%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PLA032^7 : 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 : n025.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:43:27 AM UTC 2026 % Result : Theorem 0.43s 0.63s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : PLA032^7 : TPTP v9.2.1. Released v5.5.0. % 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n025.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 13:00:01 EDT 2026 % 0.15/0.33 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.43/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.43/0.63 % SZS status Theorem % 0.43/0.63 % SZS output start Proof % 0.43/0.63 ( % 0.43/0.63 (declare-sort $$unsorted 0) % 0.43/0.63 (declare-sort tptp.mu 0) % 0.43/0.63 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.defused (-> tptp.mu $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.h (-> tptp.mu $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.bomb (-> tptp.mu $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.43/0.63 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.43/0.63 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.43/0.63 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.43/0.63 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.43/0.63 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.43/0.63 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.43/0.63 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.43/0.63 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.43/0.63 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.43/0.63 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.43/0.63 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.43/0.63 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.43/0.63 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.exists_in_world _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.43/0.63 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.43/0.63 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.43/0.63 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.43/0.63 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.43/0.63 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.43/0.63 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.43/0.63 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.43/0.63 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.43/0.63 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.43/0.63 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.43/0.63 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.43/0.63 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.43/0.63 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.43/0.63 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.43/0.63 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.43/0.63 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.43/0.63 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.43/0.63 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.43/0.63 (define @t1 () (@var "V" $$unsorted)) % 0.43/0.63 (define @t2 () (@var "X" tptp.mu)) % 0.43/0.63 (define @t3 () (_ tptp.exists_in_world @t2)) % 0.43/0.63 (define @t4 () (_ @t3 @t1)) % 0.43/0.63 (define @t5 () (@list @t2)) % 0.43/0.63 (define @t6 () (@list @t1)) % 0.43/0.63 (define @t7 () (@var "W" $$unsorted)) % 0.43/0.63 (define @t8 () (_ @t3 @t7)) % 0.43/0.63 (define @t9 () (@var "__flatten_var_0" $$unsorted)) % 0.43/0.63 (define @t10 () (@var "B" tptp.mu)) % 0.43/0.63 (define @t11 () (_ tptp.bomb @t2)) % 0.43/0.63 (define @t12 () (@var "A" tptp.mu)) % 0.43/0.63 (define @t13 () (_ tptp.mand @t11)) % 0.43/0.63 (define @t14 () (@list @t2 @t9)) % 0.43/0.63 (define @t15 () (_ tptp.defused @t2)) % 0.43/0.63 (define @t16 () (@var "D" tptp.mu)) % 0.43/0.63 (define @t17 () (_ tptp.h @t16)) % 0.43/0.63 (define @t18 () (_ (_ tptp.mimplies (_ @t13 @t17)) @t15)) % 0.43/0.63 (define @t19 () (@list @t16 @t9)) % 0.43/0.63 (define @t20 () (lambda @t19 (_ (_ tptp.mbox_s4 @t18) @t9))) % 0.43/0.63 (define @t21 () (lambda @t14 (_ (_ tptp.mexists_ind @t20) @t9))) % 0.43/0.63 (define @t22 () (lambda @t19 (_ @t18 @t9))) % 0.43/0.63 (define @t23 () (lambda @t14 (_ (_ tptp.mexists_ind @t22) @t9))) % 0.43/0.63 (define @t24 () (not (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind @t23))))) % 0.43/0.63 (define @t25 () (@var "Y" (-> $$unsorted Bool))) % 0.43/0.63 (define @t26 () (@var "X" (-> $$unsorted Bool))) % 0.43/0.63 (define @t27 () (lambda (@list @t26 @t25 @t7) (= (_ @t26 @t7) (_ @t25 @t7)))) % 0.43/0.63 (define @t28 () (@var "Phi" (-> $$unsorted Bool))) % 0.43/0.63 (define @t29 () (_ @t28 @t7)) % 0.43/0.63 (define @t30 () (not @t29)) % 0.43/0.63 (define @t31 () (@list @t28 @t7)) % 0.43/0.63 (define @t32 () (lambda @t31 @t30)) % 0.43/0.63 (define @t33 () (@var "Psi" (-> $$unsorted Bool))) % 0.43/0.63 (define @t34 () (_ @t33 @t7)) % 0.43/0.63 (define @t35 () (lambda (@list @t28 @t33 @t7) (or @t29 @t34))) % 0.43/0.63 (define @t36 () (_ @t28 @t1)) % 0.43/0.63 (define @t37 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.43/0.63 (define @t38 () (lambda (@list @t37 @t28 @t7) (forall @t6 (or (not (_ (_ @t37 @t7) @t1)) @t36)))) % 0.43/0.63 (define @t39 () (@var "P" (-> $$unsorted Bool))) % 0.43/0.63 (define @t40 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.43/0.63 (define @t41 () (_ @t40 @t39)) % 0.43/0.63 (define @t42 () (lambda (@list @t40 @t7) (forall (@list @t39) (_ @t41 @t7)))) % 0.43/0.63 (define @t43 () (@list @t7)) % 0.43/0.63 (define @t44 () (lambda @t43 true)) % 0.43/0.63 (define @t45 () (_ tptp.mnot @t33)) % 0.43/0.63 (define @t46 () (_ tptp.mnot @t28)) % 0.43/0.63 (define @t47 () (_ tptp.mor @t46)) % 0.43/0.63 (define @t48 () (@list @t28 @t33 @t9)) % 0.43/0.63 (define @t49 () (lambda @t48 (_ (_ tptp.mnot (_ @t47 @t45)) @t9))) % 0.43/0.63 (define @t50 () (lambda @t48 (_ (_ @t47 @t33) @t9))) % 0.43/0.63 (define @t51 () (lambda @t48 (_ (_ (_ tptp.mor @t45) @t28) @t9))) % 0.43/0.63 (define @t52 () (lambda @t48 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t28) @t33)) (_ (_ tptp.mimplies @t33) @t28)) @t9))) % 0.43/0.63 (define @t53 () (lambda @t48 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t28) @t33)) @t9))) % 0.43/0.63 (define @t54 () (lambda (@list @t37 @t28 @t9) (_ (_ tptp.mnot (_ (_ tptp.mbox @t37) @t46)) @t9))) % 0.43/0.63 (define @t55 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.43/0.63 (define @t56 () (_ @t55 @t2)) % 0.43/0.63 (define @t57 () (_ @t56 @t7)) % 0.43/0.63 (define @t58 () (forall @t5 (=> @t8 @t57))) % 0.43/0.63 (define @t59 () (@list @t55 @t7)) % 0.43/0.63 (define @t60 () (lambda @t59 @t58)) % 0.43/0.63 (define @t61 () (lambda @t14 (_ (_ tptp.mnot @t56) @t9))) % 0.43/0.63 (define @t62 () (@list @t55 @t9)) % 0.43/0.63 (define @t63 () (lambda @t62 (_ (_ tptp.mnot (_ tptp.mforall_ind @t61)) @t9))) % 0.43/0.63 (define @t64 () (lambda (@list @t40 @t9) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t39 @t9) (_ (_ tptp.mnot @t41) @t9)))) @t9))) % 0.43/0.63 (define @t65 () (@var "S" $$unsorted)) % 0.43/0.63 (define @t66 () (_ @t37 @t65)) % 0.43/0.63 (define @t67 () (_ @t66 @t65)) % 0.43/0.63 (define @t68 () (@list @t65)) % 0.43/0.63 (define @t69 () (forall @t68 @t67)) % 0.43/0.63 (define @t70 () (@list @t37)) % 0.43/0.63 (define @t71 () (lambda @t70 @t69)) % 0.43/0.63 (define @t72 () (@var "T" $$unsorted)) % 0.43/0.63 (define @t73 () (_ @t37 @t72)) % 0.43/0.63 (define @t74 () (_ @t66 @t72)) % 0.43/0.63 (define @t75 () (lambda @t70 (forall (@list @t65 @t72) (=> @t74 (_ @t73 @t65))))) % 0.43/0.63 (define @t76 () (@list @t72)) % 0.43/0.63 (define @t77 () (lambda @t70 (forall @t68 (exists @t76 @t74)))) % 0.43/0.63 (define @t78 () (@var "U" $$unsorted)) % 0.43/0.63 (define @t79 () (_ @t66 @t78)) % 0.43/0.63 (define @t80 () (_ @t73 @t78)) % 0.43/0.63 (define @t81 () (@list @t65 @t72 @t78)) % 0.43/0.63 (define @t82 () (lambda @t70 (forall @t81 (=> (and @t74 @t80) @t79)))) % 0.43/0.63 (define @t83 () (and @t74 @t79)) % 0.43/0.63 (define @t84 () (lambda @t70 (forall @t81 (=> @t83 @t80)))) % 0.43/0.63 (define @t85 () (= @t72 @t78)) % 0.43/0.63 (define @t86 () (lambda @t70 (forall @t81 (=> @t83 @t85)))) % 0.43/0.63 (define @t87 () (@list @t78)) % 0.43/0.63 (define @t88 () (lambda @t70 (forall @t68 (exists @t76 (and @t74 (forall @t87 (=> @t79 @t85))))))) % 0.43/0.63 (define @t89 () (_ @t37 @t78)) % 0.43/0.63 (define @t90 () (_ @t89 @t72)) % 0.43/0.63 (define @t91 () (lambda @t70 (forall @t81 (=> @t74 (exists @t87 (and @t79 @t90)))))) % 0.43/0.63 (define @t92 () (lambda @t70 (forall @t81 (=> @t83 (or @t80 @t85 @t90))))) % 0.43/0.63 (define @t93 () (lambda @t70 (forall @t81 (=> @t83 (exists @t6 (and (_ @t73 @t1) (_ @t89 @t1))))))) % 0.43/0.63 (define @t94 () (forall @t43 @t29)) % 0.43/0.63 (define @t95 () (@list @t28)) % 0.43/0.63 (define @t96 () (lambda @t95 @t94)) % 0.43/0.63 (define @t97 () (lambda @t95 (exists @t43 @t29))) % 0.43/0.63 (define @t98 () (lambda @t95 (exists @t43 @t30))) % 0.43/0.63 (define @t99 () (lambda @t95 (forall @t43 @t30))) % 0.43/0.63 (define @t100 () (_ (_ tptp.rel_s4 @t7) @t1)) % 0.43/0.63 (define @t101 () (not @t100)) % 0.43/0.63 (define @t102 () (or @t101 @t36)) % 0.43/0.63 (define @t103 () (forall @t6 @t102)) % 0.43/0.63 (define @t104 () (lambda @t31 @t103)) % 0.43/0.63 (define @t105 () (lambda (@list @t28 @t9) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t46)) @t9))) % 0.43/0.63 (define @t106 () (forall @t68 (tptp.rel_s4 @t65 @t65))) % 0.43/0.63 (define @t107 () (_ @t37 @t65 @t65)) % 0.43/0.63 (define @t108 () (@var "BOUND_VARIABLE_8790" $$unsorted)) % 0.43/0.63 (define @t109 () (@var "BOUND_VARIABLE_8739" tptp.mu)) % 0.43/0.63 (define @t110 () (not (tptp.h @t109 @t108))) % 0.43/0.63 (define @t111 () (@var "BOUND_VARIABLE_8824" tptp.mu)) % 0.43/0.63 (define @t112 () (not (tptp.rel_s4 @t1 @t108))) % 0.43/0.63 (define @t113 () (@list @t108)) % 0.43/0.63 (define @t114 () (not (tptp.exists_in_world @t109 @t1))) % 0.43/0.63 (define @t115 () (@list @t109)) % 0.43/0.63 (define @t116 () (not (forall @t115 (or @t114 (not (forall @t113 (or @t112 (tptp.defused @t111 @t108) (not (tptp.bomb @t111 @t108)) @t110))))))) % 0.43/0.63 (define @t117 () (not (tptp.exists_in_world @t111 @t1))) % 0.43/0.63 (define @t118 () (tptp.rel_s4 @t7 @t1)) % 0.43/0.63 (define @t119 () (not @t118)) % 0.43/0.63 (define @t120 () (or @t119 @t117 @t116)) % 0.43/0.63 (define @t121 () (@list @t1 @t111)) % 0.43/0.63 (define @t122 () (forall @t121 @t120)) % 0.43/0.63 (define @t123 () (lambda @t43 @t122)) % 0.43/0.63 (define @t124 () (_ @t123 @t7)) % 0.43/0.63 (define @t125 () (forall @t43 @t124)) % 0.43/0.63 (define @t126 () (_ @t28 @t7)) % 0.43/0.63 (define @t127 () (lambda @t95 (forall @t43 @t126))) % 0.43/0.63 (define @t128 () (or @t117 @t116)) % 0.43/0.63 (define @t129 () (or @t119 @t128)) % 0.43/0.63 (define @t130 () (forall @t121 @t129)) % 0.43/0.63 (define @t131 () (@list @t111)) % 0.43/0.63 (define @t132 () (forall @t131 @t129)) % 0.43/0.63 (define @t133 () (forall @t131 @t128)) % 0.43/0.63 (define @t134 () (@list @t2)) % 0.43/0.63 (define @t135 () (or @t119 @t133)) % 0.43/0.63 (define @t136 () (not (tptp.bomb @t2 @t108))) % 0.43/0.63 (define @t137 () (tptp.defused @t2 @t108)) % 0.43/0.63 (define @t138 () (not (tptp.exists_in_world @t2 @t1))) % 0.43/0.63 (define @t139 () (forall @t5 (or @t138 (not (forall @t115 (or @t114 (not (forall @t113 (or @t112 @t137 @t136 @t110))))))))) % 0.43/0.63 (define @t140 () (not (tptp.exists_in_world @t109 @t7))) % 0.43/0.63 (define @t141 () (tptp.exists_in_world @t2 @t7)) % 0.43/0.63 (define @t142 () (not @t141)) % 0.43/0.63 (define @t143 () (not (tptp.h @t109 @t1))) % 0.43/0.63 (define @t144 () (tptp.bomb @t2 @t1)) % 0.43/0.63 (define @t145 () (not @t144)) % 0.43/0.63 (define @t146 () (tptp.defused @t2 @t1)) % 0.43/0.63 (define @t147 () (forall @t6 (or @t119 @t146 @t145 @t143))) % 0.43/0.63 (define @t148 () (not @t147)) % 0.43/0.63 (define @t149 () (or @t140 @t148)) % 0.43/0.63 (define @t150 () (forall @t115 @t149)) % 0.43/0.63 (define @t151 () (not @t150)) % 0.43/0.63 (define @t152 () (or @t142 @t151)) % 