%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO497^6 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n028.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 09:12:59 AM UTC 2026 % Result : Theorem 0.44s 0.63s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO497^6 : TPTP v9.2.1. Released v4.0.0. % 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 : n028.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 : Wed Jun 3 00:17:05 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.44/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.44/0.63 % SZS status Theorem % 0.44/0.63 % SZS output start Proof % 0.44/0.63 ( % 0.44/0.63 (declare-sort $$unsorted 0) % 0.44/0.63 (declare-sort tptp.mu 0) % 0.44/0.63 (declare-const tptp.rel_s5 (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.f (-> tptp.mu $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.44/0.63 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.44/0.63 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.63 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.44/0.63 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.63 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.44/0.63 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.44/0.63 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.44/0.63 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.44/0.63 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.44/0.63 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.44/0.63 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.44/0.63 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.44/0.63 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.44/0.63 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.44/0.63 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.44/0.63 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.44/0.63 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.44/0.63 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$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)))))))) % 0.44/0.63 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.44/0.63 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.44/0.63 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.44/0.63 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.44/0.63 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.44/0.63 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.44/0.63 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.44/0.63 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.44/0.63 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.44/0.63 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.44/0.63 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.44/0.63 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.44/0.63 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s5 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.44/0.63 (define tptp.mdia_s5 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s5 (_ tptp.mnot _let_2))) _let_1))))) % 0.44/0.63 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.44/0.63 (define @t2 () (@var "X" tptp.mu)) % 0.44/0.63 (define @t3 () (_ tptp.f @t2)) % 0.44/0.63 (define @t4 () (_ @t3 @t1)) % 0.44/0.63 (define @t5 () (@list @t2 @t1)) % 0.44/0.63 (define @t6 () (lambda @t5 @t4)) % 0.44/0.63 (define @t7 () (_ tptp.mexists_ind @t6)) % 0.44/0.63 (define @t8 () (lambda @t5 (_ (_ (_ tptp.mimplies @t3) (_ tptp.mbox_s5 @t3)) @t1))) % 0.44/0.63 (define @t9 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ (_ tptp.mand (_ tptp.mbox_s5 (_ tptp.mforall_ind @t8))) (_ tptp.mdia_s5 @t7))) (_ tptp.mbox_s5 @t7))))) % 0.44/0.63 (define @t10 () (@var "Y" tptp.mu)) % 0.44/0.63 (define @t11 () (@var "W" $$unsorted)) % 0.44/0.63 (define @t12 () (lambda (@list @t2 @t10 @t11) (= @t2 @t10))) % 0.44/0.63 (define @t13 () (@var "Y" (-> $$unsorted Bool))) % 0.44/0.63 (define @t14 () (@var "X" (-> $$unsorted Bool))) % 0.44/0.63 (define @t15 () (lambda (@list @t14 @t13 @t11) (= (_ @t14 @t11) (_ @t13 @t11)))) % 0.44/0.63 (define @t16 () (@var "Phi" (-> $$unsorted Bool))) % 0.44/0.63 (define @t17 () (_ @t16 @t11)) % 0.44/0.63 (define @t18 () (not @t17)) % 0.44/0.63 (define @t19 () (@list @t16 @t11)) % 0.44/0.63 (define @t20 () (lambda @t19 @t18)) % 0.44/0.63 (define @t21 () (@var "Psi" (-> $$unsorted Bool))) % 0.44/0.63 (define @t22 () (_ @t21 @t11)) % 0.44/0.63 (define @t23 () (lambda (@list @t16 @t21 @t11) (or @t17 @t22))) % 0.44/0.63 (define @t24 () (_ tptp.mnot @t21)) % 0.44/0.63 (define @t25 () (_ tptp.mnot @t16)) % 0.44/0.63 (define @t26 () (_ tptp.mor @t25)) % 0.44/0.63 (define @t27 () (@list @t16 @t21 @t1)) % 0.44/0.63 (define @t28 () (lambda @t27 (_ (_ tptp.mnot (_ @t26 @t24)) @t1))) % 0.44/0.63 (define @t29 () (lambda @t27 (_ (_ @t26 @t21) @t1))) % 0.44/0.63 (define @t30 () (lambda @t27 (_ (_ (_ tptp.mor @t24) @t16) @t1))) % 0.44/0.63 (define @t31 () (lambda @t27 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t16) @t21)) (_ (_ tptp.mimplies @t21) @t16)) @t1))) % 0.44/0.63 (define @t32 () (lambda @t27 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t16) @t21)) @t1))) % 0.44/0.63 (define @t33 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.44/0.63 (define @t34 () (_ @t33 @t2)) % 0.44/0.63 (define @t35 () (_ @t34 @t11)) % 0.44/0.63 (define @t36 () (@list @t2)) % 0.44/0.63 (define @t37 () (forall @t36 @t35)) % 0.44/0.63 (define @t38 () (@list @t33 @t11)) % 0.44/0.63 (define @t39 () (lambda @t38 @t37)) % 0.44/0.63 (define @t40 () (@var "P" (-> $$unsorted Bool))) % 0.44/0.63 (define @t41 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.44/0.63 (define @t42 () (_ @t41 @t40)) % 0.44/0.63 (define @t43 () (lambda (@list @t41 @t11) (forall (@list @t40) (_ @t42 @t11)))) % 0.44/0.63 (define @t44 () (lambda @t5 (_ (_ tptp.mnot @t34) @t1))) % 0.44/0.63 (define @t45 () (@list @t33 @t1)) % 0.44/0.63 (define @t46 () (lambda @t45 (_ (_ tptp.mnot (_ tptp.mforall_ind @t44)) @t1))) % 0.44/0.63 (define @t47 () (lambda (@list @t41 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t40 @t1) (_ (_ tptp.mnot @t42) @t1)))) @t1))) % 0.44/0.63 (define @t48 () (@list @t11)) % 0.44/0.63 (define @t49 () (lambda @t48 true)) % 0.44/0.63 (define @t50 () (@var "V" $$unsorted)) % 0.44/0.63 (define @t51 () (_ @t16 @t50)) % 0.44/0.63 (define @t52 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.44/0.63 (define @t53 () (@list @t50)) % 0.44/0.63 (define @t54 () (lambda (@list @t52 @t16 @t11) (forall @t53 (or (not (_ (_ @t52 @t11) @t50)) @t51)))) % 0.44/0.63 (define @t55 () (lambda (@list @t52 @t16 @t1) (_ (_ tptp.mnot (_ (_ tptp.mbox @t52) @t25)) @t1))) % 0.44/0.63 (define @t56 () (@var "S" $$unsorted)) % 0.44/0.63 (define @t57 () (_ @t52 @t56)) % 0.44/0.63 (define @t58 () (@list @t56)) % 0.44/0.63 (define @t59 () (@list @t52)) % 0.44/0.63 (define @t60 () (lambda @t59 (forall @t58 (_ @t57 @t56)))) % 0.44/0.63 (define @t61 () (@var "T" $$unsorted)) % 0.44/0.63 (define @t62 () (_ @t52 @t61)) % 0.44/0.63 (define @t63 () (_ @t62 @t56)) % 0.44/0.63 (define @t64 () (_ @t57 @t61)) % 0.44/0.63 (define @t65 () (@list @t56 @t61)) % 0.44/0.63 (define @t66 () (forall @t65 (=> @t64 @t63))) % 0.44/0.63 (define @t67 () (lambda @t59 @t66)) % 0.44/0.63 (define @t68 () (@list @t61)) % 0.44/0.63 (define @t69 () (lambda @t59 (forall @t58 (exists @t68 @t64)))) % 0.44/0.63 (define @t70 () (@var "U" $$unsorted)) % 0.44/0.63 (define @t71 () (_ @t57 @t70)) % 0.44/0.63 (define @t72 () (_ @t62 @t70)) % 0.44/0.63 (define @t73 () (and @t64 @t72)) % 0.44/0.63 (define @t74 () (@list @t56 @t61 @t70)) % 0.44/0.63 (define @t75 () (forall @t74 (=> @t73 @t71))) % 0.44/0.63 (define @t76 () (lambda @t59 @t75)) % 0.44/0.63 (define @t77 () (and @t64 @t71)) % 0.44/0.63 (define @t78 () (lambda @t59 (forall @t74 (=> @t77 @t72)))) % 0.44/0.63 (define @t79 () (= @t61 @t70)) % 0.44/0.63 (define @t80 () (lambda @t59 (forall @t74 (=> @t77 @t79)))) % 0.44/0.63 (define @t81 () (@list @t70)) % 0.44/0.63 (define @t82 () (lambda @t59 (forall @t58 (exists @t68 (and @t64 (forall @t81 (=> @t71 @t79))))))) % 0.44/0.63 (define @t83 () (_ @t52 @t70)) % 0.44/0.63 (define @t84 () (_ @t83 @t61)) % 0.44/0.63 (define @t85 () (lambda @t59 (forall @t74 (=> @t64 (exists @t81 (and @t71 @t84)))))) % 0.44/0.63 (define @t86 () (lambda @t59 (forall @t74 (=> @t77 (or @t72 @t79 @t84))))) % 0.44/0.63 (define @t87 () (lambda @t59 (forall @t74 (=> @t77 (exists @t53 (and (_ @t62 @t50) (_ @t83 @t50))))))) % 0.44/0.63 (define @t88 () (forall @t48 @t17)) % 0.44/0.63 (define @t89 () (@list @t16)) % 0.44/0.63 (define @t90 () (lambda @t89 @t88)) % 0.44/0.63 (define @t91 () (lambda @t89 (forall @t48 @t18))) % 0.44/0.63 (define @t92 () (lambda @t89 (exists @t48 @t17))) % 0.44/0.63 (define @t93 () (lambda @t89 (exists @t48 @t18))) % 0.44/0.63 (define @t94 () (_ (_ tptp.rel_s5 @t11) @t50)) % 0.44/0.63 (define @t95 () (not @t94)) % 0.44/0.63 (define @t96 () (or @t95 @t51)) % 0.44/0.63 (define @t97 () (forall @t53 @t96)) % 0.44/0.63 (define @t98 () (lambda @t19 @t97)) % 0.44/0.63 (define @t99 () (@list @t16 @t1)) % 0.44/0.63 (define @t100 () (lambda @t99 (_ (_ tptp.mnot (_ tptp.mbox_s5 @t25)) @t1))) % 0.44/0.63 (define @t101 () (@var "BOUND_VARIABLE_8616" $$unsorted)) % 0.44/0.63 (define @t102 () (@var "BOUND_VARIABLE_8618" tptp.mu)) % 0.44/0.63 (define @t103 () (not (tptp.f @t102 @t101))) % 