%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET027^7 : TPTP v9.2.1. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.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 08:47:03 AM UTC 2026 % Result : Theorem 0.44s 0.67s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET027^7 : TPTP v9.2.1. Released v5.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n016.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 14:43:09 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.44/0.67 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.44/0.67 % SZS status Theorem % 0.44/0.67 % SZS output start Proof % 0.44/0.67 ( % 0.44/0.67 (declare-sort tptp.mu 0) % 0.44/0.67 (declare-sort $$unsorted 0) % 0.44/0.67 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.subset (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.member (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.44/0.67 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.44/0.67 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.44/0.67 (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)))))) % 0.44/0.67 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.67 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.44/0.67 (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))))))) % 0.44/0.67 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.44/0.67 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.44/0.67 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.44/0.67 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.44/0.67 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.44/0.67 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.44/0.67 (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)))))) % 0.44/0.67 (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) (=> (_ (_ tptp.exists_in_world _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.44/0.67 (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)))))) % 0.44/0.67 (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)))))) % 0.44/0.67 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.44/0.67 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.44/0.67 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.44/0.67 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.44/0.67 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.44/0.67 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.44/0.67 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.44/0.67 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.44/0.67 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.44/0.67 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.44/0.67 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.44/0.67 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.44/0.67 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.44/0.67 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.44/0.67 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$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_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.44/0.67 (define tptp.mdia_s4 () (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_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.44/0.67 (define @t1 () (@var "V" $$unsorted)) % 0.44/0.67 (define @t2 () (@var "X" tptp.mu)) % 0.44/0.67 (define @t3 () (_ tptp.exists_in_world @t2)) % 0.44/0.67 (define @t4 () (_ @t3 @t1)) % 0.44/0.67 (define @t5 () (@list @t2)) % 0.44/0.67 (define @t6 () (@list @t1)) % 0.44/0.67 (define @t7 () (@var "W" $$unsorted)) % 0.44/0.67 (define @t8 () (_ @t3 @t7)) % 0.44/0.67 (define @t9 () (@var "__flatten_var_0" $$unsorted)) % 0.44/0.67 (define @t10 () (@var "C" tptp.mu)) % 0.44/0.67 (define @t11 () (@var "D" tptp.mu)) % 0.44/0.67 (define @t12 () (_ tptp.member @t11)) % 0.44/0.67 (define @t13 () (_ @t12 @t10)) % 0.44/0.67 (define @t14 () (@var "B" tptp.mu)) % 0.44/0.67 (define @t15 () (_ @t12 @t14)) % 0.44/0.67 (define @t16 () (@list @t11 @t9)) % 0.44/0.67 (define @t17 () (lambda @t16 (_ (_ (_ tptp.mimplies @t15) @t13) @t9))) % 0.44/0.67 (define @t18 () (_ tptp.subset @t14)) % 0.44/0.67 (define @t19 () (_ @t18 @t10)) % 0.44/0.67 (define @t20 () (@list @t10 @t9)) % 0.44/0.67 (define @t21 () (lambda @t20 (_ (_ (_ tptp.mequiv @t19) (_ tptp.mforall_ind @t17)) @t9))) % 0.44/0.67 (define @t22 () (@list @t14 @t9)) % 0.44/0.67 (define @t23 () (lambda @t22 (_ (_ tptp.mforall_ind @t21) @t9))) % 0.44/0.67 (define @t24 () (_ @t18 @t11)) % 0.44/0.67 (define @t25 () (_ tptp.subset @t10)) % 0.44/0.67 (define @t26 () (_ @t25 @t11)) % 0.44/0.67 (define @t27 () (lambda @t16 (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t19) @t26)) @t24) @t9))) % 0.44/0.67 (define @t28 () (lambda @t20 (_ (_ tptp.mforall_ind @t27) @t9))) % 0.44/0.67 (define @t29 () (lambda @t22 (_ (_ tptp.mforall_ind @t28) @t9))) % 0.44/0.67 (define @t30 () (not (_ tptp.mvalid (_ tptp.mforall_ind @t29)))) % 0.44/0.67 (define @t31 () (@var "Y" (-> $$unsorted Bool))) % 0.44/0.67 (define @t32 () (@var "X" (-> $$unsorted Bool))) % 0.44/0.67 (define @t33 () (lambda (@list @t32 @t31 @t7) (= (_ @t32 @t7) (_ @t31 @t7)))) % 0.44/0.67 (define @t34 () (@var "Phi" (-> $$unsorted Bool))) % 0.44/0.67 (define @t35 () (_ @t34 @t7)) % 0.44/0.67 (define @t36 () (not @t35)) % 0.44/0.67 (define @t37 () (@list @t34 @t7)) % 0.44/0.67 (define @t38 () (lambda @t37 @t36)) % 0.44/0.67 (define @t39 () (@var "Psi" (-> $$unsorted Bool))) % 0.44/0.67 (define @t40 () (_ @t39 @t7)) % 0.44/0.67 (define @t41 () (lambda (@list @t34 @t39 @t7) (or @t35 @t40))) % 0.44/0.67 (define @t42 () (_ @t34 @t1)) % 0.44/0.67 (define @t43 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.44/0.67 (define @t44 () (lambda (@list @t43 @t34 @t7) (forall @t6 (or (not (_ (_ @t43 @t7) @t1)) @t42)))) % 0.44/0.67 (define @t45 () (@var "P" (-> $$unsorted Bool))) % 0.44/0.67 (define @t46 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.44/0.67 (define @t47 () (_ @t46 @t45)) % 0.44/0.67 (define @t48 () (lambda (@list @t46 @t7) (forall (@list @t45) (_ @t47 @t7)))) % 0.44/0.67 (define @t49 () (@list @t7)) % 0.44/0.67 (define @t50 () (lambda @t49 true)) % 0.44/0.67 (define @t51 () (_ tptp.mnot @t39)) % 0.44/0.67 (define @t52 () (_ tptp.mnot @t34)) % 0.44/0.67 (define @t53 () (_ tptp.mor @t52)) % 0.44/0.67 (define @t54 () (@list @t34 @t39 @t9)) % 0.44/0.67 (define @t55 () (lambda @t54 (_ (_ tptp.mnot (_ @t53 @t51)) @t9))) % 0.44/0.67 (define @t56 () (lambda @t54 (_ (_ @t53 @t39) @t9))) % 0.44/0.67 (define @t57 () (lambda @t54 (_ (_ (_ tptp.mor @t51) @t34) @t9))) % 0.44/0.67 (define @t58 () (lambda @t54 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t34) @t39)) (_ (_ tptp.mimplies @t39) @t34)) @t9))) % 0.44/0.67 (define @t59 () (lambda @t54 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t34) @t39)) @t9))) % 0.44/0.67 (define @t60 () (lambda (@list @t43 @t34 @t9) (_ (_ tptp.mnot (_ (_ tptp.mbox @t43) @t52)) @t9))) % 0.44/0.67 (define @t61 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.44/0.67 (define @t62 () (_ @t61 @t2)) % 0.44/0.67 (define @t63 () (_ @t62 @t7)) % 0.44/0.67 (define @t64 () (forall @t5 (=> @t8 @t63))) % 0.44/0.67 (define @t65 () (@list @t61 @t7)) % 0.44/0.67 (define @t66 () (lambda @t65 @t64)) % 0.44/0.67 (define @t67 () (lambda (@list @t61 @t9) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t2 @t9) (_ (_ tptp.mnot @t62) @t9)))) @t9))) % 0.44/0.67 (define @t68 () (lambda (@list @t46 @t9) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t45 @t9) (_ (_ tptp.mnot @t47) @t9)))) @t9))) % 0.44/0.67 (define @t69 () (@var "S" $$unsorted)) % 0.44/0.67 (define @t70 () (_ @t43 @t69)) % 0.44/0.67 (define @t71 () (@list @t69)) % 0.44/0.67 (define @t72 () (@list @t43)) % 0.44/0.67 (define @t73 () (lambda @t72 (forall @t71 (_ @t70 @t69)))) % 0.44/0.67 (define @t74 () (@var "T" $$unsorted)) % 0.44/0.67 (define @t75 () (_ @t43 @t74)) % 0.44/0.67 (define @t76 () (_ @t70 @t74)) % 0.44/0.67 (define @t77 () (lambda @t72 (forall (@list @t69 @t74) (=> @t76 (_ @t75 @t69))))) % 0.44/0.67 (define @t78 () (@list @t74)) % 0.44/0.67 (define @t79 () (lambda @t72 (forall @t71 (exists @t78 @t76)))) % 0.44/0.67 (define @t80 () (@var "U" $$unsorted)) % 0.44/0.67 (define @t81 () (_ @t70 @t80)) % 0.44/0.67 (define @t82 () (_ @t75 @t80)) % 0.44/0.67 (define @t83 () (@list @t69 @t74 @t80)) % 0.44/0.67 (define @t84 () (lambda @t72 (forall @t83 (=> (and @t76 @t82) @t81)))) % 0.44/0.67 (define @t85 () (and @t76 @t81)) % 0.44/0.67 (define @t86 () (lambda @t72 (forall @t83 (=> @t85 @t82)))) % 0.44/0.67 (define @t87 () (= @t74 @t80)) % 0.44/0.67 (define @t88 () (lambda @t72 (forall @t83 (=> @t85 @t87)))) % 0.44/0.67 (define @t89 () (@list @t80)) % 0.44/0.67 (define @t90 () (lambda @t72 (forall @t71 (exists @t78 (and @t76 (forall @t89 (=> @t81 @t87))))))) % 0.44/0.67 (define @t91 () (_ @t43 @t80)) % 0.44/0.67 (define @t92 () (_ @t91 @t74)) % 0.44/0.67 (define @t93 () (lambda @t72 (forall @t83 (=> @t76 (exists @t89 (and @t81 @t92)))))) % 0.44/0.67 (define @t94 () (lambda @t72 (forall @t83 (=> @t85 (or @t82 @t87 @t92))))) % 0.44/0.67 (define @t95 () (lambda @t72 (forall @t83 (=> @t85 (exists @t6 (and (_ @t75 @t1) (_ @t91 @t1))))))) % 0.44/0.67 (define @t96 () (forall @t49 @t35)) % 0.44/0.67 (define @t97 () (@list @t34)) % 0.44/0.67 (define @t98 () (lambda @t97 @t96)) % 0.44/0.67 (define @t99 () (lambda @t97 (exists @t49 @t35))) % 0.44/0.67 (define @t100 () (lambda @t97 (exists @t49 @t36))) % 0.44/0.67 (define @t101 () (lambda @t97 (forall @t49 @t36))) % 0.44/0.67 (define @t102 () (lambda @t37 (forall @t6 (or (not (_ (_ tptp.rel_s4 @t7) @t1)) @t42)))) % 0.44/0.67 (define @t103 () (lambda (@list @t34 @t9) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t52)) @t9))) % 0.44/0.67 (define @t104 () (@var "BOUND_VARIABLE_8909" tptp.mu)) % 0.44/0.67 (define @t105 () (@var "BOUND_VARIABLE_8907" tptp.mu)) % 0.44/0.67 (define @t106 () (not (tptp.subset @t105 @t104 @t7))) % 0.44/0.67 (define @t107 () (tptp.subset @t2 @t104 @t7)) % 0.44/0.67 (define @t108 () (not (tptp.exists_in_world @t104 @t7))) % 0.44/0.67 (define @t109 () (not (tptp.subset @t2 @t105 @t7))) % 0.44/0.67 (define @t110 () (not (tptp.exists_in_world @t105 @t7))) % 0.44/0.67 (define @t111 () (tptp.exists_in_world @t2 @t7)) % 0.44/0.67 (define @t112 () (not @t111)) % 0.44/0.67 (define @t113 () (or @t112 @t110 @t109 @t108 @t107 @t106)) % 0.44/0.67 (define @t114 () (forall (@list @t7 @t2 @t105 @t104) @t113)) % 0.44/0.67 (define @t115 () (@list @t2 @t105 @t104)) % 0.44/0.67 (define @t116 () (forall @t115 @t113)) % 0.44/0.67 (define @t117 () (lambda @t49 @t116)) % 0.44/0.67 (define @t118 () (_ @t117 @t7)) % 0.44/0.67 (define @t119 () (forall @t49 @t118)) % 0.44/0.67 (define @t120 () (_ @t34 @t7)) % 0.44/0.67 (define @t121 () (lambda @t97 (forall @t49 @t120))) % 0.44/0.67 (define @t122 () (or @t110 @t109 @t108 @t107 @t106)) % 0.44/0.67 (define @t123 () (or @t112 @t122)) % 0.44/0.67 (define @t124 () (forall @t115 @t123)) % 0.44/0.67 (define @t125 () (@list @t105 @t104)) % 0.44/0.67 (define @t126 () (forall @t125 @t123)) % 0.44/0.67 (define @t127 () (forall @t125 @t122)) % 0.44/0.67 (define @t128 () (@var "BOUND_VARIABLE_8855" tptp.mu)) % 0.44/0.67 (define @t129 () (@var "BOUND_VARIABLE_8884" tptp.mu)) % 0.44/0.67 (define @t130 () (or @t112 @t127)) % 0.44/0.67 (define @t131 () (tptp.subset @t2 @t128 @t7)) % 0.44/0.67 (define @t132 () (not (tptp.exists_in_world @t128 @t7))) % 0.44/0.67 (define @t133 () (@list @t129 @t128)) % 0.44/0.67 (define @t134 () (forall @t133 (or (not (tptp.exists_in_world @t129 @t7)) (not (tptp.subset @t2 @t129 @t7)) @t132 @t131 (not (tptp.subset @t129 @t128 @t7))))) % 0.44/0.67 (define @t135 () (tptp.subset @t14 @t128 @t9)) % 0.44/0.67 (define @t136 () (not (tptp.exists_in_world @t128 @t9))) % 0.44/0.67 (define @t137 () (tptp.subset @t14 @t2 @t9)) % 0.44/0.67 (define @t138 () (not @t137)) % 0.44/0.67 (define @t139 () (not (tptp.exists_in_world @t2 @t9))) % 0.44/0.67 (define @t140 () (@list @t2 @t128)) % 0.44/0.67 (define @t141 () (forall @t140 (or @t139 @t138 @t136 @t135 (not (tptp.subset @t2 @t128 @t9))))) % 0.44/0.67 (define @t142 () (@list @t2)) % 0.44/0.67 (define @t143 () (lambda @t22 @t141)) % 0.44/0.67 (define @t144 () (or @t112 (_ @t143 @t2 @t7))) % 0.44/0.67 (define @t145 () (forall @t5 @t144)) % 0.44/0.67 (define @t146 () (lambda @t49 @t145)) % 0.44/0.67 (define @t147 () (_ @t61 @t2 @t7)) % 0.44/0.67 (define @t148 () (lambda @t65 (forall @t5 (or @t112 @t147)))) % 0.44/0.67 (define @t149 () (not @t131)) % 0.44/0.67 (define @t150 () (tptp.subset @t14 @t128 @t7)) % 0.44/0.67 (define @t151 () (tptp.subset @t14 @t2 @t7)) % 0.44/0.67 (define @t152 () (not @t151)) % 0.44/0.67 (define @t153 () (or @t112 @t152 @t132 @t150 @t149)) % 0.44/0.67 (define @t154 () (or @t132 @t150 @t149)) % 0.44/0.67 (define @t155 () (or @t112 @t152 @t154)) % 0.44/0.67 (define @t156 () (forall @t140 @t155)) % 0.44/0.67 (define @t157 () (@list @t128)) % 0.44/0.67 (define @t158 () (forall @t157 @t155)) % 0.44/0.67 (define @t159 () (forall @t157 @t154)) % 0.44/0.67 (define @t160 () (@var "BOUND_VARIABLE_8829" tptp.mu)) % 0.44/0.67 (define @t161 () (@list @t160)) % 0.44/0.67 (define @t162 () (or @t112 @t152 @t159)) % 0.44/0.67 (define @t163 () (@list @t160)) % 0.44/0.67 (define @t164 () (forall @t163 (or (not (tptp.exists_in_world @t160 @t7)) (tptp.subset @t14 @t160 @t7) (not (tptp.subset @t2 @t160 @t7))))) % 0.44/0.67 (define @t165 () (_ (_ @t18 @t2) @t7)) % 0.44/0.67 (define @t166 () (not @t165)) % 0.44/0.67 (define @t167 () (or @t112 @t166 @t164)) % 0.44/0.67 (define @t168 () (or @t166 @t164)) % 0.44/0.67 (define @t169 () (_ @t19 @t9)) % 0.44/0.67 (define @t170 () (not @t169)) % 0.44/0.67 (define @t171 () (forall @t5 (or @t139 @t137 (not (tptp.subset @t10 @t2 @t9))))) % 0.44/0.67 (define @t172 () (or @t170 @t171)) % 0.44/0.67 (define @t173 () (lambda @t20 @t172)) % 0.44/0.67 (define @t174 () (or @t112 (_ @t173 @t2 @t7))) % 0.44/0.67 (define @t175 () (forall @t5 @t174)) % 0.44/0.67 (define @t176 () (lambda @t49 @t175)) % 0.44/0.67 (define @t177 () (tptp.subset @t10 @t2 @t7)) % 0.44/0.67 (define @t178 () (not (_ @t19 @t7))) % 0.44/0.67 (define @t179 () (_ (_ @t25 @t2) @t7)) % 0.44/0.67 (define @t180 () (not @t179)) % 0.44/0.67 (define @t181 () (or @t112 @t165 @t180)) % 0.44/0.67 (define @t182 () (forall @t5 @t181)) % 0.44/0.67 (define @t183 () (or @t178 @t182)) % 0.44/0.67 (define @t184 () (or @t178 @t181)) % 0.44/0.67 (define @t185 () (or @t112 @t165 @t178 @t180)) % 0.44/0.67 (define @t186 () (or @t165 @t178 @t180)) % 0.44/0.67 (define @t187 () (not (_ @t26 @t9))) % 0.44/0.67 (define @t188 () (or (_ @t24 @t9) @t170 @t187)) % 0.44/0.67 (define @t189 () (lambda @t16 @t188)) % 0.44/0.67 (define @t190 () (_ @t189 @t2 @t7)) % 0.44/0.67 (define @t191 () (or @t112 @t190)) % 0.44/0.67 (define @t192 () (forall @t5 @t191)) % 0.44/0.67 (define @t193 () (lambda @t49 @t192)) % 0.44/0.67 (define @t194 () (@list @t9)) % 0.44/0.67 (define @t195 () (lambda @t194 @t188)) % 0.44/0.67 (define @t196 () (_ @t39 @t9)) % 0.44/0.67 (define @t197 () (or @t196 @t170 @t187)) % 0.44/0.67 (define @t198 () (@list @t39 @t9)) % 0.44/0.67 (define @t199 () (or @t170 @t187)) % 0.44/0.67 (define @t200 () (not @t199)) % 0.44/0.67 (define @t201 () (lambda @t194 @t200)) % 0.44/0.67 (define @t202 () (_ @t201 @t9)) % 0.44/0.67 (define @t203 () (not @t202)) % 0.44/0.67 (define @t204 () (or @t203 @t196)) % 0.44/0.67 (define @t205 () (lambda @t198 @t204)) % 0.44/0.67 (define @t206 () (_ @t34 @t9)) % 0.44/0.67 (define @t207 () (not @t206)) % 0.44/0.67 (define @t208 () (or @t207 @t196)) % 0.44/0.67 (define @t209 () (lambda @t54 @t208)) % 0.44/0.67 (define @t210 () (not @t196)) % 0.44/0.67 (define @t211 () (lambda @t198 (not (or @t170 @t210)))) % 0.44/0.67 (define @t212 () (not (or @t207 @t210))) % 0.44/0.67 (define @t213 () (lambda @t54 @t212)) % 0.44/0.67 (define @t214 () (_ @t213 @t19)) % 0.44/0.67 (define @t215 () (lambda @t16 (_ (_ (_ @t209 (_ @t214 @t26)) @t24) @t9))) % 0.44/0.67 (define @t216 () (lambda @t20 (_ (_ @t148 @t215) @t9))) % 0.44/0.67 (define @t217 () (lambda @t22 (_ (_ @t148 @t216) @t9))) % 0.44/0.67 (define @t218 () (not @t40)) % 0.44/0.67 (define @t219 () (or @t36 @t218)) % 0.44/0.67 (define @t220 () (lambda @t49 @t219)) % 0.44/0.67 (define @t221 () (_ @t220 @t7)) % 0.44/0.67 (define @t222 () (not @t221)) % 0.44/0.67 (define @t223 () (lambda @t49 @t222)) % 0.44/0.67 (define @t224 () (lambda @t49 @t218)) % 0.44/0.67 (define @t225 () (_ @t224 @t7)) % 0.44/0.67 (define @t226 () (or @t36 @t225)) % 0.44/0.67 (define @t227 () (lambda @t49 @t226)) % 0.44/0.67 (define @t228 () (or @t36 @t40)) % 0.44/0.67 (define @t229 () (@list @t39 @t7)) % 0.44/0.67 (define @t230 () (lambda @t229 @t228)) % 0.44/0.67 (define @t231 () (lambda @t49 @t36)) % 0.44/0.67 (define @t232 () (_ @t231 @t7)) % 0.44/0.67 (define @t233 () (or @t232 @t40)) % 0.44/0.67 (define @t234 () (lambda @t229 @t233)) % 0.44/0.67 (define @t235 () (lambda @t49 @t228)) % 0.44/0.67 (define @t236 () (not @t8)) % 0.44/0.67 (define @t237 () (or @t236 @t63)) % 0.44/0.67 (define @t238 () (@quantifiers_skolemize @t114 0)) % 0.44/0.67 (define @t239 () (@quantifiers_skolemize @t114 2)) % 0.44/0.67 (define @t240 () (tptp.exists_in_world @t239 @t238)) % 0.44/0.67 (define @t241 () (@quantifiers_skolemize @t114 3)) % 0.44/0.67 (define @t242 () (tptp.subset @t239 @t241 @t238)) % 0.44/0.67 (define @t243 () (not @t242)) % 0.44/0.67 (define @t244 () (@quantifiers_skolemize @t114 1)) % 0.44/0.67 (define @t245 () (tptp.subset @t244 @t241 @t238)) % 0.44/0.67 (define @t246 () (tptp.exists_in_world @t241 @t238)) % 0.44/0.67 (define @t247 () (not @t246)) % 0.44/0.67 (define @t248 () (tptp.subset @t244 @t239 @t238)) % 0.44/0.67 (define @t249 () (not @t248)) % 0.44/0.67 (define @t250 () (not @t240)) % 0.44/0.67 (define @t251 () (tptp.exists_in_world @t244 @t238)) % 0.44/0.67 (define @t252 () (not @t251)) % 0.44/0.67 (define @t253 () (or @t252 @t250 @t249 @t247 @t245 @t243)) % 0.44/0.67 (define @t254 () (@list true)) % 0.44/0.67 (define @t255 () (@list @t253)) % 0.44/0.67 (define @t256 () (@var "BOUND_VARIABLE_8696" tptp.mu)) % 0.44/0.67 (define @t257 () (tptp.subset @t2 @t256 @t7)) % 0.44/0.67 (define @t258 () (@var "BOUND_VARIABLE_8569" tptp.mu)) % 0.44/0.67 (define @t259 () (tptp.member @t258 @t2 @t7)) % 0.44/0.67 (define @t260 () (not @t259)) % 0.44/0.67 (define @t261 () (not (tptp.exists_in_world @t258 @t7))) % 0.44/0.67 (define @t262 () (@list @t258)) % 0.44/0.67 (define @t263 () (@var "BOUND_VARIABLE_8698" tptp.mu)) % 0.44/0.67 (define @t264 () (and (or (not @t257) (not (tptp.exists_in_world @t263 @t7)) (not (tptp.member @t263 @t2 @t7)) (tptp.member @t263 @t256 @t7)) (or (not (forall @t262 (or @t261 @t260 (tptp.member @t258 @t256 @t7)))) @t257))) % 0.44/0.67 (define @t265 () (not (tptp.exists_in_world @t256 @t7))) % 0.44/0.67 (define @t266 () (or @t112 @t265 @t264)) % 0.44/0.67 (define @t267 () (@list @t2 @t256 @t263)) % 0.44/0.67 (define @t268 () (forall @t267 @t266)) % 0.44/0.67 (define @t269 () (lambda @t49 @t268)) % 0.44/0.67 (define @t270 () (_ @t269 @t7)) % 0.44/0.67 (define @t271 () (forall @t49 @t270)) % 