%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET907^7 : TPTP v9.2.1. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n018.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 08:48:57 AM UTC 2026 % Result : Theorem 0.36s 0.72s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET907^7 : TPTP v9.2.1. Released v5.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n018.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:17:05 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.52 %----Proving TH0 % 0.36/0.72 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.72 % SZS status Theorem % 0.36/0.72 % SZS output start Proof % 0.36/0.72 ( % 0.36/0.72 (declare-sort tptp.mu 0) % 0.36/0.72 (declare-sort $$unsorted 0) % 0.36/0.72 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 0.36/0.72 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.36/0.72 (declare-const tptp.empty (-> tptp.mu $$unsorted Bool)) % 0.36/0.72 (declare-const tptp.in (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.36/0.72 (declare-const tptp.qmltpeq (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.36/0.72 (declare-const tptp.subset (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.36/0.72 (declare-const tptp.set_union2 (-> tptp.mu tptp.mu tptp.mu)) % 0.36/0.72 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.36/0.72 (declare-const tptp.unordered_pair (-> tptp.mu tptp.mu tptp.mu)) % 0.36/0.72 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.36/0.72 (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)))))) % 0.36/0.72 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.36/0.72 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.36/0.72 (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))))))) % 0.36/0.72 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.36/0.72 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.72 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.36/0.72 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.72 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.36/0.72 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.72 (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)))))) % 0.36/0.72 (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)))))))) % 0.36/0.72 (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)))))) % 0.36/0.72 (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)))))) % 0.36/0.72 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.72 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.72 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.72 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.36/0.72 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.36/0.72 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.36/0.72 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.36/0.72 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.36/0.72 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.36/0.72 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.36/0.72 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.36/0.72 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.36/0.72 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.36/0.72 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.36/0.72 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$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)))))))) % 0.36/0.72 (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))))) % 0.36/0.72 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.72 (define @t2 () (@var "X" tptp.mu)) % 0.36/0.72 (define @t3 () (_ tptp.exists_in_world @t2)) % 0.36/0.72 (define @t4 () (_ @t3 @t1)) % 0.36/0.72 (define @t5 () (@list @t2)) % 0.36/0.72 (define @t6 () (@list @t1)) % 0.36/0.72 (define @t7 () (@var "W" $$unsorted)) % 0.36/0.72 (define @t8 () (_ @t3 @t7)) % 0.36/0.72 (define @t9 () (@var "V1" tptp.mu)) % 0.36/0.72 (define @t10 () (@var "V2" tptp.mu)) % 0.36/0.72 (define @t11 () (_ (_ tptp.unordered_pair @t10) @t9)) % 0.36/0.72 (define @t12 () (_ (_ tptp.exists_in_world @t11) @t1)) % 0.36/0.72 (define @t13 () (@list @t1 @t10 @t9)) % 0.36/0.72 (define @t14 () (forall @t13 @t12)) % 0.36/0.72 (define @t15 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.72 (define @t16 () (_ tptp.qmltpeq @t2)) % 0.36/0.72 (define @t17 () (@list @t2 @t15)) % 0.36/0.72 (define @t18 () (@var "Y" tptp.mu)) % 0.36/0.72 (define @t19 () (_ tptp.qmltpeq @t18)) % 0.36/0.72 (define @t20 () (_ @t16 @t18)) % 0.36/0.72 (define @t21 () (@list @t18 @t15)) % 0.36/0.72 (define @t22 () (@var "Z" tptp.mu)) % 0.36/0.72 (define @t23 () (@var "C" tptp.mu)) % 0.36/0.72 (define @t24 () (@var "B" tptp.mu)) % 0.36/0.72 (define @t25 () (_ tptp.set_union2 @t24)) % 0.36/0.72 (define @t26 () (@var "A" tptp.mu)) % 0.36/0.72 (define @t27 () (_ tptp.set_union2 @t26)) % 0.36/0.72 (define @t28 () (_ (_ tptp.qmltpeq @t26) @t24)) % 0.36/0.72 (define @t29 () (_ tptp.mimplies @t28)) % 0.36/0.72 (define @t30 () (@list @t23 @t15)) % 0.36/0.72 (define @t31 () (@list @t24 @t15)) % 0.36/0.72 (define @t32 () (@list @t26 @t15)) % 0.36/0.72 (define @t33 () (_ tptp.set_union2 @t23)) % 0.36/0.72 (define @t34 () (_ tptp.unordered_pair @t24)) % 0.36/0.72 (define @t35 () (_ tptp.unordered_pair @t26)) % 0.36/0.72 (define @t36 () (_ @t35 @t23)) % 0.36/0.72 (define @t37 () (_ tptp.unordered_pair @t23)) % 0.36/0.72 (define @t38 () (_ tptp.empty @t26)) % 0.36/0.72 (define @t39 () (_ tptp.mand @t28)) % 0.36/0.72 (define @t40 () (_ tptp.in @t24)) % 0.36/0.72 (define @t41 () (_ @t40 @t23)) % 0.36/0.72 (define @t42 () (_ tptp.in @t26)) % 0.36/0.72 (define @t43 () (_ @t42 @t23)) % 0.36/0.72 (define @t44 () (_ tptp.in @t23)) % 0.36/0.72 (define @t45 () (_ @t44 @t24)) % 0.36/0.72 (define @t46 () (_ tptp.subset @t26)) % 0.36/0.72 (define @t47 () (_ tptp.subset @t23)) % 0.36/0.72 (define @t48 () (_ @t42 @t24)) % 0.36/0.72 (define @t49 () (_ @t35 @t24)) % 0.36/0.72 (define @t50 () (_ @t25 @t26)) % 0.36/0.72 (define @t51 () (_ @t27 @t24)) % 0.36/0.72 (define @t52 () (_ tptp.qmltpeq @t51)) % 0.36/0.72 (define @t53 () (_ tptp.mnot @t38)) % 0.36/0.72 (define @t54 () (_ tptp.mimplies @t53)) % 0.36/0.72 (define @t55 () (_ @t52 @t24)) % 0.36/0.72 (define @t56 () (_ @t46 @t24)) % 0.36/0.72 (define @t57 () (lambda @t31 (_ (_ (_ tptp.mimplies @t56) @t55) @t15))) % 