0.44/0.63 (define @t104 () (not (tptp.rel_s5 @t11 @t101))) % 0.44/0.63 (define @t105 () (@var "BOUND_VARIABLE_8607" $$unsorted)) % 0.44/0.63 (define @t106 () (not (forall @t36 (not (tptp.f @t2 @t105))))) % 0.44/0.63 (define @t107 () (not (tptp.rel_s5 @t11 @t105))) % 0.44/0.63 (define @t108 () (@var "BOUND_VARIABLE_8502" $$unsorted)) % 0.44/0.63 (define @t109 () (@var "BOUND_VARIABLE_8500" tptp.mu)) % 0.44/0.63 (define @t110 () (tptp.f @t109 @t108)) % 0.44/0.63 (define @t111 () (not (tptp.rel_s5 @t50 @t108))) % 0.44/0.63 (define @t112 () (not (tptp.f @t109 @t50))) % 0.44/0.63 (define @t113 () (tptp.rel_s5 @t11 @t50)) % 0.44/0.63 (define @t114 () (not @t113)) % 0.44/0.63 (define @t115 () (or @t114 @t112 @t111 @t110)) % 0.44/0.63 (define @t116 () (@list @t50 @t109 @t108)) % 0.44/0.63 (define @t117 () (forall @t116 @t115)) % 0.44/0.63 (define @t118 () (not @t117)) % 0.44/0.63 (define @t119 () (or @t118 @t107 @t106 @t104 @t103)) % 0.44/0.63 (define @t120 () (or @t104 @t103)) % 0.44/0.63 (define @t121 () (or @t107 @t106)) % 0.44/0.63 (define @t122 () (or @t121 @t118 @t120)) % 0.44/0.63 (define @t123 () (@list @t11 @t105 @t101 @t102)) % 0.44/0.63 (define @t124 () (forall @t123 @t122)) % 0.44/0.63 (define @t125 () (forall (@list @t105 @t101 @t102) @t122)) % 0.44/0.63 (define @t126 () (forall (@list @t101 @t102) @t120)) % 0.44/0.63 (define @t127 () (@var "BOUND_VARIABLE_8554" tptp.mu)) % 0.44/0.63 (define @t128 () (forall (@list @t105) @t121)) % 0.44/0.63 (define @t129 () (@list @t50)) % 0.44/0.63 (define @t130 () (or @t128 @t118 @t126)) % 0.44/0.63 (define @t131 () (not (tptp.f @t127 @t50))) % 0.44/0.63 (define @t132 () (@list @t50 @t127)) % 0.44/0.63 (define @t133 () (tptp.f @t2 @t50)) % 0.44/0.63 (define @t134 () (not @t133)) % 0.44/0.63 (define @t135 () (forall @t36 @t134)) % 0.44/0.63 (define @t136 () (not @t135)) % 0.44/0.63 (define @t137 () (forall @t53 (or @t114 @t136))) % 0.44/0.63 (define @t138 () (or @t137 @t118 (forall @t132 (or @t114 @t131)))) % 0.44/0.63 (define @t139 () (not (tptp.rel_s5 @t1 @t50))) % 0.44/0.63 (define @t140 () (or @t139 @t131)) % 0.44/0.63 (define @t141 () (forall @t132 @t140)) % 0.44/0.63 (define @t142 () (forall @t116 (or @t139 @t112 @t111 @t110))) % 0.44/0.63 (define @t143 () (not @t142)) % 0.44/0.63 (define @t144 () (forall @t53 (or @t139 @t136))) % 0.44/0.63 (define @t145 () (@list @t1)) % 0.44/0.63 (define @t146 () (lambda @t145 (or @t144 @t143 @t141))) % 0.44/0.63 (define @t147 () (_ @t146 @t11)) % 0.44/0.63 (define @t148 () (forall @t48 @t147)) % 0.44/0.63 (define @t149 () (_ @t16 @t11)) % 0.44/0.63 (define @t150 () (lambda @t89 (forall @t48 @t149))) % 0.44/0.63 (define @t151 () (lambda @t48 @t137)) % 0.44/0.63 (define @t152 () (_ @t151 @t1)) % 0.44/0.63 (define @t153 () (or @t152 @t143 @t141)) % 0.44/0.63 (define @t154 () (lambda @t145 @t153)) % 0.44/0.63 (define @t155 () (_ @t21 @t1)) % 0.44/0.63 (define @t156 () (or @t155 @t143 @t141)) % 0.44/0.63 (define @t157 () (@list @t21 @t1)) % 0.44/0.63 (define @t158 () (tptp.f @t2 @t1)) % 0.44/0.63 (define @t159 () (lambda @t145 (not (forall @t36 (not @t158))))) % 0.44/0.63 (define @t160 () (_ @t159 @t50)) % 0.44/0.63 (define @t161 () (or @t114 @t160)) % 0.44/0.63 (define @t162 () (forall @t53 @t161)) % 0.44/0.63 (define @t163 () (lambda @t48 @t162)) % 0.44/0.63 (define @t164 () (_ @t16 @t50)) % 0.44/0.63 (define @t165 () (lambda @t19 (forall @t53 (or @t114 @t164)))) % 0.44/0.63 (define @t166 () (not @t4)) % 0.44/0.63 (define @t167 () (_ @t6 @t2 @t1)) % 0.44/0.63 (define @t168 () (not @t167)) % 0.44/0.63 (define @t169 () (forall @t36 @t168)) % 0.44/0.63 (define @t170 () (not @t169)) % 0.44/0.63 (define @t171 () (lambda @t145 @t170)) % 0.44/0.63 (define @t172 () (not (forall @t36 (not (_ @t33 @t2 @t1))))) % 0.44/0.63 (define @t173 () (_ (lambda @t45 @t172) @t6)) % 0.44/0.63 (define @t174 () (or @t143 @t141)) % 0.44/0.63 (define @t175 () (not @t174)) % 0.44/0.63 (define @t176 () (lambda @t145 @t175)) % 0.44/0.63 (define @t177 () (_ @t176 @t1)) % 0.44/0.63 (define @t178 () (not @t177)) % 0.44/0.63 (define @t179 () (or @t178 @t155)) % 0.44/0.63 (define @t180 () (lambda @t157 @t179)) % 0.44/0.63 (define @t181 () (not (_ @t16 @t1))) % 0.44/0.63 (define @t182 () (or @t181 @t155)) % 0.44/0.63 (define @t183 () (lambda @t27 @t182)) % 0.44/0.63 (define @t184 () (not @t141)) % 0.44/0.63 (define @t185 () (lambda @t145 @t184)) % 0.44/0.63 (define @t186 () (_ @t185 @t1)) % 0.44/0.63 (define @t187 () (not @t186)) % 0.44/0.63 (define @t188 () (or @t143 @t187)) % 0.44/0.63 (define @t189 () (not @t188)) % 0.44/0.63 (define @t190 () (lambda @t145 @t189)) % 0.44/0.63 (define @t191 () (not @t155)) % 0.44/0.63 (define @t192 () (@list @t127)) % 0.44/0.63 (define @t193 () (forall @t192 @t140)) % 0.44/0.63 (define @t194 () (forall @t192 @t131)) % 0.44/0.63 (define @t195 () (or @t139 @t194)) % 0.44/0.63 (define @t196 () (not @t160)) % 0.44/0.63 (define @t197 () (or @t139 @t196)) % 0.44/0.63 (define @t198 () (forall @t53 @t197)) % 0.44/0.63 (define @t199 () (not @t198)) % 0.44/0.63 (define @t200 () (lambda @t145 @t199)) % 0.44/0.63 (define @t201 () (not @t164)) % 0.44/0.63 (define @t202 () (not (forall @t53 (or @t139 @t201)))) % 0.44/0.63 (define @t203 () (lambda @t99 @t202)) % 0.44/0.63 (define @t204 () (lambda @t48 @t117)) % 0.44/0.63 (define @t205 () (_ @t204 @t1)) % 0.44/0.63 (define @t206 () (not @t205)) % 0.44/0.63 (define @t207 () (or @t206 @t191)) % 0.44/0.63 (define @t208 () (not @t207)) % 0.44/0.63 (define @t209 () (lambda @t157 @t208)) % 0.44/0.63 (define @t210 () (not (or @t181 @t191))) % 0.44/0.63 (define @t211 () (lambda @t27 @t210)) % 0.44/0.63 (define @t212 () (or @t112 @t111 @t110)) % 0.44/0.63 (define @t213 () (or @t114 @t212)) % 0.44/0.63 (define @t214 () (forall @t116 @t213)) % 0.44/0.63 (define @t215 () (@list @t109 @t108)) % 0.44/0.63 (define @t216 () (forall @t215 @t213)) % 0.44/0.63 (define @t217 () (forall @t215 @t212)) % 0.44/0.63 (define @t218 () (@var "BOUND_VARIABLE_8476" $$unsorted)) % 0.44/0.63 (define @t219 () (or @t114 @t217)) % 0.44/0.63 (define @t220 () (tptp.f @t2 @t218)) % 0.44/0.63 (define @t221 () (@list @t2 @t218)) % 0.44/0.63 (define @t222 () (forall @t221 (or @t134 (not (tptp.rel_s5 @t50 @t218)) @t220))) % 