%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU459^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:51:53 AM UTC 2026 % Result : Theorem 0.36s 0.61s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU459^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:37:20 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.36/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.61 % SZS status Theorem % 0.36/0.61 % SZS output start Proof % 0.36/0.61 ( % 0.36/0.61 (declare-sort $$unsorted 0) % 0.36/0.61 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.61 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.36/0.61 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.36/0.61 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.36/0.61 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.36/0.61 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.61 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.36/0.61 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.61 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.61 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.36/0.61 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.61 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.61 (define tptp.trans () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "Y" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.36/0.61 (define tptp.tc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_1) (forall (@list _let_3) (=> (and (_ tptp.trans _let_3) (_ (_ tptp.subrel _let_4) _let_3)) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.61 (define tptp.trc () (let ((_let_1 (@var "__flatten_var_1" $$unsorted))) (let ((_let_2 (@var "__flatten_var_0" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.rc (_ tptp.tc _let_3)) _let_2) _let_1)))))) % 0.36/0.61 (define tptp.trsc () (let ((_let_1 (@var "__flatten_var_1" $$unsorted))) (let ((_let_2 (@var "__flatten_var_0" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.sc (_ tptp.rc (_ tptp.tc _let_3))) _let_2) _let_1)))))) % 0.36/0.61 (define tptp.po () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.refl _let_1) (_ tptp.antisymm _let_1) (_ tptp.trans _let_1))))) % 0.36/0.61 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.36/0.61 (define tptp.total () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (or (= _let_1 _let_2) (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.61 (define tptp.term () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.36/0.61 (define tptp.ind () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@list _let_1))) (let ((_let_5 (@var "Y" $$unsorted))) (let ((_let_6 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_6) (forall (@list _let_2) (=> (forall _let_4 (=> (forall (@list _let_5) (=> (_ (_ (_ tptp.tc _let_6) _let_1) _let_5) (_ _let_2 _let_5))) _let_3)) (forall _let_4 _let_3))))))))))) % 0.36/0.61 (define tptp.innf () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (not (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.61 (define tptp.nfof () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "Y" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (and (_ (_ (_ tptp.trc _let_2) _let_3) _let_1) (_ (_ tptp.innf _let_2) _let_1))))))) % 0.36/0.61 (define tptp.norm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1) (exists (@list _let_2) (_ (_ (_ tptp.nfof _let_3) _let_2) _let_1)))))))) % 0.36/0.61 (define tptp.join () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ tptp.trc _let_3))) (let ((_let_5 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.36/0.61 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))))) % 0.36/0.61 (define tptp.sconfl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.36/0.61 (define tptp.confl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (_ (_ tptp.trc _let_3) _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))))) % 0.36/0.61 (define tptp.cr () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ (_ tptp.trsc _let_3) _let_2) _let_1) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))) % 0.36/0.61 (define @t1 () (not (_ tptp.infl tptp.sc))) % 0.36/0.61 (define @t2 () (@var "Y" $$unsorted)) % 0.36/0.61 (define @t3 () (@var "X" $$unsorted)) % 0.36/0.61 (define @t4 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.36/0.61 (define @t5 () (_ (_ @t4 @t3) @t2)) % 0.36/0.61 (define @t6 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.61 (define @t7 () (_ @t6 @t3)) % 0.36/0.61 (define @t8 () (_ @t7 @t2)) % 0.36/0.61 (define @t9 () (@list @t3 @t2)) % 0.36/0.61 (define @t10 () (forall @t9 (=> @t8 @t5))) % 0.36/0.61 (define @t11 () (@list @t6 @t4)) % 0.36/0.61 (define @t12 () (lambda @t11 @t10)) % 0.36/0.61 (define @t13 () (_ @t6 @t2)) % 0.36/0.61 (define @t14 () (_ @t13 @t3)) % 0.36/0.61 (define @t15 () (@list @t6 @t3 @t2)) % 0.36/0.61 (define @t16 () (lambda @t15 @t14)) % 0.36/0.61 (define @t17 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.36/0.61 (define @t18 () (_ @t17 @t6)) % 0.36/0.61 (define @t19 () (@list @t6)) % 0.36/0.61 (define @t20 () (@list @t17)) % 0.36/0.61 (define @t21 () (lambda @t20 (forall @t19 (= (_ @t17 @t18) @t18)))) % 0.36/0.61 (define @t22 () (_ tptp.subrel @t6)) % 0.36/0.61 (define @t23 () (forall @t19 (_ @t22 @t18))) % 0.36/0.61 (define @t24 () (lambda @t20 @t23)) % 0.36/0.61 (define @t25 () (_ @t22 @t4)) % 0.36/0.61 (define @t26 () (lambda @t20 (forall @t11 (=> @t25 (_ (_ tptp.subrel @t18) (_ @t17 @t4)))))) % 0.36/0.61 (define @t27 () (_ @t7 @t3)) % 0.36/0.61 (define @t28 () (@list @t3)) % 0.36/0.61 (define @t29 () (lambda @t19 (forall @t28 @t27))) % 0.36/0.61 (define @t30 () (lambda @t19 (forall @t28 (not @t27)))) % 0.36/0.61 (define @t31 () (= @t3 @t2)) % 0.36/0.61 (define @t32 () (lambda @t15 (or @t31 @t8))) % 0.36/0.61 (define @t33 () (lambda @t19 (forall @t9 (=> @t8 @t14)))) % 0.36/0.61 (define @t34 () (lambda @t19 (forall @t9 (=> (and @t8 @t14) @t31)))) % 0.36/0.61 (define @t35 () (lambda @t19 (forall @t9 (=> @t8 (not @t14))))) % 0.36/0.61 (define @t36 () (or @t14 @t8)) % 0.36/0.61 (define @t37 () (lambda @t15 @t36)) % 0.36/0.61 (define @t38 () (@var "Z" $$unsorted)) % 0.36/0.61 (define @t39 () (_ @t7 @t38)) % 0.36/0.61 (define @t40 () (@list @t3 @t2 @t38)) % 0.36/0.61 (define @t41 () (lambda @t19 (forall @t40 (=> (and @t8 (_ @t13 @t38)) @t39)))) % 0.36/0.61 (define @t42 () (@list @t4)) % 0.36/0.61 (define @t43 () (lambda @t15 (forall @t42 (=> (and (_ tptp.trans @t4) @t25) @t5)))) % 0.36/0.61 (define @t44 () (@var "__flatten_var_1" $$unsorted)) % 0.36/0.61 (define @t45 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.61 (define @t46 () (_ tptp.tc @t6)) % 0.36/0.61 (define @t47 () (_ tptp.rc @t46)) % 0.36/0.61 (define @t48 () (@list @t6 @t45 @t44)) % 0.36/0.61 (define @t49 () (lambda @t48 (_ (_ @t47 @t45) @t44))) % 0.36/0.61 (define @t50 () (lambda @t48 (_ (_ (_ tptp.sc @t47) @t45) @t44))) % 0.36/0.61 (define @t51 () (_ tptp.trans @t6)) % 0.36/0.61 (define @t52 () (lambda @t19 (and (_ tptp.refl @t6) (_ tptp.antisymm @t6) @t51))) % 0.36/0.61 (define @t53 () (lambda @t19 (and (_ tptp.asymm @t6) @t51))) % 0.36/0.61 (define @t54 () (lambda @t19 (forall @t9 (or @t31 @t8 @t14)))) % 0.36/0.61 (define @t55 () (not @t8)) % 0.36/0.61 (define @t56 () (@var "A" (-> $$unsorted Bool))) % 0.36/0.61 (define @t57 () (@list @t2)) % 0.36/0.61 (define @t58 () (_ @t56 @t3)) % 0.36/0.61 (define @t59 () (lambda @t19 (forall (@list @t56) (=> (exists @t28 @t58) (exists @t28 (and @t58 (forall @t57 (=> (_ @t56 @t2) @t55)))))))) % 0.36/0.61 (define @t60 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.61 (define @t61 () (_ @t60 @t3)) % 0.36/0.61 (define @t62 () (lambda @t19 (forall (@list @t60) (=> (forall @t28 (=> (forall @t57 (=> (_ (_ @t46 @t3) @t2) (_ @t60 @t2))) @t61)) (forall @t28 @t61))))) % 0.36/0.61 (define @t63 () (lambda (@list @t6 @t3) (not (exists @t57 @t8)))) % 0.36/0.61 (define @t64 () (_ tptp.trc @t6)) % 0.36/0.61 (define @t65 () (_ @t64 @t2)) % 0.36/0.61 (define @t66 () (lambda @t15 (and (_ @t65 @t3) (_ (_ tptp.innf @t6) @t3)))) % 0.36/0.61 (define @t67 () (lambda @t19 (forall @t28 (exists @t57 (_ (_ (_ tptp.nfof @t6) @t2) @t3))))) % 0.36/0.61 (define @t68 () (_ @t64 @t3)) % 0.36/0.61 (define @t69 () (_ @t68 @t38)) % 0.36/0.61 (define @t70 () (lambda @t15 (exists (@list @t38) (and @t69 (_ @t65 @t38))))) % 0.36/0.61 (define @t71 () (_ tptp.join @t6)) % 0.36/0.61 (define @t72 () (_ (_ @t71 @t38) @t2)) % 0.36/0.61 (define @t73 () (lambda @t19 (forall @t40 (=> (and @t39 @t8) @t72)))) % 0.36/0.61 (define @t74 () (_ @t68 @t2)) % 0.36/0.61 (define @t75 () (lambda @t19 (forall @t40 (=> (and @t39 @t74) @t72)))) % 0.36/0.61 (define @t76 () (lambda @t19 (forall @t40 (=> (and @t69 @t74) @t72)))) % 0.36/0.61 (define @t77 () (lambda @t19 (forall @t9 (=> (_ (_ (_ tptp.trsc @t6) @t3) @t2) (_ (_ @t71 @t3) @t2))))) % 0.36/0.61 (define @t78 () (_ @t6 @t3 @t2)) % 0.36/0.61 (define @t79 () (_ @t6 @t2 @t3)) % 0.36/0.61 (define @t80 () (not @t78)) % 0.36/0.61 (define @t81 () (or @t80 @t14 @t8)) % 0.36/0.61 (define @t82 () (_ @t37 @t6 @t3 @t2)) % 0.36/0.61 (define @t83 () (or @t80 @t82)) % 0.36/0.61 (define @t84 () (forall @t15 @t83)) % 0.36/0.61 (define @t85 () (_ @t17 @t6 @t3 @t2)) % 0.36/0.61 (define @t86 () (or @t80 @t85)) % 0.36/0.61 (define @t87 () (forall @t15 @t86)) % 0.36/0.61 (define @t88 () (_ (lambda @t20 @t87) @t37)) % 0.36/0.61 (define @t89 () (_ (_ @t18 @t3) @t2)) % 0.36/0.61 (define @t90 () (or @t80 @t89)) % 0.36/0.61 (define @t91 () (_ @t18 @t3 @t2)) % 0.36/0.61 (define @t92 () (or @t80 @t91)) % 0.36/0.61 (define @t93 () (forall @t9 @t92)) % 0.36/0.61 (define @t94 () (_ @t4 @t3 @t2)) % 0.36/0.61 (define @t95 () (forall @t9 (or @t80 @t94))) % 0.36/0.61 (define @t96 () (lambda @t42 @t95)) % 0.36/0.61 (define @t97 () (_ (lambda @t11 @t95) @t6)) % 0.36/0.61 (define @t98 () (or @t55 @t5)) % 0.36/0.61 (assume @p1 @t1) % 0.36/0.61 (assume @p2 true) % 0.36/0.61 (step @p3 (= tptp.subrel @t12) :rule refl :args (@t12)) % 0.36/0.61 (step @p4 (= tptp.inv @t16) :rule refl :args (@t16)) % 0.36/0.61 (step @p5 (= tptp.idem @t21) :rule refl :args (@t21)) % 0.36/0.61 (step @p6 (= tptp.infl @t24) :rule refl :args (@t24)) % 0.36/0.61 (step @p7 (= tptp.mono @t26) :rule refl :args (@t26)) % 0.36/0.61 (step @p8 (= tptp.refl @t29) :rule refl :args (@t29)) % 0.36/0.61 (step @p9 (= tptp.irrefl @t30) :rule refl :args (@t30)) % 0.36/0.61 (step @p10 (= tptp.rc @t32) :rule refl :args (@t32)) % 0.36/0.61 (step @p11 (= tptp.symm @t33) :rule refl :args (@t33)) % 0.36/0.61 (step @p12 (= tptp.antisymm @t34) :rule refl :args (@t34)) % 0.36/0.61 (step @p13 (= tptp.asymm @t35) :rule refl :args (@t35)) % 0.36/0.61 (step @p14 (= tptp.sc @t37) :rule refl :args (@t37)) % 0.36/0.61 (step @p15 (= tptp.trans @t41) :rule refl :args (@t41)) % 0.36/0.61 (step @p16 (= tptp.tc @t43) :rule refl :args (@t43)) % 0.36/0.61 (step @p17 (= tptp.trc @t49) :rule refl :args (@t49)) % 0.36/0.61 (step @p18 (= tptp.trsc @t50) :rule refl :args (@t50)) % 0.36/0.61 (step @p19 (= tptp.po @t52) :rule refl :args (@t52)) % 0.36/0.61 (step @p20 (= tptp.so @t53) :rule refl :args (@t53)) % 0.36/0.61 (step @p21 (= tptp.total @t54) :rule refl :args (@t54)) % 0.36/0.61 (step @p22 (= tptp.term @t59) :rule refl :args (@t59)) % 0.36/0.61 (step @p23 (= tptp.ind @t62) :rule refl :args (@t62)) % 0.36/0.61 (step @p24 (= tptp.innf @t63) :rule refl :args (@t63)) % 0.36/0.61 (step @p25 (= tptp.nfof @t66) :rule refl :args (@t66)) % 0.36/0.61 (step @p26 (= tptp.norm @t67) :rule refl :args (@t67)) % 0.36/0.61 (step @p27 (= tptp.join @t70) :rule refl :args (@t70)) % 0.36/0.61 (step @p28 (= tptp.lconfl @t73) :rule refl :args (@t73)) % 0.36/0.61 (step @p29 (= tptp.sconfl @t75) :rule refl :args (@t75)) % 0.36/0.61 (step @p30 (= tptp.confl @t76) :rule refl :args (@t76)) % 0.36/0.61 (step @p31 (= tptp.cr @t77) :rule refl :args (@t77)) % 0.36/0.61 (step @p32 :rule evaluate :args ((not true))) % 0.36/0.61 (step @p33 :rule quant-unused-vars :args ((= (forall @t15 true) true))) % 0.36/0.61 (step @p34 :rule bool-or-taut2 :args (false @t78 (or @t79) false)) % 0.36/0.61 (step @p35 :rule cong :premises (@p34) :args ((forall @t15 (or @t80 @t79 @t78)))) % 0.36/0.61 (step @p36 :rule trans :premises (@p35 @p33)) % 0.36/0.61 (step @p37 :rule refl :args (@t78)) % 0.36/0.61 (step @p38 :rule refl :args (@t8)) % 0.36/0.61 (step @p39 :rule cong :premises (@p38 @p37) :args ((= @t8 @t78))) % 0.36/0.61 (step @p40 :rule symm :premises (@p39)) % 0.36/0.61 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.36/0.61 (step @p42 :rule refl :args (@t79)) % 0.36/0.61 (step @p43 :rule refl :args (@t14)) % 0.36/0.61 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t14 @t79))) % 0.36/0.61 (step @p45 :rule symm :premises (@p44)) % 0.36/0.61 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.36/0.61 (step @p47 :rule refl :args (@t80)) % 0.36/0.61 (step @p48 :rule nary_cong :premises (@p47 @p46 @p41) :args (@t81)) % 0.36/0.61 (step @p49 :rule cong :premises (@p48) :args ((forall @t15 @t81))) % 0.36/0.61 (step @p50 :rule trans :premises (@p49 @p36)) % 0.36/0.61 (step @p51 :rule aci_norm :args ((= (or @t80 @t36) @t81))) % 0.36/0.61 (step @p52 :rule beta-reduce :args ((= @t82 @t36))) % 0.36/0.61 (step @p53 :rule refl :args (@t80)) % 0.36/0.61 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t83)) % 0.36/0.61 (step @p55 :rule trans :premises (@p54 @p51)) % 0.36/0.61 (step @p56 :rule cong :premises (@p55) :args (@t84)) % 0.36/0.61 (step @p57 :rule trans :premises (@p56 @p50)) % 0.36/0.61 (step @p58 :rule beta-reduce :args ((= @t88 @t84))) % 0.36/0.61 (step @p59 :rule trans :premises (@p58 @p57)) % 0.36/0.61 (step @p60 :rule cong :premises (@p59) :args ((not @t88))) % 0.36/0.61 (step @p61 :rule trans :premises (@p60 @p32)) % 0.36/0.61 (step @p62 :rule quant-merge-prenex :args ((= (forall @t19 (forall @t9 @t86)) @t87))) % 0.36/0.61 (step @p63 :rule refl :args (@t85)) % 0.36/0.61 (step @p64 :rule refl :args (@t89)) % 0.36/0.61 (step @p65 :rule cong :premises (@p64 @p63) :args ((= @t89 @t85))) % 0.36/0.61 (step @p66 :rule symm :premises (@p65)) % 0.36/0.61 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.36/0.61 (step @p68 :rule nary_cong :premises (@p47 @p67) :args (@t90)) % 0.36/0.61 (step @p69 :rule cong :premises (@p68) :args ((forall @t9 @t90))) % 0.36/0.61 (step @p70 :rule refl :args (@t91)) % 0.36/0.61 (step @p71 :rule nary_cong :premises (@p53 @p70) :args (@t92)) % 0.36/0.61 (step @p72 :rule cong :premises (@p71) :args (@t93)) % 0.36/0.61 (step @p73 :rule trans :premises (@p72 @p69)) % 0.36/0.61 (step @p74 :rule beta-reduce :args ((= (_ @t96 @t18) @t93))) % 0.36/0.61 (step @p75 :rule trans :premises (@p74 @p73)) % 0.36/0.61 (step @p76 :rule refl :args (@t18)) % 0.36/0.61 (step @p77 :rule beta-reduce :args ((= @t97 @t96))) % 0.36/0.61 (step @p78 :rule ho_cong :premises (@p77 @p76)) % 0.36/0.61 (step @p79 :rule trans :premises (@p78 @p75)) % 0.36/0.61 (step @p80 :rule cong :premises (@p79) :args ((forall @t19 (_ @t97 @t18)))) % 0.36/0.61 (step @p81 :rule trans :premises (@p80 @p62)) % 0.36/0.61 (step @p82 :rule refl :args (@t6)) % 0.36/0.61 (step @p83 :rule refl :args (@t94)) % 0.36/0.61 (step @p84 :rule refl :args (@t5)) % 0.36/0.61 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t5 @t94))) % 0.36/0.61 (step @p86 :rule symm :premises (@p85)) % 0.36/0.61 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 0.36/0.61 (step @p88 :rule cong :premises (@p41) :args (@t55)) % 0.36/0.61 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t98)) % 0.36/0.61 (step @p90 :rule cong :premises (@p89) :args ((forall @t9 @t98))) % 0.36/0.61 (step @p91 :rule bool-impl-elim :args (@t8 @t5)) % 0.36/0.61 (step @p92 :rule cong :premises (@p91) :args (@t10)) % 0.36/0.61 (step @p93 :rule trans :premises (@p92 @p90)) % 0.36/0.61 (step @p94 :rule cong :premises (@p93) :args (@t12)) % 0.36/0.61 (step @p95 :rule trans :premises (@p3 @p94)) % 0.36/0.61 (step @p96 :rule ho_cong :premises (@p95 @p82)) % 0.36/0.61 (step @p97 :rule ho_cong :premises (@p96 @p76)) % 0.36/0.61 (step @p98 :rule cong :premises (@p97) :args (@t23)) % 0.36/0.61 (step @p99 :rule trans :premises (@p98 @p81)) % 0.36/0.61 (step @p100 :rule cong :premises (@p99) :args (@t24)) % 0.36/0.61 (step @p101 :rule trans :premises (@p6 @p100)) % 0.36/0.61 (step @p102 :rule ho_cong :premises (@p101 @p14)) % 0.36/0.61 (step @p103 :rule cong :premises (@p102) :args (@t1)) % 0.36/0.61 (step @p104 :rule trans :premises (@p103 @p61)) % 0.36/0.61 (step @p105 false :rule eq_resolve :premises (@p1 @p104)) % 0.36/0.61 ) % 0.36/0.61 % SZS output end Proof % 0.36/0.61 % cvc5 exiting %------------------------------------------------------------------------------