl :args (@t49)) % 126.27/126.56 (step @p16 (= tptp.trans @t54) :rule refl :args (@t54)) % 126.27/126.56 (step @p17 (= tptp.tc @t59) :rule refl :args (@t59)) % 126.27/126.56 (step @p18 (= tptp.trc @t64) :rule refl :args (@t64)) % 126.27/126.56 (step @p19 (= tptp.trsc @t65) :rule refl :args (@t65)) % 126.27/126.56 (step @p20 (= tptp.po @t67) :rule refl :args (@t67)) % 126.27/126.56 (step @p21 (= tptp.so @t68) :rule refl :args (@t68)) % 126.27/126.56 (step @p22 (= tptp.total @t69) :rule refl :args (@t69)) % 126.27/126.56 (step @p23 (= tptp.term @t74) :rule refl :args (@t74)) % 126.27/126.56 (step @p24 (= tptp.ind @t77) :rule refl :args (@t77)) % 126.27/126.56 (step @p25 (= tptp.innf @t78) :rule refl :args (@t78)) % 126.27/126.56 (step @p26 (= tptp.nfof @t81) :rule refl :args (@t81)) % 126.27/126.56 (step @p27 (= tptp.norm @t82) :rule refl :args (@t82)) % 126.27/126.56 (step @p28 (= tptp.join @t85) :rule refl :args (@t85)) % 126.27/126.56 (step @p29 (= tptp.lconfl @t88) :rule refl :args (@t88)) % 126.27/126.56 (step @p30 (= tptp.sconfl @t90) :rule refl :args (@t90)) % 126.27/126.56 (step @p31 (= tptp.confl @t91) :rule refl :args (@t91)) % 126.27/126.56 (step @p32 (= tptp.cr @t92) :rule refl :args (@t92)) % 126.27/126.56 (step @p33 :rule refl :args (@t93)) % 126.27/126.56 (step @p34 :rule refl :args (@t96)) % 126.27/126.56 (step @p35 :rule refl :args (@t97)) % 126.27/126.56 (step @p36 :rule refl :args (@t98)) % 126.27/126.56 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t98 @t97))) % 126.27/126.56 (step @p38 :rule symm :premises (@p37)) % 126.27/126.56 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 126.27/126.56 (step @p40 :rule cong :premises (@p39) :args (@t99)) % 126.27/126.56 (step @p41 :rule refl :args (@t100)) % 126.27/126.56 (step @p42 :rule refl :args (@t101)) % 126.27/126.56 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t101 @t100))) % 126.27/126.56 (step @p44 :rule symm :premises (@p43)) % 126.27/126.56 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 126.27/126.56 (step @p46 :rule cong :premises (@p45) :args (@t102)) % 126.27/126.56 (step @p47 :rule nary_cong :premises (@p46 @p40) :args (@t103)) % 126.27/126.56 (step @p48 :rule nary_cong :premises (@p47 @p34) :args (@t104)) % 126.27/126.56 (step @p49 :rule cong :premises (@p48) :args ((forall @t105 @t104))) % 126.27/126.56 (step @p50 :rule bool-or-de-morgan :args (@t101 @t98 false)) % 126.27/126.56 (step @p51 :rule nary_cong :premises (@p50 @p34) :args (@t107)) % 126.27/126.56 (step @p52 :rule cong :premises (@p51) :args ((forall @t105 @t107))) % 126.27/126.56 (step @p53 :rule trans :premises (@p52 @p49)) % 126.27/126.56 (step @p54 :rule refl :args (@t96)) % 126.27/126.56 (step @p55 :rule beta-reduce :args ((= @t109 @t106))) % 126.27/126.56 (step @p56 :rule cong :premises (@p55) :args (@t110)) % 126.27/126.56 (step @p57 :rule nary_cong :premises (@p56 @p54) :args (@t111)) % 126.27/126.56 (step @p58 :rule cong :premises (@p57) :args (@t112)) % 126.27/126.56 (step @p59 :rule trans :premises (@p58 @p53)) % 126.27/126.56 (step @p60 :rule cong :premises (@p59) :args (@t113)) % 126.27/126.56 (step @p61 :rule refl :args (@t117)) % 126.27/126.56 (step @p62 :rule nary_cong :premises (@p61 @p60 @p33) :args (@t118)) % 126.27/126.56 (step @p63 :rule cong :premises (@p62) :args (@t119)) % 126.27/126.56 (step @p64 :rule cong :premises (@p63) :args (@t120)) % 126.27/126.56 (step @p65 :rule beta-reduce :args ((= (_ @t124 @t108) @t120))) % 126.27/126.56 (step @p66 :rule trans :premises (@p65 @p64)) % 126.27/126.56 (step @p67 :rule beta-reduce :args ((= @t125 @t108))) % 126.27/126.56 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 126.27/126.56 ; trust TRUST_THEORY_REWRITE % 126.27/126.56 (step @p68 :rule trust :premises () :args ((= @t132 @t124))) % 126.27/126.56 (step @p69 :rule ho_cong :premises (@p68 @p67)) % 126.27/126.56 (step @p70 :rule trans :premises (@p69 @p66)) % 126.27/126.56 (step @p71 :rule beta-reduce :args ((= (_ @t133 @t2) @t123))) % 126.27/126.56 (step @p72 :rule refl :args (@t2)) % 126.27/126.56 (step @p73 :rule beta-reduce :args ((= @t135 @t133))) % 126.27/126.56 (step @p74 :rule ho_cong :premises (@p73 @p72)) % 126.27/126.56 (step @p75 :rule trans :premises (@p74 @p71)) % 126.27/126.56 (step @p76 :rule beta-reduce :args ((= (_ @t139 @t5) @t137))) % 126.27/126.56 (step @p77 :rule refl :args (@t5)) % 126.27/126.56 (step @p78 :rule beta-reduce :args ((= (_ (lambda (@list @t5 @t138) (forall @t57 (or @t117 @t122 (_ @t20 @t5 @t138)))) @t2) @t139))) % 126.27/126.56 (step @p79 :rule refl :args (@t2)) % 126.27/126.56 (step @p80 :rule alpha_equiv :args (@t134 (@list @t2) (@list @t138))) % 126.27/126.56 (step @p81 :rule ho_cong :premises (@p80 @p79)) % 126.27/126.56 (step @p82 :rule trans :premises (@p81 @p78)) % 126.27/126.56 (step @p83 :rule ho_cong :premises (@p82 @p77)) % 126.27/126.56 (step @p84 :rule trans :premises (@p83 @p76)) % 126.27/126.56 (step @p85 :rule nary_cong :premises (@p84 @p75) :args (@t140)) % 126.27/126.56 (step @p86 :rule cong :premises (@p85) :args (@t141)) % 126.27/126.56 (step @p87 :rule beta-reduce :args ((= (_ @t49 @t134) @t141))) % 126.27/126.56 (step @p88 :rule trans :premises (@p87 @p86)) % 126.27/126.56 (step @p89 :rule beta-reduce :args ((= (_ @t124 @t13) @t134))) % 126.27/126.56 (step @p90 :rule refl :args (@t13)) % 126.27/126.56 (step @p91 :rule ho_cong :premises (@p68 @p90)) % 126.27/126.56 (step @p92 :rule trans :premises (@p91 @p89)) % 126.27/126.56 (step @p93 :rule refl :args (@t49)) % 126.27/126.56 (step @p94 :rule ho_cong :premises (@p93 @p92)) % 126.27/126.56 (step @p95 :rule trans :premises (@p94 @p88)) % 126.27/126.56 (step @p96 :rule cong :premises (@p95 @p70) :args (@t142)) % 126.27/126.56 (step @p97 :rule cong :premises (@p96) :args (@t143)) % 126.27/126.56 (step @p98 :rule bool-double-not-elim :args (@t143)) % 126.27/126.56 (step @p99 :rule trans :premises (@p98 @p97)) % 126.27/126.56 (step @p100 :rule ho_cong :premises (@p15 @p90)) % 126.27/126.56 (step @p101 :rule refl :args (@t93)) % 126.27/126.56 (step @p102 :rule refl :args (@t21)) % 126.27/126.56 (step @p103 :rule cong :premises (@p102 @p101) :args ((= @t21 @t93))) % 126.27/126.56 (step @p104 :rule symm :premises (@p103)) % 126.27/126.56 (step @p105 :rule eq_resolve :premises (@p102 @p104)) % 126.27/126.56 (step @p106 :rule refl :args (@t129)) % 126.27/126.56 (step @p107 :rule refl :args (@t131)) % 126.27/126.56 (step @p108 :rule nary_cong :premises (@p107 @p106 @p105) :args (@t144)) % 126.27/126.56 (step @p109 :rule cong :premises (@p108) :args ((forall @t57 @t144))) % 126.27/126.56 (step @p110 :rule aci_norm :args ((= (or (or @t131 @t129) @t21) @t144))) % 126.27/126.56 (step @p111 :rule bool-and-de-morgan :args (@t130 @t128 true)) % 126.27/126.56 (step @p112 :rule nary_cong :premises (@p111 @p102) :args ((or (not @t145) @t21))) % 126.27/126.56 (step @p113 :rule trans :premises (@p112 @p110)) % 126.27/126.56 (step @p114 :rule bool-impl-elim :args (@t145 @t21)) % 126.27/126.56 (step @p115 :rule trans :premises (@p114 @p113)) % 126.27/126.56 (step @p116 :rule cong :premises (@p115) :args ((forall @t57 (=> @t145 @t21)))) % 126.27/126.56 (step @p117 :rule trans :premises (@p116 @p109)) % 126.27/126.56 (step @p118 :rule refl :args (@t21)) % 126.27/126.56 (step @p119 :rule beta-reduce :args ((= (_ @t146 @t20) @t128))) % 126.27/126.56 (step @p120 :rule refl :args (@t20)) % 126.27/126.56 (step @p121 :rule beta-reduce :args ((= @t147 @t146))) % 126.27/126.56 (step @p122 :rule ho_cong :premises (@p121 @p120)) % 126.27/126.56 (step @p123 :rule trans :premises (@p122 @p119)) % 126.27/126.56 (step @p124 :rule beta-reduce :args ((= @t150 @t130))) % 126.27/126.56 (step @p125 :rule nary_cong :premises (@p124 @p123) :args (@t151)) % 126.27/126.56 (step @p126 :rule cong :premises (@p125 @p118) :args (@t152)) % 126.27/126.56 (step @p127 :rule cong :premises (@p126) :args ((forall @t57 @t152))) % 126.27/126.56 (step @p128 :rule trans :premises (@p127 @p117)) % 126.27/126.56 (step @p129 :rule refl :args (@t126)) % 126.27/126.56 (step @p130 :rule