0.44/0.63 (define @t223 () (not (tptp.rel_s5 @t11 @t218))) % 0.44/0.63 (define @t224 () (tptp.f @t2 @t11)) % 0.44/0.63 (define @t225 () (not @t224)) % 0.44/0.63 (define @t226 () (or @t225 @t223 @t220)) % 0.44/0.63 (define @t227 () (lambda @t48 (forall @t221 @t226))) % 0.44/0.63 (define @t228 () (_ @t227 @t50)) % 0.44/0.63 (define @t229 () (or @t114 @t228)) % 0.44/0.63 (define @t230 () (forall @t53 @t229)) % 0.44/0.63 (define @t231 () (lambda @t48 @t230)) % 0.44/0.63 (define @t232 () (or @t223 @t220)) % 0.44/0.63 (define @t233 () (or @t225 @t232)) % 0.44/0.63 (define @t234 () (forall @t221 @t233)) % 0.44/0.63 (define @t235 () (@list @t218)) % 0.44/0.63 (define @t236 () (forall @t235 @t233)) % 0.44/0.63 (define @t237 () (forall @t235 @t232)) % 0.44/0.63 (define @t238 () (or @t225 @t237)) % 0.44/0.63 (define @t239 () (forall @t53 (or @t114 @t133))) % 0.44/0.63 (define @t240 () (_ @t3 @t11)) % 0.44/0.63 (define @t241 () (not @t240)) % 0.44/0.63 (define @t242 () (or @t241 @t239)) % 0.44/0.63 (define @t243 () (forall @t53 (or @t139 @t133))) % 0.44/0.63 (define @t244 () (or @t166 @t243)) % 0.44/0.63 (define @t245 () (lambda @t5 @t244)) % 0.44/0.63 (define @t246 () (_ @t245 @t2 @t11)) % 0.44/0.63 (define @t247 () (forall @t36 @t246)) % 0.44/0.63 (define @t248 () (lambda @t48 @t247)) % 0.44/0.63 (define @t249 () (_ @t33 @t2 @t11)) % 0.44/0.63 (define @t250 () (lambda @t38 (forall @t36 @t249))) % 0.44/0.63 (define @t251 () (lambda @t48 @t239)) % 0.44/0.63 (define @t252 () (_ @t251 @t1)) % 0.44/0.63 (define @t253 () (or @t166 @t252)) % 0.44/0.63 (define @t254 () (lambda @t145 @t253)) % 0.44/0.63 (define @t255 () (lambda @t157 (or @t166 @t155))) % 0.44/0.63 (define @t256 () (_ @t3 @t50)) % 0.44/0.63 (define @t257 () (or @t114 @t256)) % 0.44/0.63 (define @t258 () (_ @t3 @t50)) % 0.44/0.63 (define @t259 () (or @t114 @t258)) % 0.44/0.63 (define @t260 () (forall @t53 @t259)) % 0.44/0.63 (define @t261 () (lambda @t48 @t260)) % 0.44/0.63 (define @t262 () (_ @t165 @t3)) % 0.44/0.63 (define @t263 () (_ @t183 @t3)) % 0.44/0.63 (define @t264 () (lambda @t5 (_ (_ @t263 @t262) @t1))) % 0.44/0.63 (define @t265 () (forall @t36 (not @t249))) % 0.44/0.63 (define @t266 () (lambda @t48 @t265)) % 0.44/0.63 (define @t267 () (_ @t266 @t11)) % 0.44/0.63 (define @t268 () (not @t267)) % 0.44/0.63 (define @t269 () (lambda @t48 @t268)) % 0.44/0.63 (define @t270 () (not @t35)) % 0.44/0.63 (define @t271 () (not (_ @t34 @t1))) % 0.44/0.63 (define @t272 () (lambda @t5 @t271)) % 0.44/0.63 (define @t273 () (_ @t272 @t2 @t11)) % 0.44/0.63 (define @t274 () (forall @t36 @t273)) % 0.44/0.63 (define @t275 () (lambda @t48 @t274)) % 0.44/0.63 (define @t276 () (lambda @t48 @t270)) % 0.44/0.63 (define @t277 () (_ @t20 @t34)) % 0.44/0.63 (define @t278 () (forall @t53 (or @t114 @t201))) % 0.44/0.63 (define @t279 () (lambda @t48 @t278)) % 0.44/0.63 (define @t280 () (_ @t279 @t11)) % 0.44/0.63 (define @t281 () (not @t280)) % 0.44/0.63 (define @t282 () (lambda @t48 @t281)) % 0.44/0.63 (define @t283 () (not @t51)) % 0.44/0.63 (define @t284 () (or @t114 @t283)) % 0.44/0.63 (define @t285 () (lambda @t48 @t18)) % 