%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU462^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.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 0.45s 0.63s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU462^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n029.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 17:36:32 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.45/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.63 % SZS status Theorem % 0.45/0.63 % SZS output start Proof % 0.45/0.63 ( % 0.45/0.63 (declare-sort $$unsorted 0) % 0.45/0.63 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.45/0.63 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.45/0.63 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.45/0.63 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.45/0.63 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.45/0.63 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.45/0.63 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.45/0.63 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.45/0.63 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.45/0.63 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.45/0.63 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.45/0.63 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.45/0.63 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.45/0.63 (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))))))))) % 0.45/0.63 (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)))))) % 0.45/0.63 (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)))))) % 0.45/0.63 (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))))) % 0.45/0.63 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.45/0.63 (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)))))))) % 0.45/0.63 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.45/0.63 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 0.45/0.63 (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)))))))) % 0.45/0.63 (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))))))) % 0.45/0.63 (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)))))))) % 0.45/0.63 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.45/0.63 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.45/0.63 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.45/0.63 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.45/0.63 (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)))))))) % 0.45/0.63 (define @t1 () (@var "Y" $$unsorted)) % 0.45/0.63 (define @t2 () (@var "X" $$unsorted)) % 0.45/0.63 (define @t3 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.45/0.63 (define @t4 () (_ (_ @t3 @t2) @t1)) % 0.45/0.63 (define @t5 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.45/0.63 (define @t6 () (_ tptp.tc @t5)) % 0.45/0.63 (define @t7 () (_ (_ @t6 @t2) @t1)) % 0.45/0.63 (define @t8 () (_ tptp.subrel @t5)) % 0.45/0.63 (define @t9 () (_ @t8 @t3)) % 0.45/0.63 (define @t10 () (_ tptp.trans @t3)) % 0.45/0.63 (define @t11 () (and @t10 @t9 @t7)) % 0.45/0.63 (define @t12 () (=> @t11 @t4)) % 0.45/0.63 (define @t13 () (@list @t5 @t2 @t1 @t3)) % 0.45/0.63 (define @t14 () (forall @t13 @t12)) % 0.45/0.63 (define @t15 () (not @t14)) % 0.45/0.63 (define @t16 () (_ @t5 @t2)) % 0.45/0.63 (define @t17 () (_ @t16 @t1)) % 0.45/0.63 (define @t18 () (@list @t2 @t1)) % 0.45/0.63 (define @t19 () (forall @t18 (=> @t17 @t4))) % 0.45/0.63 (define @t20 () (@list @t5 @t3)) % 0.45/0.63 (define @t21 () (lambda @t20 @t19)) % 0.45/0.63 (define @t22 () (_ @t5 @t1)) % 0.45/0.63 (define @t23 () (_ @t22 @t2)) % 0.45/0.63 (define @t24 () (@list @t5 @t2 @t1)) % 0.45/0.63 (define @t25 () (lambda @t24 @t23)) % 0.45/0.63 (define @t26 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.45/0.63 (define @t27 () (_ @t26 @t5)) % 0.45/0.63 (define @t28 () (@list @t5)) % 0.45/0.63 (define @t29 () (@list @t26)) % 0.45/0.63 (define @t30 () (lambda @t29 (forall @t28 (= (_ @t26 @t27) @t27)))) % 0.45/0.63 (define @t31 () (lambda @t29 (forall @t28 (_ @t8 @t27)))) % 0.45/0.63 (define @t32 () (lambda @t29 (forall @t20 (=> @t9 (_ (_ tptp.subrel @t27) (_ @t26 @t3)))))) % 0.45/0.63 (define @t33 () (_ @t16 @t2)) % 0.45/0.63 (define @t34 () (@list @t2)) % 0.45/0.63 (define @t35 () (lambda @t28 (forall @t34 @t33))) % 0.45/0.63 (define @t36 () (lambda @t28 (forall @t34 (not @t33)))) % 0.45/0.63 (define @t37 () (= @t2 @t1)) % 0.45/0.63 (define @t38 () (lambda @t24 (or @t37 @t17))) % 0.45/0.63 (define @t39 () (lambda @t28 (forall @t18 (=> @t17 @t23)))) % 0.45/0.63 (define @t40 () (lambda @t28 (forall @t18 (=> (and @t17 @t23) @t37)))) % 0.45/0.63 (define @t41 () (lambda @t28 (forall @t18 (=> @t17 (not @t23))))) % 0.45/0.63 (define @t42 () (lambda @t24 (or @t23 @t17))) % 0.45/0.63 (define @t43 () (@var "Z" $$unsorted)) % 0.45/0.63 (define @t44 () (_ @t16 @t43)) % 0.45/0.63 (define @t45 () (_ @t22 @t43)) % 0.45/0.63 (define @t46 () (and @t17 @t45)) % 0.45/0.63 (define @t47 () (@list @t2 @t1 @t43)) % 0.45/0.63 (define @t48 () (forall @t47 (=> @t46 @t44))) % 0.45/0.63 (define @t49 () (lambda @t28 @t48)) % 0.45/0.63 (define @t50 () (and @t10 @t9)) % 0.45/0.63 (define @t51 () (=> @t50 @t4)) % 0.45/0.63 (define @t52 () (@list @t3)) % 0.45/0.63 (define @t53 () (forall @t52 @t51)) % 0.45/0.63 (define @t54 () (lambda @t24 @t53)) % 0.45/0.63 (define @t55 () (@var "__flatten_var_1" $$unsorted)) % 0.45/0.63 (define @t56 () (@var "__flatten_var_0" $$unsorted)) % 0.45/0.63 (define @t57 () (_ tptp.rc @t6)) % 0.45/0.63 (define @t58 () (@list @t5 @t56 @t55)) % 0.45/0.63 (define @t59 () (lambda @t58 (_ (_ @t57 @t56) @t55))) % 0.45/0.63 (define @t60 () (lambda @t58 (_ (_ (_ tptp.sc @t57) @t56) @t55))) % 0.45/0.63 (define @t61 () (_ tptp.trans @t5)) % 0.45/0.63 (define @t62 () (lambda @t28 (and (_ tptp.refl @t5) (_ tptp.antisymm @t5) @t61))) % 0.45/0.63 (define @t63 () (lambda @t28 (and (_ tptp.asymm @t5) @t61))) % 0.45/0.63 (define @t64 () (lambda @t28 (forall @t18 (or @t37 @t17 @t23)))) % 0.45/0.63 (define @t65 () (not @t17)) % 0.45/0.63 (define @t66 () (@var "A" (-> $$unsorted Bool))) % 0.45/0.63 (define @t67 () (@list @t1)) % 0.45/0.63 (define @t68 () (_ @t66 @t2)) % 0.45/0.63 (define @t69 () (lambda @t28 (forall (@list @t66) (=> (exists @t34 @t68) (exists @t34 (and @t68 (forall @t67 (=> (_ @t66 @t1) @t65)))))))) % 0.45/0.63 (define @t70 () (@var "P" (-> $$unsorted Bool))) % 0.45/0.63 (define @t71 () (_ @t70 @t2)) % 0.45/0.63 (define @t72 () (lambda @t28 (forall (@list @t70) (=> (forall @t34 (=> (forall @t67 (=> @t7 (_ @t70 @t1))) @t71)) (forall @t34 @t71))))) % 0.45/0.63 (define @t73 () (lambda (@list @t5 @t2) (not (exists @t67 @t17)))) % 0.45/0.63 (define @t74 () (_ tptp.trc @t5)) % 0.45/0.63 (define @t75 () (_ @t74 @t1)) % 0.45/0.63 (define @t76 () (lambda @t24 (and (_ @t75 @t2) (_ (_ tptp.innf @t5) @t2)))) % 0.45/0.63 (define @t77 () (lambda @t28 (forall @t34 (exists @t67 (_ (_ (_ tptp.nfof @t5) @t1) @t2))))) % 0.45/0.63 (define @t78 () (_ @t74 @t2)) % 0.45/0.63 (define @t79 () (_ @t78 @t43)) % 0.45/0.63 (define @t80 () (lambda @t24 (exists (@list @t43) (and @t79 (_ @t75 @t43))))) % 0.45/0.63 (define @t81 () (_ tptp.join @t5)) % 0.45/0.63 (define @t82 () (_ (_ @t81 @t43) @t1)) % 0.45/0.63 (define @t83 () (lambda @t28 (forall @t47 (=> (and @t44 @t17) @t82)))) % 0.45/0.63 (define @t84 () (_ @t78 @t1)) % 0.45/0.63 (define @t85 () (lambda @t28 (forall @t47 (=> (and @t44 @t84) @t82)))) % 0.45/0.63 (define @t86 () (lambda @t28 (forall @t47 (=> (and @t79 @t84) @t82)))) % 0.45/0.63 (define @t87 () (lambda @t28 (forall @t18 (=> (_ (_ (_ tptp.trsc @t5) @t2) @t1) (_ (_ @t81 @t2) @t1))))) % 0.45/0.63 (define @t88 () (_ @t3 @t2 @t1)) % 0.45/0.63 (define @t89 () (@var "BOUND_VARIABLE_8835" (-> $$unsorted $$unsorted Bool))) % 0.45/0.63 (define @t90 () (@var "BOUND_VARIABLE_7746" $$unsorted)) % 0.45/0.63 (define @t91 () (@var "BOUND_VARIABLE_7744" $$unsorted)) % 0.45/0.63 (define @t92 () (_ @t89 @t91 @t90)) % 0.45/0.63 (define @t93 () (not (_ @t5 @t91 @t90))) % 0.45/0.63 (define @t94 () (@list @t91 @t90)) % 0.45/0.63 (define @t95 () (@var "BOUND_VARIABLE_7755" $$unsorted)) % 0.45/0.63 (define @t96 () (@var "BOUND_VARIABLE_7757" $$unsorted)) % 0.45/0.63 (define @t97 () (@list @t95 @t96 @t43)) % 0.45/0.63 (define @t98 () (not (forall @t97 (or (not (_ @t89 @t95 @t96)) (not (_ @t89 @t96 @t43)) (_ @t89 @t95 @t43))))) % 0.45/0.63 (define @t99 () (@list @t89)) % 0.45/0.63 (define @t100 () (forall @t99 (or @t98 (not (forall @t94 (or @t93 @t92))) (_ @t89 @t2 @t1)))) % 0.45/0.63 (define @t101 () (not @t100)) % 0.45/0.63 (define @t102 () (@var "BOUND_VARIABLE_8855" $$unsorted)) % 0.45/0.63 (define @t103 () (@var "BOUND_VARIABLE_8853" $$unsorted)) % 0.45/0.63 (define @t104 () (@list @t103 @t102)) % 0.45/0.63 (define @t105 () (forall @t104 (or (not (_ @t5 @t103 @t102)) (_ @t3 @t103 @t102)))) % 0.45/0.63 (define @t106 () (not @t105)) % 0.45/0.63 (define @t107 () (@var "BOUND_VARIABLE_8863" $$unsorted)) % 0.45/0.63 (define @t108 () (@var "BOUND_VARIABLE_8865" $$unsorted)) % 0.45/0.63 (define @t109 () (@list @t107 @t108 @t43)) % 0.45/0.63 (define @t110 () (forall @t109 (or (not (_ @t3 @t107 @t108)) (not (_ @t3 @t108 @t43)) (_ @t3 @t107 @t43)))) % 0.45/0.63 (define @t111 () (not @t110)) % 0.45/0.63 (define @t112 () (or @t111 @t106 @t101 @t4)) % 0.45/0.63 (define @t113 () (or @t111 @t106 @t101)) % 0.45/0.63 (define @t114 () (and @t110 @t105 @t100)) % 0.45/0.63 (define @t115 () (forall @t52 (or (not (forall @t97 (or (not (_ @t3 @t95 @t96)) (not (_ @t3 @t96 @t43)) (_ @t3 @t95 @t43)))) (not (forall @t94 (or @t93 (_ @t3 @t91 @t90)))) @t88))) % 0.45/0.63 (define @t116 () (_ @t5 @t2 @t1)) % 0.45/0.63 (define @t117 () (not @t116)) % 0.45/0.63 (define @t118 () (forall @t18 (or @t117 @t88))) % 0.45/0.63 (define @t119 () (@list @t2 @t1)) % 0.45/0.63 (define @t120 () (@list @t103 @t102)) % 0.45/0.63 (define @t121 () (forall @t47 (or (not @t88) (not (_ @t3 @t1 @t43)) (_ @t3 @t2 @t43)))) % 0.45/0.63 (define @t122 () (and @t121 @t118 @t115)) % 0.45/0.63 (define @t123 () (=> @t122 @t4)) % 0.45/0.63 (define @t124 () (lambda @t67 @t115)) % 0.45/0.63 (define @t125 () (lambda @t18 @t115)) % 0.45/0.63 (define @t126 () (lambda @t24 @t115)) % 0.45/0.63 (define @t127 () (not @t118)) % 0.45/0.63 (define @t128 () (not @t121)) % 0.45/0.63 (define @t129 () (lambda @t24 (forall @t52 (or @t128 @t127 @t88)))) % 0.45/0.63 (define @t130 () (lambda @t52 @t118)) % 0.45/0.63 (define @t131 () (_ (lambda @t20 @t118) @t5)) % 0.45/0.63 (define @t132 () (_ @t5 @t2 @t43)) % 0.45/0.63 (define @t133 () (_ @t5 @t1 @t43)) % 0.45/0.63 (define @t134 () (_ (lambda @t28 (forall @t47 (or @t117 (not @t133) @t132))) @t3)) % 0.45/0.63 (define @t135 () (_ @t131 @t3)) % 0.45/0.63 (define @t136 () (and @t134 @t135 (_ (_ (_ @t129 @t5) @t2) @t1))) % 0.45/0.63 (define @t137 () (=> @t136 @t4)) % 0.45/0.63 (define @t138 () (forall @t13 @t137)) % 0.45/0.63 (define @t139 () (or @t128 @t127 @t4)) % 0.45/0.63 (define @t140 () (and @t121 @t118)) % 0.45/0.63 (define @t141 () (and @t134 @t135)) % 0.45/0.63 (define @t142 () (=> @t141 @t4)) % 0.45/0.63 (define @t143 () (or @t65 @t4)) % 0.45/0.63 (define @t144 () (not @t45)) % 0.45/0.63 (define @t145 () (or @t65 @t144 @t44)) % 0.45/0.63 (define @t146 () (forall @t13 (or @t111 @t106 @t101 @t88))) % 0.45/0.63 (define @t147 () (@quantifiers_skolemize @t146 2)) % 0.45/0.63 (define @t148 () (@quantifiers_skolemize @t146 1)) % 0.45/0.63 (define @t149 () (@quantifiers_skolemize @t146 3)) % 0.45/0.63 (define @t150 () (_ @t149 @t148 @t147)) % 0.45/0.63 (define @t151 () (@quantifiers_skolemize @t146 0)) % 0.45/0.63 (define @t152 () (not (_ @t151 @t91 @t90))) % 0.45/0.63 (define @t153 () (forall @t99 (or @t98 (not (forall @t94 (or @t152 @t92))) (_ @t89 @t148 @t147)))) % 0.45/0.63 (define @t154 () (not @t153)) % 0.45/0.63 (define @t155 () (forall @t104 (or (not (_ @t151 @t103 @t102)) (_ @t149 @t103 @t102)))) % 0.45/0.63 (define @t156 () (not @t155)) % 0.45/0.63 (define @t157 () (forall @t109 (or (not (_ @t149 @t107 @t108)) (not (_ @t149 @t108 @t43)) (_ @t149 @t107 @t43)))) % 0.45/0.63 (define @t158 () (not @t157)) % 0.45/0.63 (define @t159 () (or @t158 @t156 @t154 @t150)) % 0.45/0.63 (define @t160 () (@list true)) % 0.45/0.63 (define @t161 () (@list @t159)) % 0.45/0.63 (define @t162 () (@var "BOUND_VARIABLE_10036" $$unsorted)) % 0.45/0.63 (define @t163 () (@var "BOUND_VARIABLE_10034" $$unsorted)) % 0.45/0.63 (define @t164 () (@var "BOUND_VARIABLE_10035" $$unsorted)) % 0.45/0.63 (define @t165 () (@list @t163 @t164 @t162)) % 0.45/0.63 (define @t166 () (forall @t97 (or (not (_ @t149 @t95 @t96)) (not (_ @t149 @t96 @t43)) (_ @t149 @t95 @t43)))) % 0.45/0.63 (define @t167 () (@list false)) % 0.45/0.63 (define @t168 () (forall @t94 (or @t152 (_ @t149 @t91 @t90)))) % 0.45/0.63 (define @t169 () (not @t168)) % 0.45/0.63 (define @t170 () (not @t166)) % 0.45/0.63 (define @t171 () (or @t170 @t169 @t150)) % 0.45/0.63 (assume @p1 @t15) % 0.45/0.63 (assume @p2 true) % 0.45/0.63 (step @p3 (= tptp.subrel @t21) :rule refl :args (@t21)) % 0.45/0.63 (step @p4 (= tptp.inv @t25) :rule refl :args (@t25)) % 0.45/0.63 (step @p5 (= tptp.idem @t30) :rule refl :args (@t30)) % 0.45/0.63 (step @p6 (= tptp.infl @t31) :rule refl :args (@t31)) % 0.45/0.63 (step @p7 (= tptp.mono @t32) :rule refl :args (@t32)) % 0.45/0.63 (step @p8 (= tptp.refl @t35) :rule refl :args (@t35)) % 0.45/0.63 (step @p9 (= tptp.irrefl @t36) :rule refl :args (@t36)) % 0.45/0.63 (step @p10 (= tptp.rc @t38) :rule refl :args (@t38)) % 0.45/0.63 (step @p11 (= tptp.symm @t39) :rule refl :args (@t39)) % 0.45/0.63 (step @p12 (= tptp.antisymm @t40) :rule refl :args (@t40)) % 0.45/0.63 (step @p13 (= tptp.asymm @t41) :rule refl :args (@t41)) % 0.45/0.63 (step @p14 (= tptp.sc @t42) :rule refl :args (@t42)) % 0.45/0.63 (step @p15 (= tptp.trans @t49) :rule refl :args (@t49)) % 0.45/0.63 (step @p16 (= tptp.tc @t54) :rule refl :args (@t54)) % 0.45/0.63 (step @p17 (= tptp.trc @t59) :rule refl :args (@t59)) % 0.45/0.63 (step @p18 (= tptp.trsc @t60) :rule refl :args (@t60)) % 0.45/0.63 (step @p19 (= tptp.po @t62) :rule refl :args (@t62)) % 0.45/0.63 (step @p20 (= tptp.so @t63) :rule refl :args (@t63)) % 0.45/0.63 (step @p21 (= tptp.total @t64) :rule refl :args (@t64)) % 0.45/0.63 (step @p22 (= tptp.term @t69) :rule refl :args (@t69)) % 0.45/0.63 (step @p23 (= tptp.ind @t72) :rule refl :args (@t72)) % 0.45/0.63 (step @p24 (= tptp.innf @t73) :rule refl :args (@t73)) % 0.45/0.63 (step @p25 (= tptp.nfof @t76) :rule refl :args (@t76)) % 0.45/0.63 (step @p26 (= tptp.norm @t77) :rule refl :args (@t77)) % 0.45/0.63 (step @p27 (= tptp.join @t80) :rule refl :args (@t80)) % 0.45/0.63 (step @p28 (= tptp.lconfl @t83) :rule refl :args (@t83)) % 0.45/0.63 (step @p29 (= tptp.sconfl @t85) :rule refl :args (@t85)) % 0.45/0.63 (step @p30 (= tptp.confl @t86) :rule refl :args (@t86)) % 0.45/0.63 (step @p31 (= tptp.cr @t87) :rule refl :args (@t87)) % 0.45/0.63 (step @p32 :rule refl :args (@t88)) % 0.45/0.63 (step @p33 :rule refl :args (@t4)) % 0.45/0.63 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t4 @t88))) % 0.45/0.63 (step @p35 :rule symm :premises (@p34)) % 0.45/0.63 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 0.45/0.63 (step @p37 :rule refl :args (@t101)) % 0.45/0.63 (step @p38 :rule refl :args (@t106)) % 0.45/0.63 (step @p39 :rule refl :args (@t111)) % 0.45/0.63 (step @p40 :rule nary_cong :premises (@p39 @p38 @p37 @p36) :args (@t112)) % 0.45/0.63 (step @p41 :rule cong 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0.45/0.63 (step @p55 :rule alpha_equiv :args (@t115 (@list @t3) (@list @t89))) % 0.45/0.63 (step @p56 :rule alpha_equiv :args (@t118 @t119 @t120)) % 0.45/0.63 (step @p57 :rule alpha_equiv :args (@t121 @t119 (@list @t107 @t108))) % 0.45/0.63 (step @p58 :rule nary_cong :premises (@p57 @p56 @p55) :args (@t122)) % 0.45/0.63 (step @p59 :rule cong :premises (@p58 @p33) :args (@t123)) % 0.45/0.63 (step @p60 :rule cong :premises (@p59) :args ((forall @t13 @t123))) % 0.45/0.63 (step @p61 :rule trans :premises (@p60 @p54)) % 0.45/0.63 (step @p62 :rule refl :args (@t4)) % 0.45/0.63 (step @p63 :rule beta-reduce :args ((= (_ @t124 @t1) @t115))) % 0.45/0.63 (step @p64 :rule refl :args (@t1)) % 0.45/0.63 (step @p65 :rule beta-reduce :args ((= (_ @t125 @t2) @t124))) % 0.45/0.63 (step @p66 :rule refl :args (@t2)) % 0.45/0.63 (step @p67 :rule beta-reduce :args ((= (_ @t126 @t5) @t125))) % 0.45/0.63 (step @p68 :rule refl :args (@t5)) % 0.45/0.63 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 0.45/0.63 ; trust TRUST_THEORY_REWRITE % 0.45/0.63 (step @p69 :rule trust :premises () :args ((= @t129 @t126))) % 0.45/0.63 (step @p70 :rule ho_cong :premises (@p69 @p68)) % 0.45/0.63 (step @p71 :rule trans :premises (@p70 @p67)) % 0.45/0.63 (step @p72 :rule ho_cong :premises (@p71 @p66)) % 0.45/0.63 (step @p73 :rule trans :premises (@p72 @p65)) % 0.45/0.63 (step @p74 :rule ho_cong :premises (@p73 @p64)) % 0.45/0.63 (step @p75 :rule trans :premises (@p74 @p63)) % 0.45/0.63 (step @p76 :rule beta-reduce :args ((= (_ @t130 @t3) @t118))) % 0.45/0.63 (step @p77 :rule refl :args (@t3)) % 0.45/0.63 (step @p78 :rule beta-reduce :args ((= @t131 @t130))) % 0.45/0.63 (step @p79 :rule ho_cong :premises (@p78 @p77)) % 0.45/0.63 (step @p80 :rule trans :premises (@p79 @p76)) % 0.45/0.63 (step @p81 :rule beta-reduce :args ((= @t134 @t121))) % 0.45/0.63 (step @p82 :rule nary_cong :premises (@p81 @p80 @p75) :args (@t136)) % 0.45/0.63 (step @p83 :rule cong :premises (@p82 @p62) :args (@t137)) % 0.45/0.63 (step @p84 :rule cong :premises (@p83) :args (@t138)) % 0.45/0.63 (step @p85 :rule trans :premises (@p84 @p61)) % 0.45/0.63 (step @p86 :rule cong :premises (@p85) :args ((not @t138))) % 0.45/0.63 (step @p87 :rule refl :args (@t127)) % 0.45/0.63 (step @p88 :rule refl :args (@t128)) % 0.45/0.63 (step @p89 :rule nary_cong :premises (@p88 @p87 @p36) :args (@t139)) % 0.45/0.63 (step @p90 :rule cong :premises (@p89) :args ((forall @t52 @t139))) % 0.45/0.63 (step @p91 :rule aci_norm :args ((= (or (or @t128 @t127) @t4) @t139))) % 0.45/0.63 (step @p92 :rule bool-and-de-morgan :args (@t121 @t118 true)) % 0.45/0.63 (step @p93 :rule nary_cong :premises (@p92 @p33) :args ((or (not @t140) @t4))) % 0.45/0.63 (step @p94 :rule trans :premises (@p93 @p91)) % 0.45/0.63 (step @p95 :rule bool-impl-elim :args (@t140 @t4)) % 0.45/0.63 (step @p96 :rule trans :premises (@p95 @p94)) % 0.45/0.63 (step @p97 :rule cong :premises (@p96) :args ((forall @t52 (=> @t140 @t4)))) % 0.45/0.63 (step @p98 :rule trans 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:premises (@p142 @p62) :args (@t51)) % 0.45/0.63 (step @p144 :rule cong :premises (@p143) :args (@t53)) % 0.45/0.63 (step @p145 :rule trans :premises (@p144 @p102)) % 0.45/0.63 (step @p146 :rule cong :premises (@p145) :args (@t54)) % 0.45/0.63 (step @p147 :rule trans :premises (@p16 @p146)) % 0.45/0.63 (step @p148 :rule ho_cong :premises (@p147 @p68)) % 0.45/0.63 (step @p149 :rule ho_cong :premises (@p148 @p66)) % 0.45/0.63 (step @p150 :rule ho_cong :premises (@p149 @p64)) % 0.45/0.63 (step @p151 :rule nary_cong :premises (@p141 @p117 @p150) :args (@t11)) % 0.45/0.63 (step @p152 :rule cong :premises (@p151 @p62) :args (@t12)) % 0.45/0.63 (step @p153 :rule cong :premises (@p152) :args (@t14)) % 0.45/0.63 (step @p154 :rule cong :premises (@p153) :args (@t15)) % 0.45/0.63 (step @p155 :rule trans :premises (@p154 @p86)) % 0.45/0.63 (step @p156 :rule eq_resolve :premises (@p1 @p155)) % 0.45/0.63 (step @p157 :rule skolemize :premises (@p156)) % 0.45/0.63 (step @p158 :rule cnf_or_neg :args (@t159 3)) % 0.45/0.63 (step @p159 :rule chain_m_resolution :premises (@p158 @p157) :args ((not @t150) @t160 @t161)) % 