refl :args (@t23)) % 126.27/126.56 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t23 @t126))) % 126.27/126.56 (step @p132 :rule symm :premises (@p131)) % 126.27/126.56 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 126.27/126.56 (step @p134 :rule cong :premises (@p133) :args (@t70)) % 126.27/126.56 (step @p135 :rule nary_cong :premises (@p134 @p105) :args (@t153)) % 126.27/126.56 (step @p136 :rule cong :premises (@p135) :args ((forall @t24 @t153))) % 126.27/126.56 (step @p137 :rule bool-impl-elim :args (@t23 @t21)) % 126.27/126.56 (step @p138 :rule cong :premises (@p137) :args (@t25)) % 126.27/126.56 (step @p139 :rule trans :premises (@p138 @p136)) % 126.27/126.56 (step @p140 :rule cong :premises (@p139) :args (@t27)) % 126.27/126.56 (step @p141 :rule trans :premises (@p4 @p140)) % 126.27/126.56 (step @p142 :rule ho_cong :premises (@p141 @p90)) % 126.27/126.56 (step @p143 :rule ho_cong :premises (@p142 @p120)) % 126.27/126.56 (step @p144 :rule refl :args (@t148)) % 126.27/126.56 (step @p145 :rule refl :args (@t50)) % 126.27/126.56 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t50 @t148))) % 126.27/126.56 (step @p147 :rule symm :premises (@p146)) % 126.27/126.56 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 126.27/126.56 (step @p149 :rule refl :args (@t149)) % 126.27/126.56 (step @p150 :rule refl :args (@t51)) % 126.27/126.56 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t51 @t149))) % 126.27/126.56 (step @p152 :rule symm :premises (@p151)) % 126.27/126.56 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 126.27/126.56 (step @p154 :rule cong :premises (@p153) :args (@t154)) % 126.27/126.56 (step @p155 :rule nary_cong :premises (@p134 @p154 @p148) :args (@t155)) % 126.27/126.56 (step @p156 :rule cong :premises (@p155) :args ((forall @t11 @t155))) % 126.27/126.56 (step @p157 :rule aci_norm :args ((= (or (or @t70 @t154) @t50) @t155))) % 126.27/126.56 (step @p158 :rule bool-and-de-morgan :args (@t23 @t51 true)) % 126.27/126.56 (step @p159 :rule nary_cong :premises (@p158 @p145) :args ((or (not @t52) @t50))) % 126.27/126.56 (step @p160 :rule trans :premises (@p159 @p157)) % 126.27/126.56 (step @p161 :rule bool-impl-elim :args (@t52 @t50)) % 126.27/126.56 (step @p162 :rule trans :premises (@p161 @p160)) % 126.27/126.56 (step @p163 :rule cong :premises (@p162) :args (@t53)) % 126.27/126.56 (step @p164 :rule trans :premises (@p163 @p156)) % 126.27/126.56 (step @p165 :rule cong :premises (@p164) :args (@t54)) % 126.27/126.56 (step @p166 :rule trans :premises (@p16 @p165)) % 126.27/126.56 (step @p167 :rule ho_cong :premises (@p166 @p120)) % 126.27/126.56 (step @p168 :rule nary_cong :premises (@p167 @p143) :args (@t55)) % 126.27/126.56 (step @p169 :rule cong :premises (@p168 @p118) :args (@t56)) % 126.27/126.56 (step @p170 :rule cong :premises (@p169) :args (@t58)) % 126.27/126.56 (step @p171 :rule trans :premises (@p170 @p128)) % 126.27/126.56 (step @p172 :rule cong :premises (@p171) :args (@t59)) % 126.27/126.56 (step @p173 :rule trans :premises (@p17 @p172)) % 126.27/126.56 (step @p174 :rule ho_cong :premises (@p173 @p100)) % 126.27/126.56 (step @p175 :rule ho_cong :premises (@p173 @p90)) % 126.27/126.56 (step @p176 :rule ho_cong :premises (@p15 @p175)) % 126.27/126.56 (step @p177 :rule cong :premises (@p176 @p174) :args (@t15)) % 126.27/126.56 (step @p178 :rule cong :premises (@p177) :args (@t17)) % 126.27/126.56 (step @p179 :rule cong :premises (@p178) :args (@t18)) % 126.27/126.56 (step @p180 :rule cong :premises (@p179) :args (@t19)) % 126.27/126.56 (step @p181 :rule trans :premises (@p180 @p99)) % 126.27/126.56 (step @p182 :rule eq_resolve :premises (@p2 @p181)) % 126.27/126.56 (step @p183 :rule eq-symm :args (@t163 @t177)) % 126.27/126.56 (step @p184 :rule eq-refl :args (@t176)) % 126.27/126.56 (step @p185 :rule skolem_intro :args (@t177)) % 126.27/126.56 (step @p186 :rule refl :args (@t176)) % 126.27/126.56 (step @p187 :rule cong :premises (@p186 @p185) :args ((= @t176 @t177))) % 126.27/126.56 (step @p188 :rule trans :premises (@p187 @p184)) % 126.27/126.56 (step @p189 :rule true_elim :premises (@p188)) % 126.27/126.56 (step @p190 :rule eq-refl :args (@t162)) % 126.27/126.56 (step @p191 :rule skolem_intro :args (@t163)) % 126.27/126.56 (step @p192 :rule refl :args (@t162)) % 126.27/126.56 (step @p193 :rule cong :premises (@p192 @p191) :args ((= @t162 @t163))) % 126.27/126.56 (step @p194 :rule trans :premises (@p193 @p190)) % 126.27/126.56 (step @p195 :rule true_elim :premises (@p194)) % 126.27/126.56 (step @p196 :rule cong :premises (@p195 @p189) :args (@t178)) % 126.27/126.56 (step @p197 :rule trans :premises (@p196 @p183)) % 126.27/126.56 (step @p198 :rule refl :args (@t179)) % 126.27/126.56 (step @p199 :rule cong :premises (@p198 @p197) :args ((=> @t179 @t178))) % 126.27/126.56 (step @p200 :rule aci_norm :args ((= (or @t117 (or @t173 @t168) @t93) @t174))) % 126.27/126.56 (step @p201 :rule refl :args (@t93)) % 126.27/126.56 (step @p202 :rule bool-and-de-morgan :args (@t172 @t167 true)) % 126.27/126.56 (step @p203 :rule refl :args (@t117)) % 126.27/126.56 (step @p204 :rule nary_cong :premises (@p203 @p202 @p201) :args (@t180)) % 126.27/126.56 (step @p205 :rule trans :premises (@p204 @p200)) % 126.27/126.56 (step @p206 :rule cong :premises (@p205) :args ((forall @t57 @t180))) % 126.27/126.56 (step @p207 :rule aci_norm :args ((= (or false @t165) @t165))) % 126.27/126.56 (step @p208 :rule refl :args (@t165)) % 126.27/126.56 (step @p209 :rule evaluate :args ((not true))) % 126.27/126.56 (step @p210 :rule eq-refl :args (@t157)) % 126.27/126.56 (step @p211 :rule cong :premises (@p210) :args (@t182)) % 126.27/126.56 (step @p212 :rule trans :premises (@p211 @p209)) % 126.27/126.56 (step @p213 :rule nary_cong :premises (@p212 @p208) :args (@t183)) % 126.27/126.56 (step @p214 :rule trans :premises (@p213 @p207)) % 126.27/126.56 (step @p215 :rule cong :premises (@p214) :args ((forall @t166 @t183))) % 126.27/126.56 (step @p216 :rule quant-var-elim-eq :args ((= (forall @t188 (or @t187 @t186 @t185)) @t183))) % 126.27/126.56 (step @p217 :rule refl :args (@t185)) % 126.27/126.56 (step @p218 :rule refl :args (@t186)) % 126.27/126.56 (step @p219 :rule eq-symm :args (@t157 @t184)) % 126.27/126.56 (step @p220 :rule cong :premises (@p219) :args (@t186)) % 126.27/126.56 (step @p221 :rule nary_cong :premises (@p220 @p218 @p217) :args (@t189)) % 126.27/126.56 (step @p222 :rule aci_norm :args ((= @t190 @t189))) % 126.27/126.56 (step @p223 :rule trans :premises (@p222 @p221)) % 126.27/126.56 (step @p224 :rule cong :premises (@p223) :args (@t191)) % 126.27/126.56 (step @p225 :rule trans :premises (@p224 @p216)) % 126.27/126.56 (step @p226 :rule cong :premises (@p225) :args (@t192)) % 126.27/126.56 (step @p227 :rule quant-merge-prenex :args ((= @t192 @t193))) % 126.27/126.56 (step @p228 :rule symm :premises (@p227)) % 126.27/126.56 (step @p229 :rule quant_var_reordering :args ((= (forall @t194 @t190) @t193))) % 126.27/126.56 (step @p230 :rule trans :premises (@p229 @p228 @p226)) % 126.27/126.56 (step @p231 :rule trans :premises (@p230 @p215)) % 126.27/126.56 (step @p232 :rule refl :args (@t185)) % 126.27/126.56 (step @p233 :rule eq-symm :args (@t184 @t157)) % 126.27/126.56 (step @p234 :rule cong :premises (@p233) :args (@t187)) % 126.27/126.56 (step @p235 :rule nary_cong :premises (@p234 @p232) :args (@t195)) % 126.27/126.56 (step @p236 :rule cong :premises (@p235) :args (@t196)) % 126.27/126.56 (step @p237 :rule trans :premises (@p236 @p231)) % 126.27/126.56 (step @p238 :rule aci_norm :args ((= (or false @t170) @t170))) % 126.27/126.56 (step @p239 :rule refl :args (@t170)) % 126.27/126.56 (step @p240 :rule nary_cong :premises (@p212 @p239) :args (@t197)) % 126.27/126.56 (step @p241 :rule trans :premises (@p240 @p238)) % 126.27/126.56 (step @p242 :rule cong :premises (@p241) :args ((forall @t171 @t197))) % 126.27/126.56 (step @p243 :rule quant-var-elim-eq :args ((= (forall @t202 (or @t201 @t200 @t199)) @t197))) % 126.27/126.56 (step @p244 :rule refl :args (@t199)) % 126.27/126.56 (step @p245 :rule