0.44/0.67 (define @t272 () (or @t265 @t264)) % 0.44/0.67 (define @t273 () (or @t112 @t272)) % 0.44/0.67 (define @t274 () (forall @t267 @t273)) % 0.44/0.67 (define @t275 () (@list @t256 @t263)) % 0.44/0.67 (define @t276 () (forall @t275 @t273)) % 0.44/0.67 (define @t277 () (forall @t275 @t272)) % 0.44/0.67 (define @t278 () (@var "BOUND_VARIABLE_8617" tptp.mu)) % 0.44/0.67 (define @t279 () (@var "BOUND_VARIABLE_8659" tptp.mu)) % 0.44/0.67 (define @t280 () (or @t112 @t277)) % 0.44/0.67 (define @t281 () (tptp.subset @t2 @t279 @t7)) % 0.44/0.67 (define @t282 () (tptp.member @t278 @t2 @t7)) % 0.44/0.67 (define @t283 () (not (tptp.exists_in_world @t278 @t7))) % 0.44/0.67 (define @t284 () (@list @t279 @t278)) % 0.44/0.67 (define @t285 () (forall @t284 (or (not (tptp.exists_in_world @t279 @t7)) (and (or (not @t281) @t283 (not @t282) (tptp.member @t278 @t279 @t7)) (or (not (forall @t262 (or @t261 @t260 (tptp.member @t258 @t279 @t7)))) @t281))))) % 0.44/0.67 (define @t286 () (tptp.subset @t14 @t279 @t9)) % 0.44/0.67 (define @t287 () (not (tptp.member @t258 @t14 @t9))) % 0.44/0.67 (define @t288 () (not (tptp.exists_in_world @t258 @t9))) % 0.44/0.67 (define @t289 () (not (tptp.member @t278 @t14 @t9))) % 0.44/0.67 (define @t290 () (not (tptp.exists_in_world @t278 @t9))) % 0.44/0.67 (define @t291 () (@list @t2 @t278)) % 0.44/0.67 (define @t292 () (forall @t291 (or @t139 (and (or @t138 @t290 @t289 (tptp.member @t278 @t2 @t9)) (or (not (forall @t262 (or @t288 @t287 (tptp.member @t258 @t2 @t9)))) @t137))))) % 0.44/0.67 (define @t293 () (lambda @t22 @t292)) % 0.44/0.67 (define @t294 () (or @t112 (_ @t293 @t2 @t7))) % 0.44/0.67 (define @t295 () (forall @t5 @t294)) % 0.44/0.67 (define @t296 () (lambda @t49 @t295)) % 0.44/0.67 (define @t297 () (forall @t262 (or @t261 (not (tptp.member @t258 @t14 @t7)) @t259))) % 0.44/0.67 (define @t298 () (not @t297)) % 0.44/0.67 (define @t299 () (or @t298 @t151)) % 0.44/0.67 (define @t300 () (not (tptp.member @t278 @t14 @t7))) % 0.44/0.67 (define @t301 () (or @t152 @t283 @t300 @t282)) % 0.44/0.67 (define @t302 () (or @t283 @t300 @t282)) % 0.44/0.67 (define @t303 () (or @t152 @t302)) % 0.44/0.67 (define @t304 () (and @t303 @t299)) % 0.44/0.67 (define @t305 () (or @t112 @t304)) % 0.44/0.67 (define @t306 () (forall @t291 @t305)) % 0.44/0.67 (define @t307 () (@list @t278)) % 0.44/0.67 (define @t308 () (forall @t307 @t305)) % 0.44/0.67 (define @t309 () (forall @t307 @t299)) % 0.44/0.67 (define @t310 () (forall @t307 @t302)) % 0.44/0.67 (define @t311 () (@list @t258)) % 0.44/0.67 (define @t312 () (or @t152 @t310)) % 0.44/0.67 (define @t313 () (forall @t307 @t303)) % 0.44/0.67 (define @t314 () (and @t313 @t309)) % 0.44/0.67 (define @t315 () (forall @t307 @t304)) % 0.44/0.67 (define @t316 () (or @t112 @t315)) % 0.44/0.67 (define @t317 () (or @t298 @t165)) % 0.44/0.67 (define @t318 () (or @t166 @t297)) % 0.44/0.67 (define @t319 () (and @t318 @t317)) % 0.44/0.67 (define @t320 () (or @t112 @t319)) % 0.44/0.67 (define @t321 () (not @t317)) % 0.44/0.67 (define @t322 () (not @t318)) % 0.44/0.67 (define @t323 () (not (or @t322 @t321))) % 0.44/0.67 (define @t324 () (or @t112 @t323)) % 0.44/0.67 (define @t325 () (forall @t262 (or @t288 @t287 (tptp.member @t258 @t10 @t9)))) % 0.44/0.67 (define @t326 () (forall @t5 (or @t139 (not (tptp.member @t2 @t14 @t9)) (tptp.member @t2 @t10 @t9)))) % 0.44/0.67 (define @t327 () (not @t326)) % 0.44/0.67 (define @t328 () (or @t327 @t169)) % 0.44/0.67 (define @t329 () (not @t328)) % 0.44/0.67 (define @t330 () (or @t170 @t326)) % 0.44/0.67 (define @t331 () (not @t330)) % 0.44/0.67 (define @t332 () (or @t331 @t329)) % 0.44/0.67 (define @t333 () (not @t332)) % 0.44/0.67 (define @t334 () (lambda @t20 @t333)) % 0.44/0.67 (define @t335 () (or @t112 (_ @t334 @t2 @t7))) % 0.44/0.67 (define @t336 () (forall @t5 @t335)) % 0.44/0.67 (define @t337 () (lambda @t49 @t336)) % 0.44/0.67 (define @t338 () (tptp.member @t2 @t10 @t7)) % 0.44/0.67 (define @t339 () (tptp.member @t2 @t14 @t7)) % 0.44/0.67 (define @t340 () (lambda @t49 (forall @t5 (or @t112 (not @t339) @t338)))) % 0.44/0.67 (define @t341 () (_ @t340 @t9)) % 0.44/0.67 (define @t342 () (not @t341)) % 0.44/0.67 (define @t343 () (or @t342 @t169)) % 0.44/0.67 (define @t344 () (not @t343)) % 0.44/0.67 (define @t345 () (or @t170 @t341)) % 0.44/0.67 (define @t346 () (not @t345)) % 0.44/0.67 (define @t347 () (or @t346 @t344)) % 0.44/0.67 (define @t348 () (not @t347)) % 0.44/0.67 (define @t349 () (lambda @t194 @t348)) % 0.44/0.67 (define @t350 () (lambda @t198 (not (or (not (or @t170 @t196)) (not (or @t210 @t169)))))) % 0.44/0.67 (define @t351 () (_ tptp.member @t2)) % 0.44/0.67 (define @t352 () (_ (_ @t351 @t10) @t7)) % 0.44/0.67 (define @t353 () (_ (_ @t351 @t14) @t7)) % 0.44/0.67 (define @t354 () (not @t353)) % 0.44/0.67 (define @t355 () (or @t112 @t354 @t352)) % 0.44/0.67 (define @t356 () (or @t354 @t352)) % 0.44/0.67 (define @t357 () (not (_ @t15 @t9))) % 0.44/0.67 (define @t358 () (or @t357 (_ @t13 @t9))) % 0.44/0.67 (define @t359 () (lambda @t16 @t358)) % 0.44/0.67 (define @t360 () (_ @t359 @t2 @t7)) % 0.44/0.67 (define @t361 () (or @t112 @t360)) % 0.44/0.67 (define @t362 () (forall @t5 @t361)) % 0.44/0.67 (define @t363 () (lambda @t49 @t362)) % 0.44/0.67 (define @t364 () (lambda @t194 @t358)) % 0.44/0.67 (define @t365 () (lambda @t198 (or @t357 @t196))) % 0.44/0.67 (define @t366 () (_ @t209 @t15)) % 0.44/0.67 (define @t367 () (lambda @t16 (_ (_ @t366 @t13) @t9))) % 0.44/0.67 (define @t368 () (or @t210 @t206)) % 0.44/0.67 (define @t369 () (not @t208)) % 0.44/0.67 (define @t370 () (not (or @t369 (not @t368)))) % 0.44/0.67 (define @t371 () (_ (lambda @t54 @t370) @t19)) % 0.44/0.67 (define @t372 () (lambda @t20 (_ (_ @t371 (_ @t148 @t367)) @t9))) % 0.44/0.67 (define @t373 () (lambda @t194 @t368)) % 0.44/0.67 (define @t374 () (_ @t373 @t9)) % 0.44/0.67 (define @t375 () (not @t374)) % 0.44/0.67 (define @t376 () (or @t369 @t375)) % 0.44/0.67 (define @t377 () (not @t376)) % 0.44/0.67 (define @t378 () (lambda @t194 @t377)) % 0.44/0.67 (define @t379 () (@var "BOUND_VARIABLE_7630" (-> $$unsorted Bool))) % 0.44/0.67 (define @t380 () (not (_ @t379 @t9))) % 0.44/0.67 (define @t381 () (@list @t379 @t9)) % 0.44/0.67 (define @t382 () (@var "BOUND_VARIABLE_7650" (-> $$unsorted Bool))) % 0.44/0.67 (define @t383 () (_ @t382 @t9)) % 0.44/0.67 (define @t384 () (lambda (@list @t382 @t9) (or @t210 @t383))) % 0.44/0.67 (define @t385 () (@list @t39)) % 0.44/0.67 (define @t386 () (lambda @t194 @t208)) % 0.44/0.67 (define @t387 () (_ @t386 @t9)) % 0.44/0.67 (define @t388 () (not @t387)) % 0.44/0.67 (define @t389 () (or @t388 @t380)) % 0.44/0.67 (define @t390 () (not @t389)) % 0.44/0.67 (define @t391 () (lambda @t381 @t390)) % 0.44/0.67 (define @t392 () (lambda @t198 @t208)) % 0.44/0.67 (define @t393 () (tptp.member @t258 @t241 @t238)) % 0.44/0.67 (define @t394 () (not (tptp.member @t258 @t244 @t238))) % 0.44/0.67 (define @t395 () (not (tptp.exists_in_world @t258 @t238))) % 0.44/0.67 (define @t396 () (forall @t262 (or @t395 @t394 @t393))) % 0.44/0.67 (define @t397 () (@quantifiers_skolemize @t396 0)) % 0.44/0.67 (define @t398 () (tptp.member @t258 @t239 @t238)) % 0.44/0.67 (define @t399 () (tptp.member @t397 @t239 @t238)) % 0.44/0.67 (define @t400 () (tptp.member @t397 @t244 @t238)) % 0.44/0.67 (define @t401 () (not @t400)) % 0.44/0.67 (define @t402 () (tptp.exists_in_world @t397 @t238)) % 0.44/0.67 (define @t403 () (not @t402)) % 0.44/0.67 (define @t404 () (or @t249 @t403 @t401 @t399)) % 0.44/0.67 (define @t405 () (and @t404 (or (not (forall @t262 (or @t395 @t394 @t398))) @t248))) % 0.44/0.67 (define @t406 () (or @t252 @t250 @t405)) % 0.44/0.67 (define @t407 () (@list false false false)) % 0.44/0.67 (define @t408 () (@list false)) % 0.44/0.67 (define @t409 () (not @t396)) % 0.44/0.67 (define @t410 () (or @t409 @t245)) % 0.44/0.67 (define @t411 () (not @t245)) % 0.44/0.67 (define @t412 () (and (or @t411 @t252 (not (tptp.member @t244 @t244 @t238)) (tptp.member @t244 @t241 @t238)) @t410)) % 0.44/0.67 (define @t413 () (or @t252 @t247 @t412)) % 0.44/0.67 (define @t414 () (tptp.member @t397 @t241 @t238)) % 0.44/0.67 (define @t415 () (or @t403 @t401 @t414)) % 0.44/0.67 (define @t416 () (@list @t415)) % 0.44/0.67 (define @t417 () (not @t399)) % 0.44/0.67 (define @t418 () (or @t243 @t403 @t417 @t414)) % 0.44/0.67 (define @t419 () (not @t418)) % 0.44/0.67 (define @t420 () (and @t418 (or (not (forall @t262 (or @t395 (not @t398) @t393))) @t242))) % 0.44/0.67 (define @t421 () (not @t420)) % 0.44/0.67 (define @t422 () (or @t250 @t247 @t420)) % 0.44/0.67 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.44/0.67 (assume @p2 (forall @t6 (exists @t5 @t4))) % 0.44/0.67 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 0.44/0.67 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 0.44/0.67 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 0.44/0.67 (assume @p6 (_ tptp.mvalid (_ tptp.mforall_ind @t23))) % 0.44/0.67 (assume @p7 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t22 (_ (_ @t18 @t14) @t9))))) % 0.44/0.67 (assume @p8 @t30) % 0.44/0.67 (assume @p9 true) % 0.44/0.67 (step @p10 (= tptp.meq_prop @t33) :rule refl :args (@t33)) % 0.44/0.67 (step @p11 (= tptp.mnot @t38) :rule refl :args (@t38)) % 0.44/0.67 (step @p12 (= tptp.mor @t41) :rule refl :args (@t41)) % 0.44/0.67 (step @p13 (= tptp.mbox @t44) :rule refl :args (@t44)) % 0.44/0.67 (step @p14 (= tptp.mforall_prop @t48) :rule refl :args (@t48)) % 0.44/0.67 (step @p15 (= tptp.mtrue @t50) :rule refl :args (@t50)) % 0.44/0.67 (step @p16 (= tptp.mand @t55) :rule