0.44/0.63 (define @t286 () (_ @t285 @t50)) % 0.44/0.63 (define @t287 () (or @t114 @t286)) % 0.44/0.63 (define @t288 () (forall @t53 @t287)) % 0.44/0.63 (define @t289 () (lambda @t48 @t288)) % 0.44/0.63 (define @t290 () (or @t18 @t22)) % 0.44/0.63 (define @t291 () (lambda @t48 @t290)) % 0.44/0.63 (define @t292 () (@list @t21 @t11)) % 0.44/0.63 (define @t293 () (lambda @t292 @t290)) % 0.44/0.63 (define @t294 () (_ @t285 @t11)) % 0.44/0.63 (define @t295 () (or @t294 @t22)) % 0.44/0.63 (define @t296 () (lambda @t292 @t295)) % 0.44/0.63 (define @t297 () (not @t22)) % 0.44/0.63 (define @t298 () (or @t18 @t297)) % 0.44/0.63 (define @t299 () (lambda @t48 @t298)) % 0.44/0.63 (define @t300 () (_ @t299 @t11)) % 0.44/0.63 (define @t301 () (not @t300)) % 0.44/0.63 (define @t302 () (lambda @t48 @t301)) % 0.44/0.63 (define @t303 () (lambda @t48 @t297)) % 0.44/0.63 (define @t304 () (_ @t303 @t11)) % 0.44/0.63 (define @t305 () (or @t18 @t304)) % 0.44/0.63 (define @t306 () (lambda @t48 @t305)) % 0.44/0.63 (define @t307 () (forall @t123 @t119)) % 0.44/0.63 (define @t308 () (@quantifiers_skolemize @t307 1)) % 0.44/0.63 (define @t309 () (forall @t36 (not (tptp.f @t2 @t308)))) % 0.44/0.63 (define @t310 () (@quantifiers_skolemize @t307 2)) % 0.44/0.63 (define @t311 () (@quantifiers_skolemize @t307 3)) % 0.44/0.63 (define @t312 () (tptp.f @t311 @t310)) % 0.44/0.63 (define @t313 () (not @t312)) % 0.44/0.63 (define @t314 () (@quantifiers_skolemize @t307 0)) % 0.44/0.63 (define @t315 () (tptp.rel_s5 @t314 @t310)) % 0.44/0.63 (define @t316 () (not @t315)) % 0.44/0.63 (define @t317 () (not @t309)) % 0.44/0.63 (define @t318 () (tptp.rel_s5 @t314 @t308)) % 0.44/0.63 (define @t319 () (not @t318)) % 0.44/0.63 (define @t320 () (forall @t116 (or (not (tptp.rel_s5 @t314 @t50)) @t112 @t111 @t110))) % 0.44/0.63 (define @t321 () (not @t320)) % 0.44/0.63 (define @t322 () (or @t321 @t319 @t317 @t316 @t313)) % 0.44/0.63 (define @t323 () (@list true)) % 0.44/0.63 (define @t324 () (@list @t322)) % 0.44/0.63 (define @t325 () (not (tptp.rel_s5 @t56 @t61))) % 0.44/0.63 (define @t326 () (_ @t52 @t61 @t56)) % 0.44/0.63 (define @t327 () (_ @t52 @t56 @t61)) % 0.44/0.63 (define @t328 () (not @t327)) % 0.44/0.63 (define @t329 () (not @t64)) % 0.44/0.63 (define @t330 () (or @t329 @t63)) % 0.44/0.63 (define @t331 () (tptp.rel_s5 @t310 @t314)) % 0.44/0.63 (define @t332 () (or @t316 @t331)) % 0.44/0.63 (define @t333 () (@list false false)) % 0.44/0.63 (define @t334 () (tptp.f @t311 @t314)) % 0.44/0.63 (define @t335 () (not @t331)) % 0.44/0.63 (define @t336 () (or @t316 @t313 @t335 @t334)) % 0.44/0.63 (define @t337 () (@list false false false false)) % 0.44/0.63 (define @t338 () (_ @t52 @t56 @t70)) % 0.44/0.63 (define @t339 () (_ @t52 @t61 @t70)) % 0.44/0.63 (define @t340 () (not @t72)) % 0.44/0.63 (define @t341 () (or @t329 @t340 @t71)) % 0.44/0.63 (define @t342 () (tptp.rel_s5 @t308 @t314)) % 0.44/0.63 (define @t343 () (or @t319 @t342)) % 0.44/0.63 (define @t344 () (tptp.rel_s5 @t314 @t314)) % 0.44/0.63 (define @t345 () (not @t342)) % 0.44/0.63 (define @t346 () (or @t319 @t345 @t344)) % 0.44/0.63 (define @t347 () (tptp.f @t311 @t308)) % 0.44/0.63 (define @t348 () (not @t334)) % 0.44/0.63 (define @t349 () (not @t344)) % 0.44/0.63 (define @t350 () (or @t349 @t348 @t319 @t347)) % 0.44/0.63 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.44/0.63 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.44/0.63 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.44/0.63 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.44/0.63 (assume @p5 @t9) % 0.44/0.63 (assume @p6 true) % 0.44/0.63 (step @p7 (= tptp.meq_ind @t12) :rule refl :args (@t12)) % 0.44/0.63 (step @p8 (= tptp.meq_prop @t15) :rule refl :args (@t15)) % 0.44/0.63 (step @p9 (= tptp.mnot @t20) :rule refl :args (@t20)) % 0.44/0.63 (step @p10 (= tptp.mor @t23) :rule refl :args (@t23)) % 0.44/0.63 (step @p11 (= tptp.mand @t28) :rule refl :args (@t28)) % 0.44/0.63 (step @p12 (= tptp.mimplies @t29) :rule refl :args (@t29)) % 0.44/0.63 (step @p13 (= tptp.mimplied @t30) :rule refl :args (@t30)) % 0.44/0.63 (step @p14 (= tptp.mequiv @t31) :rule refl :args (@t31)) % 0.44/0.63 (step @p15 (= tptp.mxor @t32) :rule refl :args (@t32)) % 0.44/0.63 (step @p16 (= tptp.mforall_ind @t39) :rule refl :args (@t39)) % 0.44/0.63 (step @p17 (= tptp.mforall_prop @t43) :rule refl :args (@t43)) % 0.44/0.63 (step @p18 (= tptp.mexists_ind @t46) :rule refl :args (@t46)) % 0.44/0.63 (step @p19 (= tptp.mexists_prop @t47) :rule refl :args (@t47)) % 0.44/0.63 (step @p20 (= tptp.mtrue @t49) :rule refl :args (@t49)) % 0.44/0.63 (step @p21 (= tptp.mbox @t54) :rule refl :args (@t54)) % 0.44/0.63 (step @p22 (= tptp.mdia @t55) :rule refl :args (@t55)) % 0.44/0.63 (step @p23 (= tptp.mreflexive @t60) :rule refl :args (@t60)) % 0.44/0.63 (step @p24 (= tptp.msymmetric @t67) :rule refl :args (@t67)) % 0.44/0.63 (step @p25 (= tptp.mserial @t69) :rule refl :args (@t69)) % 0.44/0.63 (step @p26 (= tptp.mtransitive @t76) :rule refl :args (@t76)) % 0.44/0.63 (step @p27 (= tptp.meuclidean @t78) :rule refl :args (@t78)) % 0.44/0.63 (step @p28 (= tptp.mpartially_functional @t80) :rule refl :args (@t80)) % 0.44/0.63 (step @p29 (= tptp.mfunctional @t82) :rule refl :args (@t82)) % 0.44/0.63 (step @p30 (= tptp.mweakly_dense @t85) :rule refl :args (@t85)) % 0.44/0.63 (step @p31 (= tptp.mweakly_connected @t86) :rule refl :args (@t86)) % 0.44/0.63 (step @p32 (= tptp.mweakly_directed @t87) :rule refl :args (@t87)) % 0.44/0.63 (step @p33 (= tptp.mvalid @t90) :rule refl :args (@t90)) % 0.44/0.63 (step @p34 (= tptp.minvalid @t91) :rule refl :args (@t91)) % 0.44/0.63 (step @p35 (= tptp.msatisfiable @t92) :rule refl :args (@t92)) % 0.44/0.63 (step @p36 (= tptp.mcountersatisfiable @t93) :rule refl :args (@t93)) % 0.44/0.63 (step @p37 (= tptp.mbox_s5 @t98) :rule refl :args (@t98)) % 0.44/0.63 (step @p38 (= tptp.mdia_s5 @t100) :rule refl :args (@t100)) % 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(step @p507 false :rule chain_m_resolution :premises (@p506 @p501 @p407) :args (false @t333 (@list @t347 @t309))) % 0.44/0.63 ) % 0.44/0.63 % SZS output end Proof % 0.44/0.63 % cvc5 exiting %------------------------------------------------------------------------------