0.45/0.63 (step @p160 :rule bool-double-not-elim :args (@t153)) % 0.45/0.63 (step @p161 :rule refl :args (@t159)) % 0.45/0.63 (step @p162 :rule nary_cong :premises (@p161 @p160) :args ((or @t159 (not @t154)))) % 0.45/0.63 (step @p163 :rule cnf_or_neg :args (@t159 2)) % 0.45/0.63 (step @p164 :rule eq_resolve :premises (@p163 @p162)) % 0.45/0.63 (step @p165 :rule reordering :premises (@p164) :args ((or @t153 @t159))) % 0.45/0.63 (step @p166 :rule chain_m_resolution :premises (@p165 @p157) :args (@t153 @t160 @t161)) % 0.45/0.63 (step @p167 :rule instantiate :premises (@p166) :args ((@list @t149))) % 0.45/0.63 (step @p168 :rule bool-double-not-elim :args (@t157)) % 0.45/0.63 (step @p169 :rule nary_cong :premises (@p161 @p168) :args ((or @t159 (not @t158)))) % 0.45/0.63 (step @p170 :rule cnf_or_neg :args (@t159 0)) % 0.45/0.63 (step @p171 :rule eq_resolve :premises (@p170 @p169)) % 0.45/0.63 (step @p172 :rule reordering :premises (@p171) :args ((or @t157 @t159))) % 0.45/0.63 (step @p173 :rule chain_m_resolution :premises (@p172 @p157) :args (@t157 @t160 @t161)) % 0.45/0.63 (step @p174 :rule alpha_equiv :args ((forall (@list @t163 @t164 @t162) (or (not (_ @t149 @t163 @t164)) (not (_ @t149 @t164 @t162)) (_ @t149 @t163 @t162))) @t165 (@list @t95 @t96 @t43))) % 0.45/0.63 (step @p175 :rule alpha_equiv :args (@t157 (@list @t107 @t108 @t43) @t165)) % 0.45/0.63 (step @p176 :rule trans :premises (@p175 @p174)) % 0.45/0.63 (step @p177 :rule equiv_elim1 :premises (@p176)) % 0.45/0.63 (step @p178 :rule chain_m_resolution :premises (@p177 @p173) :args (@t166 @t167 (@list @t157))) % 0.45/0.63 (step @p179 :rule bool-double-not-elim :args (@t155)) % 0.45/0.63 (step @p180 :rule nary_cong :premises (@p161 @p179) :args ((or @t159 (not @t156)))) % 0.45/0.63 (step @p181 :rule cnf_or_neg :args (@t159 1)) % 0.45/0.63 (step @p182 :rule eq_resolve :premises (@p181 @p180)) % 0.45/0.63 (step @p183 :rule reordering :premises (@p182) :args ((or @t155 @t159))) % 0.45/0.63 (step @p184 :rule chain_m_resolution :premises (@p183 @p157) :args (@t155 @t160 @t161)) % 0.45/0.63 (step @p185 :rule alpha_equiv :args (@t155 @t120 (@list @t91 @t90))) % 0.45/0.63 (step @p186 :rule equiv_elim1 :premises (@p185)) % 0.45/0.63 (step @p187 :rule chain_m_resolution :premises (@p186 @p184) :args (@t168 @t167 (@list @t155))) % 0.45/0.63 (step @p188 :rule cnf_or_pos :args (@t171)) % 0.45/0.63 (step @p189 :rule reordering :premises (@p188) :args ((or @t150 @t170 @t169 (not @t171)))) % 0.45/0.63 (step @p190 false :rule chain_m_resolution :premises (@p189 @p187 @p178 @p167 @p159) :args (false (@list false false false true) (@list @t168 @t166 @t171 @t150))) % 0.45/0.63 ) % 0.45/0.63 % SZS output end Proof % 0.45/0.63 % cvc5 exiting %------------------------------------------------------------------------------