refl :args (@t55)) % 0.44/0.67 (step @p17 (= tptp.mimplies @t56) :rule refl :args (@t56)) % 0.44/0.67 (step @p18 (= tptp.mimplied @t57) :rule refl :args (@t57)) % 0.44/0.67 (step @p19 (= tptp.mequiv @t58) :rule refl :args (@t58)) % 0.44/0.67 (step @p20 (= tptp.mxor @t59) :rule refl :args (@t59)) % 0.44/0.67 (step @p21 (= tptp.mdia @t60) :rule refl :args (@t60)) % 0.44/0.67 (step @p22 (= tptp.mforall_ind @t66) :rule refl :args (@t66)) % 0.44/0.67 (step @p23 (= tptp.mexists_ind @t67) :rule refl :args (@t67)) % 0.44/0.67 (step @p24 (= tptp.mexists_prop @t68) :rule refl :args (@t68)) % 0.44/0.67 (step @p25 (= tptp.mreflexive @t73) :rule refl :args (@t73)) % 0.44/0.67 (step @p26 (= tptp.msymmetric @t77) :rule refl :args (@t77)) % 0.44/0.67 (step @p27 (= tptp.mserial @t79) :rule refl :args (@t79)) % 0.44/0.67 (step @p28 (= tptp.mtransitive @t84) :rule refl :args (@t84)) % 0.44/0.67 (step @p29 (= tptp.meuclidean @t86) :rule refl :args (@t86)) % 0.44/0.67 (step @p30 (= tptp.mpartially_functional @t88) :rule refl :args (@t88)) % 0.44/0.67 (step @p31 (= tptp.mfunctional @t90) :rule refl :args (@t90)) % 0.44/0.67 (step @p32 (= tptp.mweakly_dense @t93) :rule refl :args (@t93)) % 0.44/0.67 (step @p33 (= tptp.mweakly_connected @t94) :rule refl :args (@t94)) % 0.44/0.67 (step @p34 (= tptp.mweakly_directed @t95) :rule refl :args (@t95)) % 0.44/0.67 (step @p35 (= tptp.mvalid @t98) :rule refl :args (@t98)) % 0.44/0.67 (step @p36 (= tptp.msatisfiable @t99) :rule refl :args (@t99)) % 0.44/0.67 (step @p37 (= tptp.mcountersatisfiable @t100) :rule refl :args (@t100)) % 0.44/0.67 (step @p38 (= tptp.minvalid @t101) :rule refl :args (@t101)) % 0.44/0.67 (step @p39 (= tptp.mbox_s4 @t102) :rule refl :args (@t102)) % 0.44/0.67 (step @p40 (= tptp.mdia_s4 @t103) :rule refl :args (@t103)) % 0.44/0.67 (step @p41 :rule quant-merge-prenex :args ((= (forall @t49 @t116) @t114))) % 0.44/0.67 (step @p42 :rule beta-reduce :args ((= @t118 @t116))) % 0.44/0.67 (step @p43 :rule cong :premises (@p42) :args (@t119)) % 0.44/0.67 (step @p44 :rule trans :premises (@p43 @p41)) % 0.44/0.67 (step @p45 :rule beta-reduce :args ((= (_ @t121 @t117) @t119))) % 0.44/0.67 (step @p46 :rule trans :premises (@p45 @p44)) % 0.44/0.67 (step @p47 :rule aci_norm :args ((= @t123 @t113))) % 0.44/0.67 (step @p48 :rule cong :premises (@p47) :args (@t124)) % 0.44/0.67 (step @p49 :rule quant-merge-prenex :args ((= (forall @t5 @t126) @t124))) % 0.44/0.67 (step @p50 :rule alpha_equiv :args (@t127 (@list @t105 @t104) (@list @t129 @t128))) % 0.44/0.67 (step @p51 :rule refl :args (@t112)) % 0.44/0.67 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t130)) % 0.44/0.67 (step @p53 :rule quant-miniscope-or :args ((= @t126 @t130))) % 0.44/0.67 (step @p54 :rule trans :premises (@p53 @p52)) % 0.44/0.67 (step @p55 :rule symm :premises (@p54)) % 0.44/0.67 (step @p56 :rule cong :premises (@p55) :args ((forall @t5 (or @t112 @t134)))) % 0.44/0.67 (step @p57 :rule trans :premises (@p56 @p49)) % 0.44/0.67 (step @p58 :rule trans :premises (@p57 @p48)) % 0.44/0.67 (step @p59 :rule beta-reduce :args ((= (_ (lambda @t22 (forall @t133 (or (not (tptp.exists_in_world @t129 @t9)) (not (tptp.subset @t14 @t129 @t9)) @t136 @t135 (not (tptp.subset @t129 @t128 @t9))))) @t2 @t7) @t134))) % 0.44/0.67 (step @p60 :rule refl :args (@t7)) % 0.44/0.67 (step @p61 :rule refl :args (@t2)) % 0.44/0.67 (step @p62 :rule alpha_equiv :args (@t141 @t142 (@list @t129))) % 0.44/0.67 (step @p63 :rule cong :premises (@p62) :args (@t143)) % 0.44/0.67 (step @p64 :rule ho_cong :premises (@p63 @p61 @p60)) % 0.44/0.67 (step @p65 :rule trans :premises (@p64 @p59)) % 0.44/0.67 (step @p66 :rule refl :args (@t112)) % 0.44/0.67 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t144)) % 0.44/0.67 (step @p68 :rule cong :premises (@p67) :args (@t145)) % 0.44/0.67 (step @p69 :rule trans :premises (@p68 @p58)) % 0.44/0.67 (step @p70 :rule cong :premises (@p69) :args (@t146)) % 0.44/0.67 (step @p71 :rule beta-reduce :args ((= (_ @t148 @t143) @t146))) % 0.44/0.67 (step @p72 :rule trans :premises (@p71 @p70)) % 0.44/0.67 (step @p73 :rule beta-reduce :args ((= (_ (lambda @t49 (forall @t140 @t153)) @t9) @t141))) % 0.44/0.67 (step @p74 :rule refl :args (@t9)) % 0.44/0.67 (step @p75 :rule aci_norm :args ((= @t155 @t153))) % 0.44/0.67 (step @p76 :rule cong :premises (@p75) :args (@t156)) % 0.44/0.67 (step @p77 :rule quant-merge-prenex :args ((= (forall @t5 @t158) @t156))) % 0.44/0.67 (step @p78 :rule alpha_equiv :args (@t159 (@list @t128) @t161)) % 0.44/0.67 (step @p79 :rule refl :args (@t152)) % 0.44/0.67 (step @p80 :rule nary_cong :premises (@p51 @p79 @p78) :args (@t162)) % 0.44/0.67 (step @p81 :rule quant-miniscope-or :args ((= @t158 @t162))) % 0.44/0.67 (step @p82 :rule trans :premises (@p81 @p80)) % 0.44/0.67 (step @p83 :rule symm :premises (@p82)) % 0.44/0.67 (step @p84 :rule cong :premises (@p83) :args ((forall @t5 (or @t112 @t152 @t164)))) % 0.44/0.67 (step @p85 :rule trans :premises (@p84 @p77)) % 0.44/0.67 (step @p86 :rule trans :premises (@p85 @p76)) % 0.44/0.67 (step @p87 :rule refl :args (@t164)) % 0.44/0.67 (step @p88 :rule refl :args (@t151)) % 0.44/0.67 (step @p89 :rule refl :args (@t165)) % 0.44/0.67 (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t165 @t151))) % 0.44/0.67 (step @p91 :rule symm :premises (@p90)) % 0.44/0.67 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 0.44/0.67 (step @p93 :rule cong :premises (@p92) :args (@t166)) % 0.44/0.67 (step @p94 :rule nary_cong :premises (@p51 @p93 @p87) :args (@t167)) % 0.44/0.67 (step @p95 :rule cong :premises (@p94) :args ((forall @t5 @t167))) % 0.44/0.67 (step @p96 :rule trans :premises (@p95 @p86)) % 0.44/0.67 (step @p97 :rule aci_norm :args ((= (or @t112 @t168) @t167))) % 0.44/0.67 (step @p98 :rule beta-reduce :args ((= (_ (lambda @t20 (or @t170 (forall @t163 (or (not (tptp.exists_in_world @t160 @t9)) (tptp.subset @t14 @t160 @t9) (not (tptp.subset @t10 @t160 @t9)))))) @t2 @t7) @t168))) % 0.44/0.67 (step @p99 :rule alpha_equiv :args (@t171 @t142 @t161)) % 0.44/0.67 (step @p100 :rule refl :args (@t170)) % 0.44/0.67 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t172)) % 0.44/0.67 (step @p102 :rule cong :premises (@p101) :args (@t173)) % 0.44/0.67 (step @p103 :rule ho_cong :premises (@p102 @p61 @p60)) % 0.44/0.67 (step @p104 :rule trans :premises (@p103 @p98)) % 0.44/0.67 (step @p105 :rule nary_cong :premises (@p66 @p104) :args (@t174)) % 0.44/0.67 (step @p106 :rule trans :premises (@p105 @p97)) % 0.44/0.67 (step @p107 :rule cong :premises (@p106) :args (@t175)) % 0.44/0.67 (step @p108 :rule trans :premises (@p107 @p96)) % 0.44/0.67 (step @p109 :rule cong :premises (@p108) :args (@t176)) % 0.44/0.67 (step @p110 :rule beta-reduce :args ((= (_ @t148 @t173) @t176))) % 0.44/0.67 (step @p111 :rule trans :premises (@p110 @p109)) % 0.44/0.67 (step @p112 :rule beta-reduce :args ((= (_ (lambda @t49 (or @t178 (forall @t5 (or @t112 @t151 (not @t177))))) @t9) @t172))) % 0.44/0.67 (step @p113 :rule refl :args (@t177)) % 0.44/0.67 (step @p114 :rule refl :args (@t179)) % 0.44/0.67 (step @p115 :rule cong :premises (@p114 @p113) :args ((= @t179 @t177))) % 0.44/0.67 (step @p116 :rule symm :premises (@p115)) % 0.44/0.67 (step @p117 :rule eq_resolve :premises (@p114 @p116)) % 0.44/0.67 (step @p118 :rule cong :premises (@p117) :args (@t180)) % 0.44/0.67 (step @p119 :rule nary_cong :premises (@p51 @p92 @p118) :args (@t181)) % 0.44/0.67 (step @p120 :rule cong :premises (@p119) :args (@t182)) % 0.44/0.67 (step @p121 :rule refl :args (@t178)) % 0.44/0.67 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t183)) % 0.44/0.67 (step @p123 :rule quant-miniscope-or :args ((= (forall @t5 @t184) @t183))) % 0.44/0.67 (step @p124 :rule aci_norm :args ((= @t185 @t184))) % 0.44/0.67 (step @p125 :rule cong :premises (@p124) :args ((forall @t5 @t185))) % 0.44/0.67 (step @p126 :rule trans :premises (@p125 @p123)) % 0.44/0.67 (step @p127 :rule trans :premises (@p126 @p122)) % 0.44/0.67 (step @p128 :rule aci_norm :args ((= (or @t112 @t186) @t185))) % 0.44/0.67 (step @p129 :rule beta-reduce :args ((= @t190 @t186))) % 0.44/0.67 (step @p130 :rule nary_cong :premises (@p66 @p129) :args (@t191)) % 0.44/0.67 (step @p131 :rule trans :premises (@p130 @p128)) % 0.44/0.67 (step @p132 :rule cong :premises (@p131) :args (@t192)) % 0.44/0.67 (step @p133 :rule trans :premises (@p132 @p127)) % 0.44/0.67 (step @p134 :rule cong :premises (@p133) :args (@t193)) % 0.44/0.67 (step @p135 :rule beta-reduce :args ((= (_ @t148 @t189) @t193))) % 0.44/0.67 (step @p136 :rule trans :premises (@p135 @p134)) % 0.44/0.67 (step @p137 :rule beta-reduce :args ((= (_ @t195 @t9) @t188))) % 0.44/0.67 (step @p138 :rule beta-reduce :args ((= (_ (lambda @t198 @t197) @t24) @t195))) % 0.44/0.67 (step @p139 :rule refl :args (@t24)) % 0.44/0.67 (step @p140 :rule aci_norm :args ((= (or @t199 @t196) @t197))) % 0.44/0.67 (step @p141 :rule refl :args (@t196)) % 0.44/0.67 (step @p142 :rule bool-double-not-elim :args (@t199)) % 0.44/0.67 (step @p143 :rule beta-reduce :args ((= @t202 @t200))) % 0.44/0.67 (step @p144 :rule cong 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0.44/0.67 (step @p569 :rule reordering :premises (@p568) :args ((or @t250 @t247 @t420 (not @t422)))) % 0.44/0.67 (step @p570 false :rule chain_m_resolution :premises (@p569 @p567 @p505 @p290 @p284) :args (false (@list true false false false) (@list @t420 @t422 @t246 @t240))) % 0.44/0.67 ) % 0.44/0.67 % SZS output end Proof % 0.44/0.67 % cvc5 exiting %------------------------------------------------------------------------------