refl :args (@t200)) % 126.27/126.56 (step @p246 :rule eq-symm :args (@t157 @t198)) % 126.27/126.56 (step @p247 :rule cong :premises (@p246) :args (@t200)) % 126.27/126.56 (step @p248 :rule nary_cong :premises (@p247 @p245 @p244) :args (@t203)) % 126.27/126.56 (step @p249 :rule aci_norm :args ((= @t204 @t203))) % 126.27/126.56 (step @p250 :rule trans :premises (@p249 @p248)) % 126.27/126.56 (step @p251 :rule cong :premises (@p250) :args (@t205)) % 126.27/126.56 (step @p252 :rule trans :premises (@p251 @p243)) % 126.27/126.56 (step @p253 :rule cong :premises (@p252) :args (@t206)) % 126.27/126.56 (step @p254 :rule quant-merge-prenex :args ((= @t206 (forall @t207 @t204)))) % 126.27/126.56 (step @p255 :rule symm :premises (@p254)) % 126.27/126.56 (step @p256 :rule trans :premises (@p255 @p253)) % 126.27/126.56 (step @p257 :rule trans :premises (@p256 @p242)) % 126.27/126.56 (step @p258 :rule refl :args (@t199)) % 126.27/126.56 (step @p259 :rule eq-symm :args (@t198 @t157)) % 126.27/126.56 (step @p260 :rule cong :premises (@p259) :args (@t201)) % 126.27/126.56 (step @p261 :rule nary_cong :premises (@p260 @p258) :args (@t208)) % 126.27/126.56 (step @p262 :rule cong :premises (@p261) :args (@t209)) % 126.27/126.56 (step @p263 :rule trans :premises (@p262 @p257)) % 126.27/126.56 (step @p264 :rule nary_cong :premises (@p263 @p237) :args ((and @t209 @t196))) % 126.27/126.56 (step @p265 :rule alpha_equiv :args (@t213 @t214 (@list @t184 @t164))) % 126.27/126.56 (step @p266 :rule alpha_equiv :args (@t218 @t214 (@list @t169 @t198))) % 126.27/126.56 (step @p267 :rule nary_cong :premises (@p266 @p265) :args (@t219)) % 126.27/126.56 (step @p268 :rule quant-miniscope-and :args ((= (forall @t105 (and @t217 @t212)) @t219))) % 126.27/126.56 (step @p269 :rule trans :premises (@p268 @p267)) % 126.27/126.56 (step @p270 :rule trans :premises (@p269 @p264)) % 126.27/126.56 (step @p271 :rule bool-or-and-distrib :args (@t216 @t211 true @t96 false)) % 126.27/126.56 (step @p272 :rule cong :premises (@p271) :args ((forall @t105 (or (and @t216 @t211) @t96)))) % 126.27/126.56 (step @p273 :rule trans :premises (@p272 @p270)) % 126.27/126.56 (step @p274 :rule beta-reduce :args ((= @t222 @t210))) % 126.27/126.56 (step @p275 :rule cong :premises (@p274) :args (@t223)) % 126.27/126.56 (step @p276 :rule beta-reduce :args ((= @t224 @t215))) % 126.27/126.56 (step @p277 :rule cong :premises (@p276) :args (@t225)) % 126.27/126.56 (step @p278 :rule nary_cong :premises (@p277 @p275) :args (@t226)) % 126.27/126.56 (step @p279 :rule nary_cong :premises (@p278 @p54) :args (@t227)) % 126.27/126.56 (step @p280 :rule cong :premises (@p279) :args (@t228)) % 126.27/126.56 (step @p281 :rule trans :premises (@p280 @p273)) % 126.27/126.56 (step @p282 :rule cong :premises (@p281) :args (@t229)) % 126.27/126.56 (step @p283 :rule nary_cong :premises (@p61 @p282 @p33) :args (@t230)) % 126.27/126.56 (step @p284 :rule cong :premises (@p283) :args (@t231)) % 126.27/126.56 (step @p285 :rule trans :premises (@p284 @p206)) % 126.27/126.56 (step @p286 :rule cong :premises (@p285) :args (@t232)) % 126.27/126.56 (step @p287 :rule aci_norm :args ((= (or false @t158) @t158))) % 126.27/126.56 (step @p288 :rule refl :args (@t158)) % 126.27/126.56 (step @p289 :rule nary_cong :premises (@p212 @p288) :args (@t233)) % 126.27/126.56 (step @p290 :rule trans :premises (@p289 @p287)) % 126.27/126.56 (step @p291 :rule cong :premises (@p290) :args ((forall @t159 @t233))) % 126.27/126.56 (step @p292 :rule quant-var-elim-eq :args ((= (forall @t235 @t234) @t233))) % 126.27/126.56 (step @p293 :rule aci_norm :args ((= @t212 @t234))) % 126.27/126.56 (step @p294 :rule cong :premises (@p293) :args (@t236)) % 126.27/126.56 (step @p295 :rule trans :premises (@p294 @p292)) % 126.27/126.56 (step @p296 :rule cong :premises (@p295) :args (@t237)) % 126.27/126.56 (step @p297 :rule quant-merge-prenex :args ((= @t237 @t238))) % 126.27/126.56 (step @p298 :rule symm :premises (@p297)) % 126.27/126.56 (step @p299 :rule quant_var_reordering :args ((= @t213 @t238))) % 126.27/126.56 (step @p300 :rule trans :premises (@p299 @p298 @p296)) % 126.27/126.56 (step @p301 :rule trans :premises (@p300 @p291)) % 126.27/126.56 (step @p302 :rule nary_cong :premises (@p275 @p54) :args (@t239)) % 126.27/126.56 (step @p303 :rule cong :premises (@p302) :args (@t240)) % 126.27/126.56 (step @p304 :rule trans :premises (@p303 @p301)) % 126.27/126.56 (step @p305 :rule cong :premises (@p304) :args (@t241)) % 126.27/126.56 (step @p306 :rule nary_cong :premises (@p61 @p305 @p33) :args (@t242)) % 126.27/126.56 (step @p307 :rule cong :premises (@p306) :args (@t243)) % 126.27/126.56 (step @p308 :rule refl :args (@t136)) % 126.27/126.56 (step @p309 :rule nary_cong :premises (@p61 @p305 @p308) :args (@t244)) % 126.27/126.56 (step @p310 :rule cong :premises (@p309) :args (@t245)) % 126.27/126.56 (step @p311 :rule nary_cong :premises (@p310 @p307) :args (@t246)) % 126.27/126.56 (step @p312 :rule cong :premises (@p311) :args (@t247)) % 126.27/126.56 (step @p313 :rule cong :premises (@p312 @p286) :args (@t248)) % 126.27/126.56 (step @p314 :rule cong :premises (@p198 @p313) :args ((=> @t179 @t248))) % 126.27/126.56 (assume-push @p455 @t179) % 126.27/126.56 (step @p316 :rule instantiate :premises (@p182) :args ((@list @t221))) % 126.27/126.56 (step-pop @p456 :rule scope :premises (@p316)) % 126.27/126.56 (step @p317 :rule process_scope :premises (@p456) :args (@t248)) % 126.27/126.56 (step @p319 :rule eq_resolve :premises (@p317 @p314)) % 126.27/126.56 (step @p320 :rule eq_resolve :premises (@p319 @p199)) % 126.27/126.56 (step @p321 :rule implies_elim :premises (@p320)) % 126.27/126.56 (step @p322 :rule chain_m_resolution :premises (@p321 @p182) :args (@t249 @t250 (@list @t179))) % 126.27/126.56 (step @p323 :rule eq-symm :args (@t175 @t161)) % 126.27/126.56 (step @p324 :rule cong :premises (@p323) :args (@t251)) % 126.27/126.56 (step @p325 :rule refl :args (@t249)) % 126.27/126.56 (step @p326 :rule cong :premises (@p325 @p324) :args (@t252)) % 126.27/126.56 ; WARNING: add trust step for TRUST % 126.27/126.56 ; trust TRUST THEORY_LEMMA % 126.27/126.56 (step @p327 :rule trust :premises () :args (@t252)) % 126.27/126.56 (step @p328 :rule eq_resolve :premises (@p327 @p326)) % 126.27/126.56 (step @p329 :rule implies_elim :premises (@p328)) % 126.27/126.56 (step @p330 :rule chain_m_resolution :premises (@p329 @p322) :args (@t253 @t250 (@list @t249))) % 126.27/126.56 (step @p331 :rule refl :args (@t256)) % 126.27/126.56 (step @p332 :rule aci_norm :args ((= @t258 @t257))) % 126.27/126.56 (step @p333 :rule cong :premises (@p332 @p331) :args (@t259)) % 126.27/126.56 (step @p334 :rule refl :args (@t253)) % 126.27/126.56 (step @p335 :rule cong :premises (@p334 @p333) :args ((=> @t253 @t259))) % 126.27/126.56 (assume-push @p457 @t253) % 126.27/126.56 (step @p337 :rule instantiate :premises (@p330) :args ((@list @t254 @t254))) % 126.27/126.56 (step-pop @p458 :rule scope :premises (@p337)) % 126.27/126.56 (step @p338 :rule process_scope :premises (@p458) :args (@t259)) % 126.27/126.56 (step @p340 :rule eq_resolve :premises (@p338 @p335)) % 126.27/126.56 (step @p341 :rule implies_elim :premises (@p340)) % 126.27/126.56 (step @p342 :rule chain_m_resolution :premises (@p341 @p330) :args (@t260 @t250 (@list @t253))) % 126.27/126.56 (step @p343 :rule bool-double-not-elim :args (@t3)) % 126.27/126.56 (step @p344 :rule bool-double-not-elim :args (@t6)) % 126.27/126.56 (step @p345 :rule bool-double-not-elim :args (@t8)) % 126.27/126.56 (step @p346 :rule nary_cong :premises (@p345 @p344 @p343) :args (@t264)) % 126.27/126.56 (step @p347 :rule aci_norm :args ((= (or @t263 (or @t262 @t261)) @t264))) % 126.27/126.56 (step @p348 :rule trans :premises (@p347 @p346)) % 126.27/126.56 (step @p349 :rule bool-and-de-morgan :args (@t7 @t4 true)) % 126.27/126.56 (step @p350 :rule refl :args (@t263)) % 126.27/126.56 (step @p351 :rule nary_cong :premises (@p350 @p349) :args ((or @t263 (not (and @t7 @t4))))) % 126.27/126.56 (step @p352 :rule bool-and-de-morgan :args (@t9 @t7 (and @t4))) % 