0.36/0.72 (define @t58 () (lambda @t32 (_ (_ tptp.mforall_ind @t57) @t15))) % 0.36/0.72 (define @t59 () (_ tptp.subset @t49)) % 0.36/0.72 (define @t60 () (_ @t59 @t23)) % 0.36/0.72 (define @t61 () (lambda @t30 (_ (_ (_ tptp.mequiv @t60) (_ (_ tptp.mand @t43) @t41)) @t15))) % 0.36/0.72 (define @t62 () (lambda @t31 (_ (_ tptp.mforall_ind @t61) @t15))) % 0.36/0.72 (define @t63 () (lambda @t32 (_ (_ tptp.mforall_ind @t62) @t15))) % 0.36/0.72 (define @t64 () (_ (_ tptp.qmltpeq (_ (_ tptp.set_union2 @t36) @t24)) @t24)) % 0.36/0.72 (define @t65 () (lambda @t30 (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t48) @t45)) @t64) @t15))) % 0.36/0.72 (define @t66 () (lambda @t31 (_ (_ tptp.mforall_ind @t65) @t15))) % 0.36/0.72 (define @t67 () (lambda @t32 (_ (_ tptp.mforall_ind @t66) @t15))) % 0.36/0.72 (define @t68 () (not (_ tptp.mvalid (_ tptp.mforall_ind @t67)))) % 0.36/0.72 (define @t69 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.72 (define @t70 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.72 (define @t71 () (lambda (@list @t70 @t69 @t7) (= (_ @t70 @t7) (_ @t69 @t7)))) % 0.36/0.72 (define @t72 () (@var "Phi" (-> $$unsorted Bool))) % 0.36/0.72 (define @t73 () (_ @t72 @t7)) % 0.36/0.72 (define @t74 () (not @t73)) % 0.36/0.72 (define @t75 () (@list @t72 @t7)) % 0.36/0.72 (define @t76 () (lambda @t75 @t74)) % 0.36/0.72 (define @t77 () (@var "Psi" (-> $$unsorted Bool))) % 0.36/0.72 (define @t78 () (_ @t77 @t7)) % 0.36/0.72 (define @t79 () (lambda (@list @t72 @t77 @t7) (or @t73 @t78))) % 0.36/0.72 (define @t80 () (_ @t72 @t1)) % 0.36/0.72 (define @t81 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.72 (define @t82 () (lambda (@list @t81 @t72 @t7) (forall @t6 (or (not (_ (_ @t81 @t7) @t1)) @t80)))) % 0.36/0.72 (define @t83 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.72 (define @t84 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.36/0.72 (define @t85 () (_ @t84 @t83)) % 0.36/0.72 (define @t86 () (lambda (@list @t84 @t7) (forall (@list @t83) (_ @t85 @t7)))) % 0.36/0.72 (define @t87 () (@list @t7)) % 0.36/0.72 (define @t88 () (lambda @t87 true)) % 0.36/0.72 (define @t89 () (_ tptp.mnot @t77)) % 0.36/0.72 (define @t90 () (_ tptp.mnot @t72)) % 0.36/0.72 (define @t91 () (_ tptp.mor @t90)) % 0.36/0.72 (define @t92 () (@list @t72 @t77 @t15)) % 0.36/0.72 (define @t93 () (lambda @t92 (_ (_ tptp.mnot (_ @t91 @t89)) @t15))) % 0.36/0.72 (define @t94 () (lambda @t92 (_ (_ @t91 @t77) @t15))) % 0.36/0.72 (define @t95 () (lambda @t92 (_ (_ (_ tptp.mor @t89) @t72) @t15))) % 0.36/0.72 (define @t96 () (lambda @t92 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t72) @t77)) (_ (_ tptp.mimplies @t77) @t72)) @t15))) % 0.36/0.72 (define @t97 () (lambda @t92 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t72) @t77)) @t15))) % 0.36/0.72 (define @t98 () (lambda (@list @t81 @t72 @t15) (_ (_ tptp.mnot (_ (_ tptp.mbox @t81) @t90)) @t15))) % 0.36/0.72 (define @t99 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.36/0.72 (define @t100 () (_ @t99 @t2)) % 0.36/0.72 (define @t101 () (_ @t100 @t7)) % 0.36/0.72 (define @t102 () (forall @t5 (=> @t8 @t101))) % 0.36/0.72 (define @t103 () (@list @t99 @t7)) % 0.36/0.72 (define @t104 () (lambda @t103 @t102)) % 0.36/0.72 (define @t105 () (lambda (@list @t99 @t15) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mnot @t100) @t15)))) @t15))) % 0.36/0.72 (define @t106 () (lambda (@list @t84 @t15) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t83 @t15) (_ (_ tptp.mnot @t85) @t15)))) @t15))) % 0.36/0.72 (define @t107 () (@var "S" $$unsorted)) % 0.36/0.72 (define @t108 () (_ @t81 @t107)) % 0.36/0.72 (define @t109 () (@list @t107)) % 0.36/0.72 (define @t110 () (@list @t81)) % 0.36/0.72 (define @t111 () (lambda @t110 (forall @t109 (_ @t108 @t107)))) % 0.36/0.72 (define @t112 () (@var "T" $$unsorted)) % 0.36/0.72 (define @t113 () (_ @t81 @t112)) % 0.36/0.72 (define @t114 () (_ @t108 @t112)) % 0.36/0.72 (define @t115 () (lambda @t110 (forall (@list @t107 @t112) (=> @t114 (_ @t113 @t107))))) % 0.36/0.72 (define @t116 () (@list @t112)) % 0.36/0.72 (define @t117 () (lambda @t110 (forall @t109 (exists @t116 @t114)))) % 0.36/0.72 (define @t118 () (@var "U" $$unsorted)) % 0.36/0.72 (define @t119 () (_ @t108 @t118)) % 0.36/0.72 (define @t120 () (_ @t113 @t118)) % 0.36/0.72 (define @t121 () (@list @t107 @t112 @t118)) % 0.36/0.72 (define @t122 () (lambda @t110 (forall @t121 (=> (and @t114 @t120) @t119)))) % 0.36/0.72 (define @t123 () (and @t114 @t119)) % 0.36/0.72 (define @t124 () (lambda @t110 (forall @t121 (=> @t123 @t120)))) % 0.36/0.72 (define @t125 () (= @t112 @t118)) % 0.36/0.72 (define @t126 () (lambda @t110 (forall @t121 (=> @t123 @t125)))) % 0.36/0.72 (define @t127 () (@list @t118)) % 0.36/0.72 (define @t128 () (lambda @t110 (forall @t109 (exists @t116 (and @t114 (forall @t127 (=> @t119 @t125))))))) % 0.36/0.72 (define @t129 () (_ @t81 @t118)) % 0.36/0.72 (define @t130 () (_ @t129 @t112)) % 0.36/0.72 (define @t131 () (lambda @t110 (forall @t121 (=> @t114 (exists @t127 (and @t119 @t130)))))) % 0.36/0.72 (define @t132 () (lambda @t110 (forall @t121 (=> @t123 (or @t120 @t125 @t130))))) % 0.36/0.72 (define @t133 () (lambda @t110 (forall @t121 (=> @t123 (exists @t6 (and (_ @t113 @t1) (_ @t129 @t1))))))) % 0.36/0.72 (define @t134 () (forall @t87 @t73)) % 0.36/0.72 (define @t135 () (@list @t72)) % 0.36/0.72 (define @t136 () (lambda @t135 @t134)) % 0.36/0.72 (define @t137 () (lambda @t135 (exists @t87 @t73))) % 0.36/0.72 (define @t138 () (lambda @t135 (exists @t87 @t74))) % 0.36/0.72 (define @t139 () (lambda @t135 (forall @t87 @t74))) % 0.36/0.72 (define @t140 () (lambda @t75 (forall @t6 (or (not (_ (_ tptp.rel_s4 @t7) @t1)) @t80)))) % 0.36/0.72 (define @t141 () (lambda (@list @t72 @t15) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t90)) @t15))) % 0.36/0.72 (define @t142 () (@var "BOUND_VARIABLE_11720" tptp.mu)) % 0.36/0.72 (define @t143 () (@var "BOUND_VARIABLE_11722" tptp.mu)) % 0.36/0.72 (define @t144 () (not (tptp.in @t143 @t142 @t7))) % 0.36/0.72 (define @t145 () (tptp.qmltpeq (tptp.set_union2 (tptp.unordered_pair @t2 @t143) @t142) @t142 @t7)) % 0.36/0.72 (define @t146 () (not (tptp.exists_in_world @t143 @t7))) % 0.36/0.72 (define @t147 () (not (tptp.in @t2 @t142 @t7))) % 0.36/0.72 (define @t148 () (not (tptp.exists_in_world @t142 @t7))) % 0.36/0.72 (define @t149 () (tptp.exists_in_world @t2 @t7)) % 0.36/0.72 (define @t150 () (not @t149)) % 0.36/0.72 (define @t151 () (or @t150 @t148 @t147 @t146 @t145 @t144)) % 0.36/0.72 (define @t152 () (forall (@list @t7 @t2 @t142 @t143) @t151)) % 0.36/0.72 (define @t153 () (@list @t2 @t142 @t143)) % 0.36/0.72 (define @t154 () (forall @t153 @t151)) % 0.36/0.72 (define @t155 () (lambda @t87 @t154)) % 0.36/0.72 (define @t156 () (_ @t155 @t7)) % 0.36/0.72 (define @t157 () (forall @t87 @t156)) % 0.36/0.72 (define @t158 () (_ @t72 @t7)) % 0.36/0.72 (define @t159 () (lambda @t135 (forall @t87 @t158))) % 0.36/0.72 (define @t160 () (or @t148 @t147 @t146 @t145 @t144)) % 0.36/0.72 (define @t161 () (or @t150 @t160)) % 0.36/0.72 (define @t162 () (forall @t153 @t161)) % 0.36/0.72 (define @t163 () (@list @t142 @t143)) % 0.36/0.72 (define @t164 () (forall @t163 @t161)) % 0.36/0.72 (define @t165 () (forall @t163 @t160)) % 0.36/0.72 (define @t166 () (@var "BOUND_VARIABLE_11661" tptp.mu)) % 0.36/0.72 (define @t167 () (@var "BOUND_VARIABLE_11692" tptp.mu)) % 0.36/0.72 (define @t168 () (or @t150 @t165)) % 0.36/0.72 (define @t169 () (not (tptp.exists_in_world @t166 @t7))) % 0.36/0.72 (define @t170 () (@list @t167 @t166)) % 0.36/0.72 (define @t171 () (forall @t170 (or (not (tptp.exists_in_world @t167 @t7)) (not (tptp.in @t2 @t167 @t7)) @t169 (tptp.qmltpeq (tptp.set_union2 (tptp.unordered_pair @t2 @t166) @t167) @t167 @t7) (not (tptp.in @t166 @t167 @t7))))) % 0.36/0.72 (define @t172 () (tptp.unordered_pair @t26 @t166)) % 0.36/0.72 (define @t173 () (not (tptp.exists_in_world @t166 @t15))) % 0.36/0.72 (define @t174 () (tptp.set_union2 @t172 @t2)) % 0.36/0.72 (define @t175 () (tptp.in @t26 @t2 @t15)) % 0.36/0.72 (define @t176 () (not @t175)) % 0.36/0.72 (define @t177 () (not (tptp.exists_in_world @t2 @t15))) % 0.36/0.72 (define @t178 () (@list @t2 @t166)) % 0.36/0.72 (define @t179 () (forall @t178 (or @t177 @t176 @t173 (tptp.qmltpeq @t174 @t2 @t15) (not (tptp.in @t166 @t2 @t15))))) % 0.36/0.72 (define @t180 () (@list @t2)) % 0.36/0.72 (define @t181 () (lambda @t32 @t179)) % 0.36/0.72 (define @t182 () (or @t150 (_ @t181 @t2 @t7))) % 0.36/0.72 (define @t183 () (forall @t5 @t182)) % 0.36/0.72 (define @t184 () (lambda @t87 @t183)) % 0.36/0.72 (define @t185 () (_ @t99 @t2 @t7)) % 0.36/0.72 (define @t186 () (lambda @t103 (forall @t5 (or @t150 @t185)))) % 0.36/0.72 (define @t187 () (not (tptp.in @t166 @t2 @t7))) % 0.36/0.72 (define @t188 () (tptp.qmltpeq @t174 @t2 @t7)) % 0.36/0.72 (define @t189 () (tptp.in @t26 @t2 @t7)) % 0.36/0.72 (define @t190 () (not @t189)) % 0.36/0.72 (define @t191 () (or @t150 @t190 @t169 @t188 @t187)) % 0.36/0.72 (define @t192 () (or @t169 @t188 @t187)) % 0.36/0.72 (define @t193 () (or @t150 @t190 @t192)) % 0.36/0.72 (define @t194 () (forall @t178 @t193)) % 0.36/0.72 (define @t195 () (@list @t166)) % 0.36/0.72 (define @t196 () (forall @t195 @t193)) % 0.36/0.72 (define @t197 () (forall @t195 @t192)) % 0.36/0.72 (define @t198 () (@var "BOUND_VARIABLE_11632" tptp.mu)) % 0.36/0.72 (define @t199 () (@list @t198)) % 0.36/0.72 (define @t200 () (or @t150 @t190 @t197)) % 0.36/0.72 (define @t201 () (tptp.unordered_pair @t26 @t198)) % 0.36/0.72 (define @t202 () (@list @t198)) % 0.36/0.72 (define @t203 () (forall @t202 (or (not (tptp.exists_in_world @t198 @t7)) (tptp.qmltpeq (tptp.set_union2 @t201 @t2) @t2 @t7) (not (tptp.in @t198 @t2 @t7))))) % 0.36/0.72 (define @t204 () (_ (_ @t42 @t2) @t7)) % 0.36/0.72 (define @t205 () (not @t204)) % 0.36/0.72 (define @t206 () (or @t150 @t205 @t203)) % 0.36/0.72 (define @t207 () (or @t205 @t203)) % 0.36/0.72 (define @t208 () (not (_ @t48 @t15))) % 0.36/0.72 (define @t209 () (tptp.unordered_pair @t26 @t2)) % 0.36/0.72 (define @t210 () (tptp.set_union2 @t209 @t24)) % 0.36/0.72 (define @t211 () (forall @t5 (or @t177 (tptp.qmltpeq @t210 @t24 @t15) (not (tptp.in @t2 @t24 @t15))))) % 0.36/0.72 (define @t212 () (or @t208 @t211)) % 0.36/0.72 (define @t213 () (lambda @t31 @t212)) % 0.36/0.72 (define @t214 () (or @t150 (_ @t213 @t2 @t7))) % 0.36/0.72 (define @t215 () (forall @t5 @t214)) % 0.36/0.72 (define @t216 () (lambda @t87 @t215)) % 0.36/0.72 (define @t217 () (tptp.in @t2 @t24 @t7)) % 0.36/0.72 (define @t218 () (tptp.qmltpeq @t210 @t24 @t7)) % 0.36/0.72 (define @t219 () (not (_ @t48 @t7))) % 0.36/0.72 (define @t220 () (_ (_ (_ tptp.in @t2) @t24) @t7)) % 0.36/0.72 (define @t221 () (not @t220)) % 0.36/0.72 (define @t222 () (_ @t35 @t2)) % 0.36/0.72 (define @t223 () (_ (_ tptp.set_union2 @t222) @t24)) % 0.36/0.72 (define @t224 () (_ (_ (_ tptp.qmltpeq @t223) @t24) @t7)) % 0.36/0.72 (define @t225 () (or @t150 @t224 @t221)) % 0.36/0.72 (define @t226 () (forall @t5 @t225)) % 0.36/0.72 (define @t227 () (or @t219 @t226)) % 0.36/0.72 (define @t228 () (or @t219 @t225)) % 0.36/0.72 (define @t229 () (or @t150 @t224 @t219 @t221)) % 0.36/0.72 (define @t230 () (or @t224 @t219 @t221)) % 0.36/0.72 (define @t231 () (not (_ @t45 @t15))) % 0.36/0.72 (define @t232 () (or (_ @t64 @t15) @t208 @t231)) % 0.36/0.72 (define @t233 () (lambda @t30 @t232)) % 0.36/0.72 (define @t234 () (_ @t233 @t2 @t7)) % 0.36/0.72 (define @t235 () (or @t150 @t234)) % 0.36/0.72 (define @t236 () (forall @t5 @t235)) % 0.36/0.72 (define @t237 () (lambda @t87 @t236)) % 0.36/0.72 (define @t238 () (@list @t15)) % 0.36/0.72 (define @t239 () (lambda @t238 @t232)) % 0.36/0.72 (define @t240 () (_ @t77 @t15)) % 0.36/0.72 (define @t241 () (or @t240 @t208 @t231)) % 0.36/0.72 (define @t242 () (@list @t77 @t15)) % 0.36/0.72 (define @t243 () (or @t208 @t231)) % 0.36/0.72 (define @t244 () (not @t243)) % 0.36/0.72 (define @t245 () (lambda @t238 @t244)) % 0.36/0.72 (define @t246 () (_ @t245 @t15)) % 0.36/0.72 (define @t247 () (not @t246)) % 0.36/0.72 (define @t248 () (or @t247 @t240)) % 0.36/0.72 (define @t249 () (lambda @t242 @t248)) % 0.36/0.72 (define @t250 () (_ @t72 @t15)) % 0.36/0.72 (define @t251 () (not @t250)) % 0.36/0.72 (define @t252 () (or @t251 @t240)) % 0.36/0.72 (define @t253 () (lambda @t92 @t252)) % 0.36/0.72 (define @t254 () (not @t240)) % 0.36/0.72 (define @t255 () (lambda @t242 (not (or @t208 @t254)))) % 0.36/0.72 (define @t256 () (not (or @t251 @t254))) % 0.36/0.72 (define @t257 () (lambda @t92 @t256)) % 0.36/0.72 (define @t258 () (_ @t257 @t48)) % 0.36/0.72 (define @t259 () (lambda @t30 (_ (_ (_ @t253 (_ @t258 @t45)) @t64) @t15))) % 0.36/0.72 (define @t260 () (lambda @t31 (_ (_ @t186 @t259) @t15))) % 0.36/0.72 (define @t261 () (lambda @t32 (_ (_ @t186 @t260) @t15))) % 0.36/0.72 (define @t262 () (not @t78)) % 0.36/0.72 (define @t263 () (or @t74 @t262)) % 0.36/0.72 (define @t264 () (lambda @t87 @t263)) % 0.36/0.72 (define @t265 () (_ @t264 @t7)) % 0.36/0.72 (define @t266 () (not @t265)) % 0.36/0.72 (define @t267 () (lambda @t87 @t266)) % 0.36/0.72 (define @t268 () (lambda @t87 @t262)) % 0.36/0.72 (define @t269 () (_ @t268 @t7)) % 0.36/0.72 (define @t270 () (or @t74 @t269)) % 0.36/0.72 (define @t271 () (lambda @t87 @t270)) % 0.36/0.72 (define @t272 () (or @t74 @t78)) % 0.36/0.72 (define @t273 () (@list @t77 @t7)) % 0.36/0.72 (define @t274 () (lambda @t273 @t272)) % 0.36/0.72 (define @t275 () (lambda @t87 @t74)) % 0.36/0.72 (define @t276 () (_ @t275 @t7)) % 0.36/0.72 (define @t277 () (or @t276 @t78)) % 0.36/0.72 (define @t278 () (lambda @t273 @t277)) % 0.36/0.72 (define @t279 () (lambda @t87 @t272)) % 0.36/0.72 (define @t280 () (not @t8)) % 0.36/0.72 (define @t281 () (or @t280 @t101)) % 0.36/0.72 (define @t282 () (@quantifiers_skolemize @t152 0)) % 0.36/0.72 (define @t283 () (@quantifiers_skolemize @t152 1)) % 0.36/0.72 (define @t284 () (tptp.exists_in_world @t283 @t282)) % 0.36/0.72 (define @t285 () (@quantifiers_skolemize @t152 2)) % 0.36/0.72 (define @t286 () (@quantifiers_skolemize @t152 3)) % 0.36/0.72 (define @t287 () (tptp.in @t286 @t285 @t282)) % 0.36/0.72 (define @t288 () (not @t287)) % 0.36/0.72 (define @t289 () (tptp.unordered_pair @t283 @t286)) % 0.36/0.72 (define @t290 () (tptp.qmltpeq (tptp.set_union2 @t289 @t285) @t285 @t282)) % 0.36/0.72 (define @t291 () (tptp.exists_in_world @t286 @t282)) % 0.36/0.72 (define @t292 () (not @t291)) % 0.36/0.72 (define @t293 () (tptp.in @t283 @t285 @t282)) % 0.36/0.72 (define @t294 () (not @t293)) % 0.36/0.72 (define @t295 () (tptp.exists_in_world @t285 @t282)) % 0.36/0.72 (define @t296 () (not @t295)) % 0.36/0.72 (define @t297 () (not @t284)) % 0.36/0.72 (define @t298 () (or @t297 @t296 @t294 @t292 @t290 @t288)) % 0.36/0.72 (define @t299 () (@list true)) % 0.36/0.72 (define @t300 () (@list @t298)) % 0.36/0.72 (define @t301 () (@var "BOUND_VARIABLE_11517" tptp.mu)) % 0.36/0.72 (define @t302 () (@var "BOUND_VARIABLE_11515" tptp.mu)) % 0.36/0.72 (define @t303 () (tptp.in @t302 @t301 @t7)) % 0.36/0.72 (define @t304 () (tptp.in @t2 @t301 @t7)) % 0.36/0.72 (define @t305 () (tptp.subset (tptp.unordered_pair @t2 @t302) @t301 @t7)) % 0.36/0.72 (define @t306 () (and (or (not @t305) (and @t304 @t303)) (or @t305 (not @t304) (not @t303)))) % 0.36/0.72 (define @t307 () (not (tptp.exists_in_world @t301 @t7))) % 0.36/0.72 (define @t308 () (not (tptp.exists_in_world @t302 @t7))) % 0.36/0.72 (define @t309 () (or @t150 @t308 @t307 @t306)) % 0.36/0.72 (define @t310 () (@list @t2 @t302 @t301)) % 0.36/0.72 (define @t311 () (forall @t310 @t309)) % 0.36/0.72 (define @t312 () (lambda @t87 @t311)) % 0.36/0.72 (define @t313 () (_ @t312 @t7)) % 0.36/0.72 (define @t314 () (forall @t87 @t313)) % 0.36/0.72 (define @t315 () (or @t308 @t307 @t306)) % 0.36/0.72 (define @t316 () (or @t150 @t315)) % 0.36/0.72 (define @t317 () (forall @t310 @t316)) % 0.36/0.72 (define @t318 () (@list @t302 @t301)) % 0.36/0.72 (define @t319 () (forall @t318 @t316)) % 0.36/0.72 (define @t320 () (forall @t318 @t315)) % 0.36/0.72 (define @t321 () (@var "BOUND_VARIABLE_11439" tptp.mu)) % 0.36/0.72 (define @t322 () (@var "BOUND_VARIABLE_11482" tptp.mu)) % 0.36/0.72 (define @t323 () (or @t150 @t320)) % 0.36/0.72 (define @t324 () (tptp.in @t322 @t321 @t7)) % 0.36/0.72 (define @t325 () (tptp.in @t2 @t321 @t7)) % 0.36/0.72 (define @t326 () (not @t325)) % 0.36/0.72 (define @t327 () (tptp.subset (tptp.unordered_pair @t2 @t322) @t321 @t7)) % 0.36/0.72 (define @t328 () (not (tptp.exists_in_world @t321 @t7))) % 0.36/0.72 (define @t329 () (@list @t322 @t321)) % 0.36/0.72 (define @t330 () (forall @t329 (or (not (tptp.exists_in_world @t322 @t7)) @t328 (and (or (not @t327) (and @t325 @t324)) (or @t327 @t326 (not @t324)))))) % 0.36/0.72 (define @t331 () (tptp.in @t322 @t321 @t15)) % 0.36/0.72 (define @t332 () (tptp.in @t26 @t321 @t15)) % 0.36/0.72 (define @t333 () (not @t332)) % 0.36/0.72 (define @t334 () (tptp.subset (tptp.unordered_pair @t26 @t322) @t321 @t15)) % 0.36/0.72 (define @t335 () (not (tptp.exists_in_world @t321 @t15))) % 0.36/0.72 (define @t336 () (tptp.in @t2 @t321 @t15)) % 0.36/0.72 (define @t337 () (tptp.subset @t209 @t321 @t15)) % 0.36/0.72 (define @t338 () (@list @t2 @t321)) % 0.36/0.72 (define @t339 () (forall @t338 (or @t177 @t335 (and (or (not @t337) (and @t332 @t336)) (or @t337 @t333 (not @t336)))))) % 0.36/0.72 (define @t340 () (lambda @t32 @t339)) % 0.36/0.72 (define @t341 () (or @t150 (_ @t340 @t2 @t7))) % 0.36/0.72 (define @t342 () (forall @t5 @t341)) % 0.36/0.72 (define @t343 () (lambda @t87 @t342)) % 0.36/0.72 (define @t344 () (tptp.in @t26 @t321 @t7)) % 0.36/0.72 (define @t345 () (tptp.subset @t209 @t321 @t7)) % 0.36/0.72 (define @t346 () (and (or (not @t345) (and @t344 @t325)) (or @t345 (not @t344) @t326))) % 0.36/0.72 (define @t347 () (or @t150 @t328 @t346)) % 0.36/0.72 (define @t348 () (or @t328 @t346)) % 0.36/0.72 (define @t349 () (or @t150 @t348)) % 0.36/0.72 (define @t350 () (forall @t338 @t349)) % 0.36/0.72 (define @t351 () (@list @t321)) % 0.36/0.72 (define @t352 () (forall @t351 @t349)) % 0.36/0.72 (define @t353 () (forall @t351 @t348)) % 0.36/0.72 (define @t354 () (@var "BOUND_VARIABLE_11404" tptp.mu)) % 0.36/0.72 (define @t355 () (@list @t354)) % 0.36/0.72 (define @t356 () (or @t150 @t353)) % 0.36/0.72 (define @t357 () (tptp.in @t2 @t354 @t7)) % 0.36/0.72 (define @t358 () (tptp.in @t26 @t354 @t7)) % 0.36/0.72 (define @t359 () (tptp.subset @t209 @t354 @t7)) % 0.36/0.72 (define @t360 () (@list @t354)) % 0.36/0.72 (define @t361 () (forall @t360 (or (not (tptp.exists_in_world @t354 @t7)) (and (or (not @t359) (and @t358 @t357)) (or @t359 (not @t358) (not @t357)))))) % 0.36/0.72 (define @t362 () (tptp.in @t24 @t354 @t15)) % 0.36/0.72 (define @t363 () (tptp.in @t26 @t354 @t15)) % 0.36/0.72 (define @t364 () (tptp.unordered_pair @t26 @t24)) % 0.36/0.72 (define @t365 () (tptp.subset @t364 @t354 @t15)) % 0.36/0.72 (define @t366 () (tptp.in @t24 @t2 @t15)) % 0.36/0.72 (define @t367 () (tptp.subset @t364 @t2 @t15)) % 0.36/0.72 (define @t368 () (forall @t5 (or @t177 (and (or (not @t367) (and @t175 @t366)) (or @t367 @t176 (not @t366)))))) % 0.36/0.72 (define @t369 () (lambda @t31 @t368)) % 0.36/0.72 (define @t370 () (or @t150 (_ @t369 @t2 @t7))) % 0.36/0.72 (define @t371 () (forall @t5 @t370)) % 0.36/0.72 (define @t372 () (lambda @t87 @t371)) % 0.36/0.72 (define @t373 () (tptp.in @t24 @t2 @t7)) % 0.36/0.72 (define @t374 () (tptp.subset @t364 @t2 @t7)) % 0.36/0.72 (define @t375 () (_ (_ @t40 @t2) @t7)) % 0.36/0.72 (define @t376 () (not @t375)) % 0.36/0.72 (define @t377 () (_ (_ @t59 @t2) @t7)) % 0.36/0.72 (define @t378 () (or @t377 @t205 @t376)) % 0.36/0.72 (define @t379 () (and @t204 @t375)) % 0.36/0.72 (define @t380 () (not @t377)) % 0.36/0.72 (define @t381 () (or @t380 @t379)) % 0.36/0.72 (define @t382 () (and @t381 @t378)) % 0.36/0.72 (define @t383 () (or @t150 @t382)) % 0.36/0.72 (define @t384 () (or @t380 (not (or @t205 @t376)))) % 0.36/0.72 (define @t385 () (not @t378)) % 0.36/0.72 (define @t386 () (not @t384)) % 0.36/0.72 (define @t387 () (not (or @t386 @t385))) % 0.36/0.72 (define @t388 () (or @t150 @t387)) % 0.36/0.72 (define @t389 () (not (_ @t41 @t15))) % 0.36/0.72 (define @t390 () (not (_ @t43 @t15))) % 0.36/0.72 (define @t391 () (_ @t60 @t15)) % 0.36/0.72 (define @t392 () (or @t391 @t390 @t389)) % 0.36/0.72 (define @t393 () (or @t390 @t389)) % 0.36/0.72 (define @t394 () (not @t393)) % 0.36/0.72 (define @t395 () (not @t391)) % 0.36/0.72 (define @t396 () (not (or (not (or @t395 @t394)) (not @t392)))) % 0.36/0.72 (define @t397 () (lambda @t30 @t396)) % 0.36/0.72 (define @t398 () (_ @t397 @t2 @t7)) % 0.36/0.72 (define @t399 () (or @t150 @t398)) % 0.36/0.72 (define @t400 () (forall @t5 @t399)) % 0.36/0.72 (define @t401 () (lambda @t87 @t400)) % 0.36/0.72 (define @t402 () (lambda @t238 @t394)) % 0.36/0.72 (define @t403 () (_ @t402 @t15)) % 0.36/0.72 (define @t404 () (not @t403)) % 0.36/0.72 (define @t405 () (or @t404 @t391)) % 0.36/0.72 (define @t406 () (not @t405)) % 0.36/0.72 (define @t407 () (or @t395 @t403)) % 0.36/0.72 (define @t408 () (not @t407)) % 0.36/0.72 (define @t409 () (or @t408 @t406)) % 0.36/0.72 (define @t410 () (not @t409)) % 0.36/0.72 (define @t411 () (lambda @t238 @t410)) % 0.36/0.72 (define @t412 () (lambda @t242 (not (or (not (or @t395 @t240)) (not (or @t254 @t391)))))) % 0.36/0.72 (define @t413 () (lambda @t242 (not (or @t390 @t254)))) % 0.36/0.72 (define @t414 () (_ @t257 @t43)) % 0.36/0.72 (define @t415 () (or @t254 @t250)) % 0.36/0.72 (define @t416 () (not @t252)) % 0.36/0.72 (define @t417 () (not (or @t416 (not @t415)))) % 0.36/0.72 (define @t418 () (_ (lambda @t92 @t417) @t60)) % 0.36/0.72 (define @t419 () (lambda @t30 (_ (_ @t418 (_ @t414 @t41)) @t15))) % 0.36/0.72 (define @t420 () (lambda @t31 (_ (_ @t186 @t419) @t15))) % 0.36/0.72 (define @t421 () (lambda @t238 @t415)) % 0.36/0.72 (define @t422 () (_ @t421 @t15)) % 0.36/0.72 (define @t423 () (not @t422)) % 0.36/0.72 (define @t424 () (or @t416 @t423)) % 0.36/0.72 (define @t425 () (not @t424)) % 0.36/0.72 (define @t426 () (lambda @t238 @t425)) % 0.36/0.72 (define @t427 () (@var "BOUND_VARIABLE_7630" (-> $$unsorted Bool))) % 0.36/0.72 (define @t428 () (not (_ @t427 @t15))) % 0.36/0.72 (define @t429 () (@list @t427 @t15)) % 0.36/0.72 (define @t430 () (@var "BOUND_VARIABLE_7650" (-> $$unsorted Bool))) % 0.36/0.72 (define @t431 () (_ @t430 @t15)) % 0.36/0.72 (define @t432 () (lambda (@list @t430 @t15) (or @t254 @t431))) % 0.36/0.72 (define @t433 () (@list @t77)) % 0.36/0.72 (define @t434 () (lambda @t238 @t252)) % 0.36/0.72 (define @t435 () (_ @t434 @t15)) % 0.36/0.72 (define @t436 () (not @t435)) % 0.36/0.72 (define @t437 () (or @t436 @t428)) % 0.36/0.72 (define @t438 () (not @t437)) % 0.36/0.72 (define @t439 () (lambda @t429 @t438)) % 0.36/0.72 (define @t440 () (lambda @t242 @t252)) % 0.36/0.72 (define @t441 () (@var "BOUND_VARIABLE_11273" tptp.mu)) % 0.36/0.72 (define @t442 () (tptp.qmltpeq (tptp.set_union2 @t2 @t441) @t441 @t7)) % 0.36/0.72 (define @t443 () (not (tptp.subset @t2 @t441 @t7))) % 0.36/0.72 (define @t444 () (not (tptp.exists_in_world @t441 @t7))) % 0.36/0.72 (define @t445 () (or @t150 @t444 @t443 @t442)) % 0.36/0.72 (define @t446 () (@list @t2 @t441)) % 0.36/0.72 (define @t447 () (forall @t446 @t445)) % 0.36/0.72 (define @t448 () (lambda @t87 @t447)) % 0.36/0.72 (define @t449 () (_ @t448 @t7)) % 0.36/0.72 (define @t450 () (forall @t87 @t449)) % 0.36/0.72 (define @t451 () (or @t444 @t443 @t442)) % 0.36/0.72 (define @t452 () (or @t150 @t451)) % 0.36/0.72 (define @t453 () (forall @t446 @t452)) % 0.36/0.72 (define @t454 () (@list @t441)) % 0.36/0.72 (define @t455 () (forall @t454 @t452)) % 0.36/0.72 (define @t456 () (forall @t454 @t451)) % 0.36/0.72 (define @t457 () (@var "BOUND_VARIABLE_11250" tptp.mu)) % 0.36/0.72 (define @t458 () (@list @t457)) % 0.36/0.72 (define @t459 () (or @t150 @t456)) % 0.36/0.72 (define @t460 () (@list @t457)) % 0.36/0.72 (define @t461 () (forall @t460 (or (not (tptp.exists_in_world @t457 @t7)) (not (tptp.subset @t2 @t457 @t7)) (tptp.qmltpeq (tptp.set_union2 @t2 @t457) @t457 @t7)))) % 0.36/0.72 (define @t462 () (tptp.set_union2 @t26 @t2)) % 0.36/0.72 (define @t463 () (forall @t5 (or @t177 (not (tptp.subset @t26 @t2 @t15)) (tptp.qmltpeq @t462 @t2 @t15)))) % 0.36/0.72 (define @t464 () (lambda @t32 @t463)) % 0.36/0.72 (define @t465 () (or @t150 (_ @t464 @t2 @t7))) % 0.36/0.72 (define @t466 () (forall @t5 @t465)) % 0.36/0.72 (define @t467 () (lambda @t87 @t466)) % 0.36/0.72 (define @t468 () (tptp.qmltpeq @t462 @t2 @t7)) % 0.36/0.72 (define @t469 () (tptp.subset @t26 @t2 @t7)) % 0.36/0.72 (define @t470 () (_ @t27 @t2)) % 0.36/0.72 (define @t471 () (_ (_ (_ tptp.qmltpeq @t470) @t2) @t7)) % 0.36/0.72 (define @t472 () (_ (_ @t46 @t2) @t7)) % 0.36/0.72 (define @t473 () (not @t472)) % 0.36/0.72 (define @t474 () (or @t150 @t473 @t471)) % 0.36/0.72 (define @t475 () (or @t473 @t471)) % 0.36/0.72 (define @t476 () (not (_ @t56 @t15))) % 0.36/0.72 (define @t477 () (or @t476 (_ @t55 @t15))) % 0.36/0.72 (define @t478 () (lambda @t31 @t477)) % 0.36/0.72 (define @t479 () (_ @t478 @t2 @t7)) % 0.36/0.72 (define @t480 () (or @t150 @t479)) % 0.36/0.72 (define @t481 () (forall @t5 @t480)) % 0.36/0.72 (define @t482 () (lambda @t87 @t481)) % 0.36/0.72 (define @t483 () (lambda @t238 @t477)) % 0.36/0.72 (define @t484 () (lambda @t242 (or @t476 @t240))) % 0.36/0.72 (define @t485 () (_ @t253 @t56)) % 0.36/0.72 (define @t486 () (lambda @t31 (_ (_ @t485 @t55) @t15))) % 0.36/0.72 (define @t487 () (tptp.unordered_pair @t10 @t9)) % 0.36/0.72 (define @t488 () (tptp.exists_in_world @t487 @t1)) % 0.36/0.72 (define @t489 () (tptp.subset @t289 @t285 @t282)) % 0.36/0.72 (define @t490 () (not @t489)) % 0.36/0.72 (define @t491 () (tptp.exists_in_world @t289 @t282)) % 0.36/0.72 (define @t492 () (not @t491)) % 0.36/0.72 (define @t493 () (or @t492 @t296 @t490 @t290)) % 0.36/0.72 (define @t494 () (or @t489 @t294 @t288)) % 0.36/0.72 (define @t495 () (not @t494)) % 0.36/0.72 (define @t496 () (and (or @t490 (and @t293 @t287)) @t494)) % 0.36/0.72 (define @t497 () (not @t496)) % 0.36/0.72 (define @t498 () (or @t297 @t292 @t296 @t496)) % 0.36/0.72 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.36/0.72 (assume @p2 (forall @t6 (exists @t5 @t4))) % 0.36/0.72 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 0.36/0.72 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 0.36/0.72 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 0.36/0.72 (assume @p6 @t14) % 0.36/0.72 (assume @p7 (forall @t13 (_ (_ tptp.exists_in_world (_ (_ tptp.set_union2 @t10) @t9)) @t1))) % 0.36/0.72 (assume @p8 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ @t16 @t2) @t15))))) % 0.36/0.72 (assume @p9 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t21 (_ (_ (_ tptp.mimplies @t20) (_ @t19 @t2)) @t15))) @t15))))) % 0.36/0.72 (assume @p10 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t21 (_ (_ tptp.mforall_ind (lambda (@list @t22 @t15) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t20) (_ @t19 @t22))) (_ @t16 @t22)) @t15))) @t15))) @t15))))) % 0.36/0.72 (assume @p11 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ @t29 (_ (_ tptp.qmltpeq (_ @t27 @t23)) (_ @t25 @t23))) @t15))) @t15))) @t15))))) % 0.36/0.72 (assume @p12 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ @t29 (_ (_ tptp.qmltpeq (_ @t33 @t26)) (_ @t33 @t24))) @t15))) @t15))) @t15))))) % 0.36/0.72 (assume @p13 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ @t29 (_ (_ tptp.qmltpeq @t36) (_ @t34 @t23))) @t15))) @t15))) @t15))))) % 0.36/0.72 (assume @p14 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ @t29 (_ (_ tptp.qmltpeq (_ @t37 @t26)) (_ @t37 @t24))) @t15))) @t15))) @t15))))) % 0.36/0.72 (assume @p15 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ (_ tptp.mimplies (_ @t39 @t38)) (_ tptp.empty @t24)) @t15))) @t15))))) % 0.36/0.72 (assume @p16 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ (_ tptp.mimplies (_ @t39 @t43)) @t41) @t15))) @t15))) @t15))))) % 0.36/0.72 (assume @p17 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ (_ tptp.mimplies (_ @t39 (_ @t44 @t26))) @t45) @t15))) @t15))) @t15))))) % 0.36/0.72 (assume @p18 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ (_ tptp.mimplies (_ @t39 (_ @t46 @t23))) (_ (_ tptp.subset @t24) @t23)) @t15))) @t15))) @t15))))) % 0.36/0.72 (assume @p19 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ (_ tptp.mimplies (_ @t39 (_ @t47 @t26))) (_ @t47 @t24)) @t15))) @t15))) @t15))))) % 0.36/0.72 (assume @p20 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ (_ tptp.mimplies @t48) (_ tptp.mnot (_ @t40 @t26))) @t15))) @t15))))) % 0.36/0.72 (assume @p21 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ (_ tptp.qmltpeq @t49) (_ @t34 @t26)) @t15))) @t15))))) % 0.36/0.72 (assume @p22 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ @t52 @t50) @t15))) @t15))))) % 0.36/0.72 (assume @p23 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ @t54 (_ tptp.mnot (_ tptp.empty @t51))) @t15))) @t15))))) % 0.36/0.72 (assume @p24 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ @t54 (_ tptp.mnot (_ tptp.empty @t50))) @t15))) @t15))))) % 0.36/0.72 (assume @p25 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ (_ tptp.qmltpeq (_ @t27 @t26)) @t26) @t15))) @t15))))) % 0.36/0.72 (assume @p26 (_ tptp.mvalid (_ tptp.mexists_ind (lambda @t32 (_ @t38 @t15))))) % 0.36/0.72 (assume @p27 (_ tptp.mvalid (_ tptp.mexists_ind (lambda @t32 (_ @t53 @t15))))) % 0.36/0.72 (assume @p28 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t32 (_ (_ tptp.mforall_ind (lambda @t31 (_ (_ @t46 @t26) @t15))) @t15))))) % 0.36/0.72 (assume @p29 (_ tptp.mvalid (_ tptp.mforall_ind @t58))) % 0.36/0.72 (assume @p30 (_ tptp.mvalid (_ tptp.mforall_ind @t63))) % 0.36/0.72 (assume @p31 @t68) % 0.36/0.72 (assume @p32 true) % 0.36/0.72 (step @p33 (= tptp.meq_prop @t71) :rule refl :args (@t71)) % 0.36/0.72 (step @p34 (= tptp.mnot @t76) :rule refl :args (@t76)) % 0.36/0.72 (step @p35 (= tptp.mor @t79) :rule refl :args (@t79)) % 0.36/0.72 (step @p36 (= tptp.mbox @t82) :rule refl :args (@t82)) % 0.36/0.72 (step @p37 (= tptp.mforall_prop @t86) :rule refl :args (@t86)) % 0.36/0.72 (step @p38 (= tptp.mtrue @t88) :rule refl :args (@t88)) % 0.36/0.72 (step @p39 (= tptp.mand @t93) :rule refl :args (@t93)) % 0.36/0.72 (step @p40 (= tptp.mimplies @t94) :rule refl :args (@t94)) % 0.36/0.72 (step @p41 (= tptp.mimplied @t95) :rule refl :args (@t95)) % 0.36/0.72 (step @p42 (= tptp.mequiv @t96) :rule refl :args (@t96)) % 0.36/0.72 (step @p43 (= tptp.mxor @t97) :rule refl :args (@t97)) % 0.36/0.72 (step @p44 (= tptp.mdia @t98) :rule refl :args (@t98)) % 0.36/0.72 (step @p45 (= tptp.mforall_ind @t104) :rule refl :args (@t104)) % 0.36/0.72 (step @p46 (= tptp.mexists_ind @t105) :rule refl :args (@t105)) % 0.36/0.72 (step @p47 (= tptp.mexists_prop @t106) :rule refl :args (@t106)) % 0.36/0.72 (step @p48 (= tptp.mreflexive @t111) :rule refl :args (@t111)) % 0.36/0.72 (step @p49 (= tptp.msymmetric @t115) :rule refl :args (@t115)) % 0.36/0.72 (step @p50 (= tptp.mserial @t117) :rule refl :args (@t117)) % 0.36/0.72 (step @p51 (= tptp.mtransitive @t122) :rule refl :args (@t122)) % 0.36/0.72 (step @p52 (= tptp.meuclidean @t124) :rule refl :args (@t124)) % 0.36/0.72 (step @p53 (= tptp.mpartially_functional @t126) :rule refl :args (@t126)) % 0.36/0.72 (step @p54 (= tptp.mfunctional @t128) :rule refl :args (@t128)) % 0.36/0.72 (step @p55 (= tptp.mweakly_dense @t131) :rule refl :args (@t131)) % 0.36/0.72 (step @p56 (= tptp.mweakly_connected @t132) :rule refl :args (@t132)) % 0.36/0.72 (step @p57 (= tptp.mweakly_directed @t133) :rule refl :args (@t133)) % 0.36/0.72 (step @p58 (= tptp.mvalid @t136) :rule refl :args (@t136)) % 0.36/0.72 (step @p59 (= tptp.msatisfiable @t137) :rule refl :args (@t137)) % 0.36/0.72 (step @p60 (= tptp.mcountersatisfiable @t138) :rule refl :args (@t138)) % 0.36/0.72 (step @p61 (= tptp.minvalid @t139) :rule refl :args (@t139)) % 0.36/0.72 (step @p62 (= tptp.mbox_s4 @t140) :rule refl :args (@t140)) % 0.36/0.72 (step @p63 (= tptp.mdia_s4 @t141) :rule refl :args (@t141)) % 0.36/0.72 (step @p64 :rule quant-merge-prenex :args ((= (forall @t87 @t154) @t152))) % 0.36/0.72 (step @p65 :rule beta-reduce :args ((= @t156 @t154))) % 0.36/0.72 (step @p66 :rule cong :premises (@p65) :args (@t157)) % 0.36/0.72 (step @p67 :rule trans :premises (@p66 @p64)) % 0.36/0.72 (step @p68 :rule beta-reduce :args ((= (_ @t159 @t155) @t157))) % 0.36/0.72 (step @p69 :rule trans :premises (@p68 @p67)) % 0.36/0.72 (step @p70 :rule aci_norm :args ((= @t161 @t151))) % 0.36/0.72 (step @p71 :rule cong :premises (@p70) :args (@t162)) % 0.36/0.72 (step @p72 :rule quant-merge-prenex :args ((= (forall @t5 @t164) @t162))) % 0.36/0.72 (step @p73 :rule alpha_equiv :args (@t165 (@list @t142 @t143) (@list @t167 @t166))) % 0.36/0.72 (step @p74 :rule refl :args (@t150)) % 0.36/0.72 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t168)) % 0.36/0.72 (step @p76 :rule quant-miniscope-or :args ((= @t164 @t168))) % 0.36/0.72 (step @p77 :rule trans :premises (@p76 @p75)) % 0.36/0.72 (step @p78 :rule symm :premises (@p77)) % 0.36/0.72 (step @p79 :rule cong :premises (@p78) :args ((forall @t5 (or @t150 @t171)))) % 0.36/0.72 (step @p80 :rule trans :premises (@p79 @p72)) % 0.36/0.72 (step @p81 :rule trans :premises (@p80 @p71)) % 0.36/0.72 (step @p82 :rule beta-reduce :args ((= (_ (lambda @t32 (forall @t170 (or (not (tptp.exists_in_world @t167 @t15)) (not (tptp.in @t26 @t167 @t15)) @t173 (tptp.qmltpeq (tptp.set_union2 @t172 @t167) @t167 @t15) (not (tptp.in @t166 @t167 @t15))))) @t2 @t7) @t171))) % 0.36/0.72 (step @p83 :rule refl :args (@t7)) % 0.36/0.72 (step @p84 :rule refl :args (@t2)) % 0.36/0.72 (step @p85 :rule alpha_equiv :args (@t179 @t180 (@list @t167))) % 0.36/0.72 (step @p86 :rule cong :premises (@p85) :args (@t181)) % 0.36/0.72 (step @p87 :rule ho_cong :premises (@p86 @p84 @p83)) % 0.36/0.72 (step @p88 :rule trans :premises (@p87 @p82)) % 0.36/0.72 (step @p89 :rule refl :args (@t150)) % 0.36/0.72 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t182)) % 0.36/0.72 (step @p91 :rule cong :premises (@p90) :args (@t183)) % 0.36/0.72 (step @p92 :rule trans :premises (@p91 @p81)) % 0.36/0.72 (step @p93 :rule cong :premises (@p92) :args (@t184)) % 0.36/0.72 (step @p94 :rule beta-reduce :args ((= (_ @t186 @t181) @t184))) % 0.36/0.72 (step @p95 :rule trans :premises (@p94 @p93)) % 0.36/0.72 (step @p96 :rule beta-reduce :args ((= (_ (lambda @t87 (forall @t178 @t191)) @t15) @t179))) % 0.36/0.72 (step @p97 :rule refl :args (@t15)) % 0.36/0.72 (step @p98 :rule aci_norm :args ((= @t193 @t191))) % 0.36/0.72 (step @p99 :rule cong :premises (@p98) :args (@t194)) % 0.36/0.72 (step @p100 :rule quant-merge-prenex :args ((= (forall @t5 @t196) @t194))) % 0.36/0.72 (step @p101 :rule alpha_equiv :args (@t197 (@list @t166) @t199)) % 0.36/0.72 (step @p102 :rule refl :args (@t190)) % 0.36/0.72 (step @p103 :rule nary_cong :premises (@p74 @p102 @p101) :args (@t200)) % 0.36/0.72 (step @p104 :rule quant-miniscope-or :args ((= @t196 @t200))) % 0.36/0.72 (step @p105 :rule trans :premises (@p104 @p103)) % 0.36/0.72 (step @p106 :rule symm :premises (@p105)) % 0.36/0.72 (step @p107 :rule cong :premises (@p106) :args ((forall @t5 (or @t150 @t190 @t203)))) % 0.36/0.72 (step @p108 :rule trans :premises (@p107 @p100)) % 0.36/0.72 (step @p109 :rule trans :premises (@p108 @p99)) % 0.36/0.72 (step @p110 :rule refl :args (@t203)) % 0.36/0.72 (step @p111 :rule refl :args (@t189)) % 0.36/0.72 (step @p112 :rule refl :args (@t204)) % 0.36/0.72 (step @p113 :rule cong :premises (@p112 @p111) :args ((= @t204 @t189))) % 0.36/0.72 (step @p114 :rule symm :premises (@p113)) % 0.36/0.72 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 0.36/0.72 (step @p116 :rule cong :premises (@p115) :args (@t205)) % 0.36/0.72 (step @p117 :rule nary_cong :premises (@p74 @p116 @p110) :args (@t206)) % 0.36/0.72 (step @p118 :rule cong :premises (@p117) :args ((forall @t5 @t206))) % 0.36/0.72 (step @p119 :rule trans :premises (@p118 @p109)) % 0.36/0.72 (step @p120 :rule aci_norm :args ((= (or @t150 @t207) @t206))) % 0.36/0.72 (step @p121 :rule beta-reduce :args ((= (_ (lambda @t31 (or @t208 (forall @t202 (or (not (tptp.exists_in_world @t198 @t15)) (tptp.qmltpeq (tptp.set_union2 @t201 @t24) @t24 @t15) (not (tptp.in @t198 @t24 @t15)))))) @t2 @t7) @t207))) % 0.36/0.72 (step @p122 :rule alpha_equiv :args (@t211 @t180 @t199)) % 0.36/0.72 (step @p123 :rule refl :args (@t208)) % 0.36/0.72 (step @p124 :rule nary_cong :premises (@p123 @p122) :args (@t212)) % 0.36/0.72 (step @p125 :rule cong :premises (@p124) :args (@t213)) % 0.36/0.72 (step @p126 :rule ho_cong :premises (@p125 @p84 @p83)) % 0.36/0.72 (step @p127 :rule trans :premises (@p126 @p121)) % 0.36/0.72 (step @p128 :rule nary_cong :premises (@p89 @p127) :args (@t214)) % 0.36/0.72 (step @p129 :rule trans :premises (@p128 @p120)) % 0.36/0.72 (step @p130 :rule cong :premises (@p129) :args (@t215)) % 0.36/0.72 (step @p131 :rule trans :premises (@p130 @p119)) % 0.36/0.72 (step @p132 :rule cong :premises (@p131) :args (@t216)) % 0.36/0.72 (step @p133 :rule beta-reduce :args ((= (_ @t186 @t213) @t216))) % 0.36/0.72 (step @p134 :rule trans :premises (@p133 @p132)) % 0.36/0.72 (step @p135 :rule beta-reduce :args ((= (_ (lambda @t87 (or @t219 (forall @t5 (or @t150 @t218 (not @t217))))) @t15) @t212))) % 0.36/0.72 (step @p136 :rule refl :args (@t217)) % 0.36/0.72 (step @p137 :rule refl :args (@t220)) % 0.36/0.72 (step @p138 :rule cong :premises (@p137 @p136) :args ((= @t220 @t217))) % 0.36/0.72 (step @p139 :rule symm :premises (@p138)) % 0.36/0.72 (step @p140 :rule eq_resolve :premises (@p137 @p139)) % 0.36/0.72 (step @p141 :rule cong :premises (@p140) :args (@t221)) % 0.36/0.72 (step @p142 :rule refl :args ((tptp.qmltpeq @t223 @t24 @t7))) % 0.36/0.72 (step @p143 :rule refl :args (@t24)) % 0.36/0.72 (step @p144 :rule refl :args ((tptp.set_union2 @t222 @t24))) % 0.36/0.72 (step @p145 :rule refl :args (@t209)) % 0.36/0.72 (step @p146 :rule cong :premises (@p145 @p143) :args (@t210)) % 0.36/0.72 (step @p147 :rule trans :premises (@p146 @p144)) % 0.36/0.72 (step @p148 :rule cong :premises (@p147 @p143 @p83) :args (@t218)) % 0.36/0.72 (step @p149 :rule trans :premises (@p148 @p142)) % 0.36/0.72 (step @p150 :rule refl :args (tptp.qmltpeq)) % 0.36/0.72 (step @p151 :rule ho_cong :premises (@p150 @p147)) % 0.36/0.72 (step @p152 :rule ho_cong :premises (@p151 @p143)) % 0.36/0.72 (step @p153 :rule ho_cong :premises (@p152 @p83)) % 0.36/0.72 (step @p154 :rule cong :premises (@p153 @p149) :args ((= (_ (_ (_ tptp.qmltpeq @t210) @t24) @t7) @t218))) % 0.36/0.72 (step @p155 :rule symm :premises (@p154)) % 0.36/0.72 (step @p156 :rule refl :args (@t224)) % 0.36/0.72 (step @p157 :rule eq_resolve :premises (@p156 @p155)) % 0.36/0.72 (step @p158 :rule refl :args (tptp.set_union2)) % 0.36/0.72 (step @p159 :rule ho_cong :premises (@p158 @p145)) % 0.36/0.72 (step @p160 :rule ho_cong :premises (@p159 @p143)) % 0.36/0.72 (step @p161 :rule cong :premises (@p160 @p147) :args ((= (_ (_ tptp.set_union2 @t209) @t24) @t210))) % 0.36/0.72 (step @p162 :rule symm :premises (@p161)) % 0.36/0.72 (step @p163 :rule refl :args (@t223)) % 0.36/0.72 (step @p164 :rule eq_resolve :premises (@p163 @p162)) % 0.36/0.72 (step @p165 :rule refl :args (@t222)) % 0.36/0.72 (step @p166 :rule cong :premises (@p165 @p145) :args ((= @t222 @t209))) % 0.36/0.72 (step @p167 :rule symm :premises (@p166)) % 0.36/0.72 (step @p168 :rule eq_resolve :premises (@p165 @p167)) % 0.36/0.72 (step @p169 :rule ho_cong :premises (@p158 @p168)) % 0.36/0.72 (step @p170 :rule ho_cong :premises (@p169 @p143)) % 0.36/0.72 (step @p171 :rule trans :premises (@p170 @p164)) % 0.36/0.72 (step @p172 :rule ho_cong :premises (@p150 @p171)) % 0.36/0.72 (step @p173 :rule ho_cong :premises (@p172 @p143)) % 0.36/0.72 (step @p174 :rule ho_cong :premises (@p173 @p83)) % 0.36/0.72 (step @p175 :rule trans :premises (@p174 @p157)) % 0.36/0.72 (step @p176 :rule nary_cong :premises (@p74 @p175 @p141) :args (@t225)) % 0.36/0.72 (step @p177 :rule cong :premises (@p176) :args (@t226)) % 0.36/0.72 (step @p178 :rule refl :args (@t219)) % 0.36/0.72 (step @p179 :rule nary_cong :premises (@p178 @p177) :args (@t227)) % 0.36/0.72 (step @p180 :rule quant-miniscope-or :args ((= (forall @t5 @t228) @t227))) % 0.36/0.72 (step @p181 :rule aci_norm :args ((= @t229 @t228))) % 0.36/0.72 (step @p182 :rule cong :premises (@p181) :args ((forall @t5 @t229))) % 0.36/0.72 (step @p183 :rule trans :premises (@p182 @p180)) % 0.36/0.72 (step @p184 :rule trans :premises (@p183 @p179)) % 0.36/0.72 (step @p185 :rule aci_norm :args ((= (or @t150 @t230) @t229))) % 0.36/0.72 (step @p186 :rule beta-reduce :args ((= @t234 @t230))) % 0.36/0.72 (step @p187 :rule nary_cong :premises (@p89 @p186) :args (@t235)) % 0.36/0.72 (step @p188 :rule trans :premises (@p187 @p185)) % 0.36/0.72 (step @p189 :rule cong :premises (@p188) :args (@t236)) % 0.36/0.72 (step @p190 :rule trans :premises (@p189 @p184)) % 0.36/0.72 (step @p191 :rule cong :premises (@p190) :args (@t237)) % 0.36/0.72 (step @p192 :rule beta-reduce :args ((= (_ @t186 @t233) @t237))) % 0.36/0.72 (step @p193 :rule trans :premises (@p192 @p191)) % 0.36/0.72 (step @p194 :rule beta-reduce :args ((= (_ @t239 @t15) @t232))) % 0.36/0.72 (step @p195 :rule beta-reduce :args ((= (_ (lambda @t242 @t241) @t64) @t239))) % 0.36/0.72 (step @p196 :rule refl :args (@t64)) % 0.36/0.72 (step @p197 :rule aci_norm :args ((= (or @t243 @t240) @t241))) % 0.36/0.72 (step @p198 :rule refl :args (@t240)) % 0.36/0.72 (step @p199 :rule bool-double-not-elim :args (@t243)) % 0.36/0.72 (step @p200 :rule beta-reduce :args ((= @t246 @t244))) % 0.36/0.72 (step @p201 :rule cong :premises (@p200) :args (@t247)) % 0.36/0.72 (step @p202 :rule trans :premises (@p201 @p199)) % 0.36/0.72 (step @p203 :rule nary_cong :premises (@p202 @p198) :args (@t248)) % 0.36/0.72 (step @p204 :rule trans :premises (@p203 @p197)) % 0.36/0.72 (step @p205 :rule cong :premises (@p204) :args (@t249)) % 0.36/0.72 (step @p206 :rule beta-reduce :args ((= (_ @t253 @t245) @t249))) % 0.36/0.72 (step @p207 :rule trans :premises (@p206 @p205)) % 0.36/0.72 (step @p208 :rule beta-reduce :args ((= (_ @t255 @t45) @t245))) % 0.36/0.72 (step @p209 :rule refl :args (@t45)) % 0.36/0.72 (step @p210 :rule beta-reduce :args ((= @t258 @t255))) % 0.36/0.72 (step @p211 :rule ho_cong :premises (@p210 @p209)) % 0.36/0.72 (step @p212 :rule trans :premises (@p211 @p208)) % 0.36/0.72 (step @p213 :rule refl :args (@t253)) % 0.36/0.72 (step @p214 :rule ho_cong :premises (@p213 @p212)) % 0.36/0.72 (step @p215 :rule trans :premises (@p214 @p207)) % 0.36/0.72 (step @p216 :rule ho_cong :premises (@p215 @p196)) % 0.36/0.72 (step @p217 :rule trans :premises (@p216 @p195)) % 0.36/0.72 (step @p218 :rule ho_cong :premises (@p217 @p97)) % 0.36/0.72 (step @p219 :rule trans :premises (@p218 @p194)) % 0.36/0.72 (step @p220 :rule cong :premises (@p219) :args (@t259)) % 0.36/0.72 (step @p221 :rule refl :args (@t186)) % 0.36/0.72 (step @p222 :rule ho_cong :premises (@p221 @p220)) % 0.36/0.72 (step @p223 :rule trans :premises (@p222 @p193)) % 0.36/0.72 (step @p224 :rule ho_cong :premises (@p223 @p97)) % 0.36/0.72 (step @p225 :rule trans :premises (@p224 @p135)) % 0.36/0.72 (step @p226 :rule cong :premises (@p225) :args (@t260)) % 0.36/0.72 (step @p227 :rule ho_cong :premises (@p221 @p226)) % 0.36/0.72 (step @p228 :rule trans :premises (@p227 @p134)) % 0.36/0.72 (step @p229 :rule ho_cong :premises (@p228 @p97)) % 0.36/0.72 (step @p230 :rule trans :premises (@p229 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((or @t297 @t296 @t292 @t496 (not @t498)))) % 0.36/0.72 (step @p719 false :rule chain_m_resolution :premises (@p718 @p716 @p575 @p353 @p347 @p341) :args (false (@list true false false false false) (@list @t496 @t498 @t291 @t295 @t284))) % 0.36/0.72 ) % 0.36/0.72 % SZS output end Proof % 0.36/0.72 % cvc5 exiting %------------------------------------------------------------------------------