%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU495^1 : 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 : n025.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:51:56 AM UTC 2026 % Result : Theorem 0.36s 0.64s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.14 % Problem : SEU495^1 : TPTP v9.2.1. Released v3.6.0. % 0.11/0.15 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.36 % Computer : n025.cluster.edu % 0.17/0.36 % Model : x86_64 x86_64 % 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.36 % Memory : 8042.1875MB % 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.36 % CPULimit : 300 % 0.17/0.36 % WCLimit : 300 % 0.17/0.36 % DateTime : Tue Jun 2 17:39:01 EDT 2026 % 0.17/0.36 % CPUTime : % 0.28/0.52 %----Proving TH0 % 0.36/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.64 % SZS status Theorem % 0.36/0.64 % SZS output start Proof % 0.36/0.64 ( % 0.36/0.64 (declare-sort $$unsorted 0) % 0.36/0.64 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.64 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.36/0.64 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.36/0.64 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.36/0.64 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.36/0.64 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.64 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.36/0.64 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.64 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.64 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.36/0.64 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.64 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.64 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.36/0.64 (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))))))))) % 0.36/0.64 (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)))))) % 0.36/0.64 (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)))))) % 0.36/0.64 (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))))) % 0.36/0.64 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.36/0.64 (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)))))))) % 0.36/0.64 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.36/0.64 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 0.36/0.64 (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)))))))) % 0.36/0.64 (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))))))) % 0.36/0.64 (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)))))))) % 0.36/0.64 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.36/0.64 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.36/0.64 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.36/0.64 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.36/0.64 (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)))))))) % 0.36/0.64 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.64 (define @t2 () (=> (_ tptp.total @t1) (_ tptp.total (_ tptp.inv @t1)))) % 0.36/0.64 (define @t3 () (@list @t1)) % 0.36/0.64 (define @t4 () (forall @t3 @t2)) % 0.36/0.64 (define @t5 () (not @t4)) % 0.36/0.64 (define @t6 () (@var "Y" $$unsorted)) % 0.36/0.64 (define @t7 () (@var "X" $$unsorted)) % 0.36/0.64 (define @t8 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.36/0.64 (define @t9 () (_ (_ @t8 @t7) @t6)) % 0.36/0.64 (define @t10 () (_ @t1 @t7)) % 0.36/0.64 (define @t11 () (_ @t10 @t6)) % 0.36/0.64 (define @t12 () (@list @t7 @t6)) % 0.36/0.64 (define @t13 () (@list @t1 @t8)) % 0.36/0.64 (define @t14 () (lambda @t13 (forall @t12 (=> @t11 @t9)))) % 0.36/0.64 (define @t15 () (_ @t1 @t6)) % 0.36/0.64 (define @t16 () (_ @t15 @t7)) % 0.36/0.64 (define @t17 () (@list @t1 @t7 @t6)) % 0.36/0.64 (define @t18 () (lambda @t17 @t16)) % 0.36/0.64 (define @t19 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.36/0.64 (define @t20 () (_ @t19 @t1)) % 0.36/0.64 (define @t21 () (@list @t19)) % 0.36/0.64 (define @t22 () (lambda @t21 (forall @t3 (= (_ @t19 @t20) @t20)))) % 0.36/0.64 (define @t23 () (_ tptp.subrel @t1)) % 0.36/0.64 (define @t24 () (lambda @t21 (forall @t3 (_ @t23 @t20)))) % 0.36/0.64 (define @t25 () (_ @t23 @t8)) % 0.36/0.64 (define @t26 () (lambda @t21 (forall @t13 (=> @t25 (_ (_ tptp.subrel @t20) (_ @t19 @t8)))))) % 0.36/0.64 (define @t27 () (_ @t10 @t7)) % 0.36/0.64 (define @t28 () (@list @t7)) % 0.36/0.64 (define @t29 () (lambda @t3 (forall @t28 @t27))) % 0.36/0.64 (define @t30 () (lambda @t3 (forall @t28 (not @t27)))) % 0.36/0.64 (define @t31 () (= @t7 @t6)) % 0.36/0.64 (define @t32 () (lambda @t17 (or @t31 @t11))) % 0.36/0.64 (define @t33 () (lambda @t3 (forall @t12 (=> @t11 @t16)))) % 0.36/0.64 (define @t34 () (lambda @t3 (forall @t12 (=> (and @t11 @t16) @t31)))) % 0.36/0.64 (define @t35 () (lambda @t3 (forall @t12 (=> @t11 (not @t16))))) % 0.36/0.64 (define @t36 () (lambda @t17 (or @t16 @t11))) % 0.36/0.64 (define @t37 () (@var "Z" $$unsorted)) % 0.36/0.64 (define @t38 () (_ @t10 @t37)) % 0.36/0.64 (define @t39 () (@list @t7 @t6 @t37)) % 0.36/0.64 (define @t40 () (lambda @t3 (forall @t39 (=> (and @t11 (_ @t15 @t37)) @t38)))) % 0.36/0.64 (define @t41 () (lambda @t17 (forall (@list @t8) (=> (and (_ tptp.trans @t8) @t25) @t9)))) % 0.36/0.64 (define @t42 () (@var "__flatten_var_1" $$unsorted)) % 0.36/0.64 (define @t43 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.64 (define @t44 () (_ tptp.tc @t1)) % 0.36/0.64 (define @t45 () (_ tptp.rc @t44)) % 0.36/0.64 (define @t46 () (@list @t1 @t43 @t42)) % 0.36/0.64 (define @t47 () (lambda @t46 (_ (_ @t45 @t43) @t42))) % 0.36/0.64 (define @t48 () (lambda @t46 (_ (_ (_ tptp.sc @t45) @t43) @t42))) % 0.36/0.64 (define @t49 () (_ tptp.trans @t1)) % 0.36/0.64 (define @t50 () (lambda @t3 (and (_ tptp.refl @t1) (_ tptp.antisymm @t1) @t49))) % 0.36/0.64 (define @t51 () (lambda @t3 (and (_ tptp.asymm @t1) @t49))) % 0.36/0.64 (define @t52 () (or @t31 @t11 @t16)) % 0.36/0.64 (define @t53 () (forall @t12 @t52)) % 0.36/0.64 (define @t54 () (lambda @t3 @t53)) % 0.36/0.64 (define @t55 () (@var "A" (-> $$unsorted Bool))) % 0.36/0.64 (define @t56 () (@list @t6)) % 0.36/0.64 (define @t57 () (_ @t55 @t7)) % 0.36/0.64 (define @t58 () (lambda @t3 (forall (@list @t55) (=> (exists @t28 @t57) (exists @t28 (and @t57 (forall @t56 (=> (_ @t55 @t6) (not @t11))))))))) % 0.36/0.64 (define @t59 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.64 (define @t60 () (_ @t59 @t7)) % 0.36/0.64 (define @t61 () (lambda @t3 (forall (@list @t59) (=> (forall @t28 (=> (forall @t56 (=> (_ (_ @t44 @t7) @t6) (_ @t59 @t6))) @t60)) (forall @t28 @t60))))) % 0.36/0.64 (define @t62 () (lambda (@list @t1 @t7) (not (exists @t56 @t11)))) % 0.36/0.64 (define @t63 () (_ tptp.trc @t1)) % 0.36/0.64 (define @t64 () (_ @t63 @t6)) % 0.36/0.64 (define @t65 () (lambda @t17 (and (_ @t64 @t7) (_ (_ tptp.innf @t1) @t7)))) % 0.36/0.64 (define @t66 () (lambda @t3 (forall @t28 (exists @t56 (_ (_ (_ tptp.nfof @t1) @t6) @t7))))) % 0.36/0.64 (define @t67 () (_ @t63 @t7)) % 0.36/0.64 (define @t68 () (_ @t67 @t37)) % 0.36/0.64 (define @t69 () (lambda @t17 (exists (@list @t37) (and @t68 (_ @t64 @t37))))) % 0.36/0.64 (define @t70 () (_ tptp.join @t1)) % 0.36/0.64 (define @t71 () (_ (_ @t70 @t37) @t6)) % 0.36/0.64 (define @t72 () (lambda @t3 (forall @t39 (=> (and @t38 @t11) @t71)))) % 0.36/0.64 (define @t73 () (_ @t67 @t6)) % 0.36/0.64 (define @t74 () (lambda @t3 (forall @t39 (=> (and @t38 @t73) @t71)))) % 0.36/0.64 (define @t75 () (lambda @t3 (forall @t39 (=> (and @t68 @t73) @t71)))) % 0.36/0.64 (define @t76 () (lambda @t3 (forall @t12 (=> (_ (_ (_ tptp.trsc @t1) @t7) @t6) (_ (_ @t70 @t7) @t6))))) % 0.36/0.64 (define @t77 () (@var "BOUND_VARIABLE_8853" $$unsorted)) % 0.36/0.64 (define @t78 () (@var "BOUND_VARIABLE_8851" $$unsorted)) % 0.36/0.64 (define @t79 () (_ @t1 @t78 @t77)) % 0.36/0.64 (define @t80 () (_ @t1 @t77 @t78)) % 0.36/0.64 (define @t81 () (= @t78 @t77)) % 0.36/0.64 (define @t82 () (_ @t1 @t6 @t7)) % 0.36/0.64 (define @t83 () (_ @t1 @t7 @t6)) % 0.36/0.64 (define @t84 () (forall @t12 (or @t31 @t83 @t82))) % 0.36/0.64 (define @t85 () (not @t84)) % 0.36/0.64 (define @t86 () (or @t85 @t81 @t80 @t79)) % 0.36/0.64 (define @t87 () (or @t81 @t80 @t79)) % 0.36/0.64 (define @t88 () (or @t85 @t87)) % 0.36/0.64 (define @t89 () (@list @t1 @t78 @t77)) % 0.36/0.64 (define @t90 () (forall @t89 @t88)) % 0.36/0.64 (define @t91 () (@list @t78 @t77)) % 0.36/0.64 (define @t92 () (forall @t91 @t88)) % 0.36/0.64 (define @t93 () (forall @t91 @t87)) % 0.36/0.64 (define @t94 () (or @t85 @t93)) % 0.36/0.64 (define @t95 () (forall @t12 (or @t31 @t82 @t83))) % 0.36/0.64 (define @t96 () (or @t31 @t16 @t11)) % 0.36/0.64 (define @t97 () (lambda @t12 @t16)) % 0.36/0.64 (define @t98 () (_ @t97 @t6 @t7)) % 0.36/0.64 (define @t99 () (_ @t97 @t7 @t6)) % 0.36/0.64 (define @t100 () (or @t31 @t99 @t98)) % 0.36/0.64 (define @t101 () (forall @t12 @t100)) % 0.36/0.64 (define @t102 () (lambda @t3 @t84)) % 0.36/0.64 (define @t103 () (_ @t18 @t1)) % 0.36/0.64 (define @t104 () (_ @t102 @t1)) % 0.36/0.64 (define @t105 () (=> @t104 (_ @t102 @t103))) % 0.36/0.64 (define @t106 () (forall @t3 @t105)) % 0.36/0.64 (define @t107 () (forall @t89 @t86)) % 0.36/0.64 (define @t108 () (@quantifiers_skolemize @t107 0)) % 0.36/0.64 (define @t109 () (forall @t12 (or @t31 (_ @t108 @t7 @t6) (_ @t108 @t6 @t7)))) % 0.36/0.64 (define @t110 () (@quantifiers_skolemize @t107 2)) % 0.36/0.64 (define @t111 () (@quantifiers_skolemize @t107 1)) % 0.36/0.64 (define @t112 () (_ @t108 @t111 @t110)) % 0.36/0.64 (define @t113 () (_ @t108 @t110 @t111)) % 0.36/0.64 (define @t114 () (= @t111 @t110)) % 0.36/0.64 (define @t115 () (not @t109)) % 0.36/0.64 (define @t116 () (or @t115 @t114 @t113 @t112)) % 0.36/0.64 (define @t117 () (@list true)) % 0.36/0.64 (define @t118 () (@list @t116)) % 0.36/0.64 (define @t119 () (or @t114 @t112 @t113)) % 0.36/0.64 (define @t120 () (not @t119)) % 0.36/0.64 (assume @p1 @t5) % 0.36/0.64 (assume @p2 true) % 0.36/0.64 (step @p3 (= tptp.subrel @t14) :rule refl :args (@t14)) % 0.36/0.64 (step @p4 (= tptp.inv @t18) :rule refl :args (@t18)) % 0.36/0.64 (step @p5 (= tptp.idem @t22) :rule refl :args (@t22)) % 0.36/0.64 (step @p6 (= tptp.infl @t24) :rule refl :args (@t24)) % 0.36/0.64 (step @p7 (= tptp.mono @t26) :rule refl :args (@t26)) % 0.36/0.64 (step @p8 (= tptp.refl @t29) :rule refl :args (@t29)) % 0.36/0.64 (step @p9 (= tptp.irrefl @t30) :rule refl :args (@t30)) % 0.36/0.64 (step @p10 (= tptp.rc @t32) :rule refl :args (@t32)) % 0.36/0.64 (step @p11 (= tptp.symm @t33) :rule refl :args (@t33)) % 0.36/0.64 (step @p12 (= tptp.antisymm @t34) :rule refl :args (@t34)) % 0.36/0.64 (step @p13 (= tptp.asymm @t35) :rule refl :args (@t35)) % 0.36/0.64 (step @p14 (= tptp.sc @t36) :rule refl :args (@t36)) % 0.36/0.64 (step @p15 (= tptp.trans @t40) :rule refl :args (@t40)) % 0.36/0.64 (step @p16 (= tptp.tc @t41) :rule refl :args (@t41)) % 0.36/0.64 (step @p17 (= tptp.trc @t47) :rule refl :args (@t47)) % 0.36/0.64 (step @p18 (= tptp.trsc @t48) :rule refl :args (@t48)) % 0.36/0.64 (step @p19 (= tptp.po @t50) :rule refl :args (@t50)) % 0.36/0.64 (step @p20 (= tptp.so @t51) :rule refl :args (@t51)) % 0.36/0.64 (step @p21 (= tptp.total @t54) :rule refl :args (@t54)) % 0.36/0.64 (step @p22 (= tptp.term @t58) :rule refl :args (@t58)) % 0.36/0.64 (step @p23 (= tptp.ind @t61) :rule refl :args (@t61)) % 0.36/0.64 (step @p24 (= tptp.innf @t62) :rule refl :args (@t62)) % 0.36/0.64 (step @p25 (= tptp.nfof @t65) :rule refl :args (@t65)) % 0.36/0.64 (step @p26 (= tptp.norm @t66) :rule refl :args (@t66)) % 0.36/0.64 (step @p27 (= tptp.join @t69) :rule refl :args (@t69)) % 0.36/0.64 (step @p28 (= tptp.lconfl @t72) :rule refl :args (@t72)) % 0.36/0.64 (step @p29 (= tptp.sconfl @t74) :rule refl :args (@t74)) % 0.36/0.64 (step @p30 (= tptp.confl @t75) :rule refl :args (@t75)) % 0.36/0.64 (step @p31 (= tptp.cr @t76) :rule refl :args (@t76)) % 0.36/0.64 (step @p32 :rule aci_norm :args ((= @t88 @t86))) % 0.36/0.64 (step @p33 :rule cong :premises (@p32) :args (@t90)) % 0.36/0.64 (step @p34 :rule quant-merge-prenex :args ((= (forall @t3 @t92) @t90))) % 0.36/0.64 (step @p35 :rule alpha_equiv :args (@t93 (@list @t78 @t77) (@list @t7 @t6))) % 0.36/0.64 (step @p36 :rule refl :args (@t85)) % 0.36/0.64 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t94)) % 0.36/0.64 (step @p38 :rule quant-miniscope-or :args ((= @t92 @t94))) % 0.36/0.64 (step @p39 :rule trans :premises (@p38 @p37)) % 0.36/0.64 (step @p40 :rule symm :premises (@p39)) % 0.36/0.64 (step @p41 :rule cong :premises (@p40) :args ((forall @t3 (or @t85 @t95)))) % 0.36/0.64 (step @p42 :rule trans :premises (@p41 @p34)) % 0.36/0.64 (step @p43 :rule trans :premises (@p42 @p33)) % 0.36/0.64 (step @p44 :rule bool-impl-elim :args (@t84 @t95)) % 0.36/0.64 (step @p45 :rule cong :premises (@p44) :args ((forall @t3 (=> @t84 @t95)))) % 0.36/0.64 (step @p46 :rule trans :premises (@p45 @p43)) % 0.36/0.64 (step @p47 :rule refl :args (@t83)) % 0.36/0.64 (step @p48 :rule refl :args (@t11)) % 0.36/0.64 (step @p49 :rule cong :premises (@p48 @p47) :args ((= @t11 @t83))) % 0.36/0.64 (step @p50 :rule symm :premises (@p49)) % 0.36/0.64 (step @p51 :rule eq_resolve :premises (@p48 @p50)) % 0.36/0.64 (step @p52 :rule refl :args (@t82)) % 0.36/0.64 (step @p53 :rule refl :args (@t16)) % 0.36/0.64 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t16 @t82))) % 0.36/0.64 (step @p55 :rule symm :premises (@p54)) % 0.36/0.64 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.36/0.64 (step @p57 :rule refl :args (@t31)) % 0.36/0.64 (step @p58 :rule nary_cong :premises (@p57 @p56 @p51) :args (@t96)) % 0.36/0.64 (step @p59 :rule cong :premises (@p58) :args ((forall @t12 @t96))) % 0.36/0.64 (step @p60 :rule beta-reduce :args ((= @t98 @t11))) % 0.36/0.64 (step @p61 :rule beta-reduce :args ((= @t99 @t16))) % 0.36/0.64 (step @p62 :rule refl :args (@t31)) % 0.36/0.64 (step @p63 :rule nary_cong :premises (@p62 @p61 @p60) :args (@t100)) % 0.36/0.64 (step @p64 :rule cong :premises (@p63) :args (@t101)) % 0.36/0.64 (step @p65 :rule trans :premises (@p64 @p59)) % 0.36/0.64 (step @p66 :rule beta-reduce :args ((= (_ @t102 @t97) @t101))) % 0.36/0.64 (step @p67 :rule trans :premises (@p66 @p65)) % 0.36/0.64 (step @p68 :rule beta-reduce :args ((= @t103 @t97))) % 0.36/0.64 (step @p69 :rule refl :args (@t102)) % 0.36/0.64 (step @p70 :rule ho_cong :premises (@p69 @p68)) % 0.36/0.64 (step @p71 :rule trans :premises (@p70 @p67)) % 0.36/0.64 (step @p72 :rule beta-reduce :args ((= @t104 @t84))) % 0.36/0.64 (step @p73 :rule cong :premises (@p72 @p71) :args (@t105)) % 0.36/0.64 (step @p74 :rule cong :premises (@p73) :args (@t106)) % 0.36/0.64 (step @p75 :rule trans :premises (@p74 @p46)) % 0.36/0.64 (step @p76 :rule cong :premises (@p75) :args ((not @t106))) % 0.36/0.64 (step @p77 :rule refl :args (@t1)) % 0.36/0.64 (step @p78 :rule ho_cong :premises (@p4 @p77)) % 0.36/0.64 (step @p79 :rule nary_cong :premises (@p57 @p51 @p56) :args (@t52)) % 0.36/0.64 (step @p80 :rule cong :premises (@p79) :args (@t53)) % 0.36/0.64 (step @p81 :rule cong :premises (@p80) :args (@t54)) % 0.36/0.64 (step @p82 :rule trans :premises (@p21 @p81)) % 0.36/0.64 (step @p83 :rule ho_cong :premises (@p82 @p78)) % 0.36/0.64 (step @p84 :rule ho_cong :premises (@p82 @p77)) % 0.36/0.64 (step @p85 :rule cong :premises (@p84 @p83) :args (@t2)) % 0.36/0.64 (step @p86 :rule cong :premises (@p85) :args (@t4)) % 0.36/0.64 (step @p87 :rule cong :premises (@p86) :args (@t5)) % 0.36/0.64 (step @p88 :rule trans :premises (@p87 @p76)) % 0.36/0.64 (step @p89 :rule eq_resolve :premises (@p1 @p88)) % 0.36/0.64 (step @p90 :rule skolemize :premises (@p89)) % 0.36/0.64 (step @p91 :rule bool-double-not-elim :args (@t109)) % 0.36/0.64 (step @p92 :rule refl :args (@t116)) % 0.36/0.64 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or @t116 (not @t115)))) % 0.36/0.64 (step @p94 :rule cnf_or_neg :args (@t116 0)) % 0.36/0.64 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 0.36/0.64 (step @p96 :rule reordering :premises (@p95) :args ((or @t109 @t116))) % 0.36/0.64 (step @p97 :rule chain_m_resolution :premises (@p96 @p90) :args (@t109 @t117 @t118)) % 0.36/0.64 (step @p98 :rule cnf_or_neg :args (@t116 3)) % 0.36/0.64 (step @p99 :rule chain_m_resolution :premises (@p98 @p90) :args ((not @t112) @t117 @t118)) % 0.36/0.64 (step @p100 :rule cnf_or_neg :args (@t116 2)) % 0.36/0.64 (step @p101 :rule chain_m_resolution :premises (@p100 @p90) :args ((not @t113) @t117 @t118)) % 0.36/0.64 (step @p102 :rule cnf_or_neg :args (@t116 1)) % 0.36/0.64 (step @p103 :rule chain_m_resolution :premises (@p102 @p90) :args ((not @t114) @t117 @t118)) % 0.36/0.64 (step @p104 :rule cnf_or_pos :args (@t119)) % 0.36/0.64 (step @p105 :rule reordering :premises (@p104) :args ((or @t114 @t113 @t112 @t120))) % 0.36/0.64 (step @p106 :rule chain_m_resolution :premises (@p105 @p103 @p101 @p99) :args (@t120 (@list true true true) (@list @t114 @t113 @t112))) % 0.36/0.64 (assume-push @p113 @t109) % 0.36/0.64 (step @p108 :rule instantiate :premises (@p97) :args ((@list @t111 @t110))) % 0.36/0.64 (step-pop @p114 :rule scope :premises (@p108)) % 0.36/0.64 (step @p109 :rule process_scope :premises (@p114) :args (@t119)) % 0.36/0.64 (step @p111 :rule implies_elim :premises (@p109)) % 0.36/0.64 (step @p112 false :rule chain_m_resolution :premises (@p111 @p106 @p97) :args (false (@list true false) (@list @t119 @t109))) % 0.36/0.64 ) % 0.36/0.64 % SZS output end Proof % 0.36/0.64 % cvc5 exiting %------------------------------------------------------------------------------