126.27/126.56 (step @p353 :rule trans :premises (@p352 @p351)) % 126.27/126.56 (step @p354 :rule trans :premises (@p353 @p348)) % 126.27/126.56 (step @p355 :rule cong :premises (@p354) :args (@t265)) % 126.27/126.56 (step @p356 :rule cong :premises (@p355) :args (@t266)) % 126.27/126.56 (step @p357 :rule exists-elim :args ((= @t12 @t266))) % 126.27/126.56 (step @p358 :rule trans :premises (@p357 @p356)) % 126.27/126.56 (step @p359 :rule eq_resolve :premises (@p1 @p358)) % 126.27/126.56 (step @p360 :rule skolemize :premises (@p359)) % 126.27/126.56 (step @p361 :rule cnf_or_neg :args (@t269 2)) % 126.27/126.56 (step @p362 :rule chain_m_resolution :premises (@p361 @p360) :args ((not @t267) @t270 (@list @t269))) % 126.27/126.56 (step @p363 :rule aci_norm :args ((= (or false false @t267) @t267))) % 126.27/126.56 (step @p364 :rule eq-symm :args (@t254 @t157)) % 126.27/126.56 (step @p365 :rule beta-reduce :args ((= @t273 (= @t254 @t157)))) % 126.27/126.56 (step @p366 :rule trans :premises (@p365 @p364)) % 126.27/126.56 (step @p367 :rule quant-unused-vars :args ((= (forall @t159 true) true))) % 126.27/126.56 (step @p368 :rule beta-reduce :args ((= @t274 @t181))) % 126.27/126.56 (step @p369 :rule trans :premises (@p368 @p210)) % 126.27/126.56 (step @p370 :rule cong :premises (@p369) :args (@t275)) % 126.27/126.56 (step @p371 :rule trans :premises (@p370 @p367)) % 126.27/126.56 (step @p372 :rule cong :premises (@p371) :args (@t276)) % 126.27/126.56 (step @p373 :rule trans :premises (@p372 @p209)) % 126.27/126.56 (step @p374 :rule quant-unused-vars :args ((= (forall @t116 true) true))) % 126.27/126.56 (step @p375 :rule bool-or-taut2 :args (false @t277 (or @t279) false)) % 126.27/126.56 (step @p376 :rule cong :premises (@p375) :args ((forall @t116 (or (not @t277) @t279 @t277)))) % 126.27/126.56 (step @p377 :rule trans :premises (@p376 @p374)) % 126.27/126.56 (step @p378 :rule beta-reduce :args ((= @t280 @t277))) % 126.27/126.56 (step @p379 :rule beta-reduce :args ((= @t281 @t278))) % 126.27/126.56 (step @p380 :rule cong :premises (@p379) :args (@t282)) % 126.27/126.56 (step @p381 :rule beta-reduce :args ((= @t283 @t277))) % 126.27/126.56 (step @p382 :rule cong :premises (@p381) :args (@t284)) % 126.27/126.56 (step @p383 :rule nary_cong :premises (@p382 @p380 @p378) :args (@t285)) % 126.27/126.56 (step @p384 :rule cong :premises (@p383) :args (@t286)) % 126.27/126.56 (step @p385 :rule trans :premises (@p384 @p377)) % 126.27/126.56 (step @p386 :rule cong :premises (@p385) :args (@t287)) % 126.27/126.56 (step @p387 :rule trans :premises (@p386 @p209)) % 126.27/126.56 (step @p388 :rule nary_cong :premises (@p387 @p373 @p366) :args (@t288)) % 126.27/126.56 (step @p389 :rule trans :premises (@p388 @p363)) % 126.27/126.56 (step @p390 :rule refl :args (@t257)) % 126.27/126.56 (step @p391 :rule cong :premises (@p390 @p389) :args ((=> @t257 @t288))) % 126.27/126.56 (assume-push @p459 @t257) % 126.27/126.56 (step @p393 :rule instantiate :premises (@p459) :args ((@list @t272))) % 126.27/126.56 (step-pop @p460 :rule scope :premises (@p393)) % 126.27/126.56 (step @p394 :rule process_scope :premises (@p460) :args (@t288)) % 126.27/126.56 (step @p396 :rule eq_resolve :premises (@p394 @p391)) % 126.27/126.56 (step @p397 :rule implies_elim :premises (@p396)) % 126.27/126.56 (step @p398 :rule reordering :premises (@p397) :args ((or @t267 @t289))) % 126.27/126.56 (step @p399 :rule chain_m_resolution :premises (@p398 @p362) :args (@t289 @t270 (@list @t267))) % 126.27/126.56 (step @p400 :rule cnf_equiv_pos2 :args (@t260)) % 126.27/126.56 (step @p401 :rule reordering :premises (@p400) :args ((or @t257 @t290 (not @t260)))) % 126.27/126.57 (step @p402 :rule chain_m_resolution :premises (@p401 @p399 @p342) :args (@t290 @t291 (@list @t257 @t260))) % 126.27/126.57 (step @p403 :rule refl :args (@t301)) % 126.27/126.57 (step @p404 :rule bool-double-not-elim :args (@t256)) % 126.27/126.57 (step @p405 :rule nary_cong :premises (@p404 @p403) :args ((or (not @t290) @t301))) % 126.27/126.57 (assume-push @p461 @t290) % 126.27/126.57 (step @p407 :rule skolemize :premises (@p461)) % 126.27/126.57 (step-pop @p462 :rule scope :premises (@p407)) % 126.27/126.57 (step @p408 :rule process_scope :premises (@p462) :args (@t301)) % 126.27/126.57 (step @p410 :rule implies_elim :premises (@p408)) % 126.27/126.57 (step @p411 :rule eq_resolve :premises (@p410 @p405)) % 126.27/126.57 (step @p412 :rule chain_m_resolution :premises (@p411 @p402) :args (@t301 @t270 (@list @t256))) % 126.27/126.57 (step @p413 :rule bool-double-not-elim :args (@t298)) % 126.27/126.57 (step @p414 :rule refl :args (@t300)) % 126.27/126.57 (step @p415 :rule nary_cong :premises (@p414 @p413) :args ((or @t300 (not @t299)))) % 126.27/126.57 (step @p416 :rule cnf_or_neg :args (@t300 0)) % 126.27/126.57 (step @p417 :rule eq_resolve :premises (@p416 @p415)) % 126.27/126.57 (step @p418 :rule reordering :premises (@p417) :args ((or @t298 @t300))) % 126.27/126.57 (step @p419 :rule chain_m_resolution :premises (@p418 @p412) :args (@t298 @t270 @t302)) % 126.27/126.57 (step @p420 :rule bool-double-not-elim :args (@t296)) % 126.27/126.57 (step @p421 :rule nary_cong :premises (@p414 @p420) :args ((or @t300 (not @t297)))) % 126.27/126.57 (step @p422 :rule cnf_or_neg :args (@t300 1)) % 126.27/126.57 (step @p423 :rule eq_resolve :premises (@p422 @p421)) % 126.27/126.57 (step @p424 :rule reordering :premises (@p423) :args ((or @t296 @t300))) % 126.27/126.57 (step @p425 :rule chain_m_resolution :premises (@p424 @p412) :args (@t296 @t270 @t302)) % 126.27/126.57 (assume-push @p463 @t296) % 126.27/126.57 (step @p427 :rule instantiate :premises (@p463) :args (@t303)) % 126.27/126.57 (step-pop @p464 :rule scope :premises (@p427)) % 126.27/126.57 (step @p428 :rule process_scope :premises (@p464) :args (@t304)) % 126.27/126.57 (step @p430 :rule implies_elim :premises (@p428)) % 126.27/126.57 (step @p431 :rule chain_m_resolution :premises (@p430 @p425) :args (@t304 @t250 (@list @t296))) % 126.27/126.57 (step @p432 :rule bool-double-not-elim :args (@t294)) % 126.27/126.57 (step @p433 :rule nary_cong :premises (@p414 @p432) :args ((or @t300 (not @t295)))) % 126.27/126.57 (step @p434 :rule cnf_or_neg :args (@t300 2)) % 126.27/126.57 (step @p435 :rule eq_resolve :premises (@p434 @p433)) % 126.27/126.57 (step @p436 :rule reordering :premises (@p435) :args ((or @t294 @t300))) % 126.27/126.57 (step @p437 :rule chain_m_resolution :premises (@p436 @p412) :args (@t294 @t270 @t302)) % 126.27/126.57 (assume-push @p465 @t294) % 126.27/126.57 (step @p439 :rule instantiate :premises (@p465) :args (@t303)) % 126.27/126.57 (step-pop @p466 :rule scope :premises (@p439)) % 126.27/126.57 (step @p440 :rule process_scope :premises (@p466) :args (@t305)) % 126.27/126.57 (step @p442 :rule implies_elim :premises (@p440)) % 126.27/126.57 (step @p443 :rule chain_m_resolution :premises (@p442 @p437) :args (@t305 @t250 (@list @t294))) % 126.27/126.57 (step @p444 :rule cnf_or_neg :args (@t300 3)) % 126.27/126.57 (step @p445 :rule chain_m_resolution :premises (@p444 @p412) :args ((not @t293) @t270 @t302)) % 126.27/126.57 (step @p446 :rule cnf_or_pos :args (@t308)) % 126.27/126.57 (step @p447 :rule reordering :premises (@p446) :args ((or @t293 @t306 @t307 @t309))) % 126.27/126.57 (step @p448 :rule chain_m_resolution :premises (@p447 @p445 @p443 @p431) :args (@t309 (@list true false false) (@list @t293 @t305 @t304))) % 126.27/126.57 (assume-push @p467 @t298) % 126.27/126.57 (step @p450 :rule instantiate :premises (@p467) :args ((@list @t254 @t157 @t254))) % 126.27/126.57 (step-pop @p468 :rule scope :premises (@p450)) % 126.27/126.57 (step @p451 :rule process_scope :premises (@p468) :args (@t308)) % 126.27/126.57 (step @p453 :rule implies_elim :premises (@p451)) % 126.27/126.57 (step @p454 false :rule chain_m_resolution :premises (@p453 @p448 @p419) :args (false @t291 (@list @t308 @t298))) % 126.27/126.57 ) % 126.27/126.57 % SZS output end Proof % 126.27/126.57 % cvc5 exiting %------------------------------------------------------------------------------