0.43/0.63 (define @t153 () (forall @t5 @t152)) % 0.43/0.63 (define @t154 () (lambda @t43 @t153)) % 0.43/0.63 (define @t155 () (or @t119 (_ @t154 @t1))) % 0.43/0.63 (define @t156 () (forall @t6 @t155)) % 0.43/0.63 (define @t157 () (lambda @t43 @t156)) % 0.43/0.63 (define @t158 () (_ @t28 @t1)) % 0.43/0.63 (define @t159 () (lambda @t31 (forall @t6 (or @t119 @t158)))) % 0.43/0.63 (define @t160 () (not (tptp.rel_s4 @t9 @t1))) % 0.43/0.63 (define @t161 () (forall @t6 (or @t160 @t146 @t145 @t143))) % 0.43/0.63 (define @t162 () (not (tptp.exists_in_world @t109 @t9))) % 0.43/0.63 (define @t163 () (not (forall @t115 (or @t162 (not @t161))))) % 0.43/0.63 (define @t164 () (lambda @t14 @t163)) % 0.43/0.63 (define @t165 () (_ @t164 @t2 @t7)) % 0.43/0.63 (define @t166 () (or @t142 @t165)) % 0.43/0.63 (define @t167 () (forall @t5 @t166)) % 0.43/0.63 (define @t168 () (lambda @t43 @t167)) % 0.43/0.63 (define @t169 () (_ @t55 @t2 @t7)) % 0.43/0.63 (define @t170 () (lambda @t59 (forall @t5 (or @t142 @t169)))) % 0.43/0.63 (define @t171 () (@list @t9)) % 0.43/0.63 (define @t172 () (tptp.h @t16 @t1)) % 0.43/0.63 (define @t173 () (not @t172)) % 0.43/0.63 (define @t174 () (forall @t6 (or @t160 @t146 @t145 @t173))) % 0.43/0.63 (define @t175 () (lambda @t19 @t174)) % 0.43/0.63 (define @t176 () (_ @t175 @t109 @t9)) % 0.43/0.63 (define @t177 () (not @t176)) % 0.43/0.63 (define @t178 () (or @t162 @t177)) % 0.43/0.63 (define @t179 () (forall @t115 @t178)) % 0.43/0.63 (define @t180 () (not @t179)) % 0.43/0.63 (define @t181 () (lambda @t171 @t180)) % 0.43/0.63 (define @t182 () (forall @t5 (or (not (tptp.exists_in_world @t2 @t9)) (not (_ @t55 @t2 @t9))))) % 0.43/0.63 (define @t183 () (not @t182)) % 0.43/0.63 (define @t184 () (lambda @t62 @t183)) % 0.43/0.63 (define @t185 () (_ @t17 @t1)) % 0.43/0.63 (define @t186 () (not @t185)) % 0.43/0.63 (define @t187 () (_ @t11 @t1)) % 0.43/0.63 (define @t188 () (not @t187)) % 0.43/0.63 (define @t189 () (_ @t15 @t1)) % 0.43/0.63 (define @t190 () (or @t119 @t189 @t188 @t186)) % 0.43/0.63 (define @t191 () (or @t189 @t188 @t186)) % 0.43/0.63 (define @t192 () (not (_ @t17 @t9))) % 0.43/0.63 (define @t193 () (_ @t11 @t9)) % 0.43/0.63 (define @t194 () (not @t193)) % 0.43/0.63 (define @t195 () (_ @t15 @t9)) % 0.43/0.63 (define @t196 () (or @t195 @t194 @t192)) % 0.43/0.63 (define @t197 () (lambda @t171 @t196)) % 0.43/0.63 (define @t198 () (_ @t197 @t1)) % 0.43/0.63 (define @t199 () (or @t119 @t198)) % 0.43/0.63 (define @t200 () (forall @t6 @t199)) % 0.43/0.63 (define @t201 () (lambda @t43 @t200)) % 0.43/0.63 (define @t202 () (_ @t33 @t9)) % 0.43/0.63 (define @t203 () (or @t202 @t194 @t192)) % 0.43/0.63 (define @t204 () (@list @t33 @t9)) % 0.43/0.63 (define @t205 () (or @t194 @t192)) % 0.43/0.63 (define @t206 () (not @t205)) % 0.43/0.63 (define @t207 () (lambda @t171 @t206)) % 0.43/0.63 (define @t208 () (_ @t207 @t9)) % 0.43/0.63 (define @t209 () (not @t208)) % 0.43/0.63 (define @t210 () (or @t209 @t202)) % 0.43/0.63 (define @t211 () (lambda @t204 @t210)) % 0.43/0.63 (define @t212 () (not (_ @t28 @t9))) % 0.43/0.63 (define @t213 () (or @t212 @t202)) % 0.43/0.63 (define @t214 () (lambda @t48 @t213)) % 0.43/0.63 (define @t215 () (not @t202)) % 0.43/0.63 (define @t216 () (lambda @t204 (not (or @t194 @t215)))) % 0.43/0.63 (define @t217 () (not (or @t212 @t215))) % 0.43/0.63 (define @t218 () (_ (lambda @t48 @t217) @t11)) % 0.43/0.63 (define @t219 () (_ (_ @t214 (_ @t218 @t17)) @t15)) % 0.43/0.63 (define @t220 () (lambda @t19 (_ (_ @t159 @t219) @t9))) % 0.43/0.63 (define @t221 () (not @t34)) % 0.43/0.63 (define @t222 () (or @t30 @t221)) % 0.43/0.63 (define @t223 () (lambda @t43 @t222)) % 0.43/0.63 (define @t224 () (_ @t223 @t7)) % 0.43/0.63 (define @t225 () (not @t224)) % 0.43/0.63 (define @t226 () (lambda @t43 @t225)) % 0.43/0.63 (define @t227 () (lambda @t43 @t221)) % 0.43/0.63 (define @t228 () (_ @t227 @t7)) % 0.43/0.63 (define @t229 () (or @t30 @t228)) % 0.43/0.63 (define @t230 () (lambda @t43 @t229)) % 0.43/0.63 (define @t231 () (or @t30 @t34)) % 0.43/0.63 (define @t232 () (@list @t33 @t7)) % 0.43/0.63 (define @t233 () (lambda @t232 @t231)) % 0.43/0.63 (define @t234 () (lambda @t43 @t30)) % 0.43/0.63 (define @t235 () (_ @t234 @t7)) % 0.43/0.63 (define @t236 () (or @t235 @t34)) % 0.43/0.63 (define @t237 () (lambda @t232 @t236)) % 0.43/0.63 (define @t238 () (lambda @t43 @t231)) % 0.43/0.63 (define @t239 () (forall @t5 (or @t142 (not @t169)))) % 0.43/0.63 (define @t240 () (lambda @t43 @t239)) % 0.43/0.63 (define @t241 () (_ @t240 @t7)) % 0.43/0.63 (define @t242 () (not @t241)) % 0.43/0.63 (define @t243 () (lambda @t43 @t242)) % 0.43/0.63 (define @t244 () (not @t57)) % 0.43/0.63 (define @t245 () (or @t142 @t244)) % 0.43/0.63 (define @t246 () (not (_ @t56 @t9))) % 0.43/0.63 (define @t247 () (lambda @t14 @t246)) % 0.43/0.63 (define @t248 () (_ @t247 @t2 @t7)) % 0.43/0.63 (define @t249 () (or @t142 @t248)) % 0.43/0.63 (define @t250 () (forall @t5 @t249)) % 0.43/0.63 (define @t251 () (lambda @t43 @t250)) % 0.43/0.63 (define @t252 () (lambda @t43 @t244)) % 0.43/0.63 (define @t253 () (_ @t32 @t56)) % 0.43/0.63 (define @t254 () (not @t8)) % 0.43/0.63 (define @t255 () (or @t254 @t57)) % 0.43/0.63 (define @t256 () (@var "BOUND_VARIABLE_8863" tptp.mu)) % 0.43/0.63 (define @t257 () (tptp.h @t256 @t1)) % 0.43/0.63 (define @t258 () (@var "BOUND_VARIABLE_8937" tptp.mu)) % 0.43/0.63 (define @t259 () (not (tptp.exists_in_world @t256 @t1))) % 0.43/0.63 (define @t260 () (@list @t256)) % 0.43/0.63 (define @t261 () (not (forall @t260 (or @t259 (and (not (tptp.defused @t258 @t1)) (tptp.bomb @t258 @t1) @t257))))) % 0.43/0.63 (define @t262 () (not (tptp.exists_in_world @t258 @t1))) % 0.43/0.63 (define @t263 () (or @t119 @t262 @t261)) % 0.43/0.63 (define @t264 () (forall (@list @t7 @t1 @t258) @t263)) % 0.43/0.63 (define @t265 () (@quantifiers_skolemize @t264 2)) % 0.43/0.63 (define @t266 () (@quantifiers_skolemize @t264 1)) % 0.43/0.63 (define @t267 () (@quantifiers_skolemize @t264 0)) % 0.43/0.63 (define @t268 () (@list @t1 @t258)) % 0.43/0.63 (define @t269 () (forall @t268 @t263)) % 0.43/0.63 (define @t270 () (lambda @t43 @t269)) % 0.43/0.63 (define @t271 () (_ @t270 @t7)) % 0.43/0.63 (define @t272 () (forall @t43 @t271)) % 0.43/0.63 (define @t273 () (or @t262 @t261)) % 0.43/0.63 (define @t274 () (or @t119 @t273)) % 0.43/0.63 (define @t275 () (forall @t268 @t274)) % 0.43/0.63 (define @t276 () (@list @t258)) % 0.43/0.63 (define @t277 () (forall @t276 @t274)) % 0.43/0.63 (define @t278 () (forall @t276 @t273)) % 0.43/0.63 (define @t279 () (or @t119 @t278)) % 0.43/0.63 (define @t280 () (forall @t5 (or @t138 (not (forall @t260 (or @t259 (and (not @t146) @t144 @t257))))))) % 0.43/0.63 (define @t281 () (not (forall @t260 (or (not (tptp.exists_in_world @t256 @t7)) (and (not (tptp.defused @t2 @t7)) (tptp.bomb @t2 @t7) (tptp.h @t256 @t7)))))) % 0.43/0.63 (define @t282 () (lambda @t43 (forall @t5 (or @t142 @t281)))) % 0.43/0.63 (define @t283 () (_ @t282 @t1)) % 0.43/0.63 (define @t284 () (or @t119 @t283)) % 0.43/0.63 (define @t285 () (forall @t6 @t284)) % 0.43/0.63 (define @t286 () (lambda @t43 @t285)) % 0.43/0.63 (define @t287 () (tptp.h @t256 @t9)) % 0.43/0.63 (define @t288 () (tptp.bomb @t2 @t9)) % 0.43/0.63 (define @t289 () (tptp.defused @t2 @t9)) % 0.43/0.63 (define @t290 () (not (tptp.exists_in_world @t256 @t9))) % 0.43/0.63 (define @t291 () (not (forall @t260 (or @t290 (and (not @t289) @t288 @t287))))) % 0.43/0.63 (define @t292 () (lambda @t14 @t291)) % 0.43/0.63 (define @t293 () (_ @t292 @t2 @t7)) % 0.43/0.63 (define @t294 () (or @t142 @t293)) % 0.43/0.63 (define @t295 () (forall @t5 @t294)) % 0.43/0.63 (define @t296 () (lambda @t43 @t295)) % 0.43/0.63 (define @t297 () (_ (_ tptp.h @t256) @t9)) % 0.43/0.63 (define @t298 () (not @t195)) % 0.43/0.63 (define @t299 () (and @t298 @t193 @t297)) % 0.43/0.63 (define @t300 () (or @t290 @t299)) % 0.43/0.63 (define @t301 () (not @t297)) % 0.43/0.63 (define @t302 () (not @t301)) % 0.43/0.63 (define @t303 () (not @t194)) % 0.43/0.63 (define @t304 () (and @t298 @t303 @t302)) % 0.43/0.63 (define @t305 () (or @t195 @t194 @t301)) % 0.43/0.63 (define @t306 () (or @t290 (not @t305))) % 0.43/0.63 (define @t307 () (lambda @t19 @t196)) % 0.43/0.63 (define @t308 () (_ @t307 @t256 @t9)) % 0.43/0.63 (define @t309 () (not @t308)) % 0.43/0.63 (define @t310 () (or @t290 @t309)) % 0.43/0.63 (define @t311 () (forall @t260 @t310)) % 0.43/0.63 (define @t312 () (not @t311)) % 0.43/0.63 (define @t313 () (lambda @t171 @t312)) % 0.43/0.63 (define @t314 () (lambda @t19 (_ @t219 @t9))) % 0.43/0.63 (define @t315 () (lambda @t14 (_ (_ @t184 @t314) @t9))) % 0.43/0.63 (define @t316 () (tptp.exists_in_world @t265 @t266)) % 0.43/0.63 (define @t317 () (tptp.bomb @t265 @t266)) % 0.43/0.63 (define @t318 () (tptp.defused @t265 @t266)) % 0.43/0.63 (define @t319 () (not @t318)) % 0.43/0.63 (define @t320 () (forall @t260 (or (not (tptp.exists_in_world @t256 @t266)) (and @t319 @t317 (tptp.h @t256 @t266))))) % 0.43/0.63 (define @t321 () (not @t320)) % 0.43/0.63 (define @t322 () (not @t316)) % 0.43/0.63 (define @t323 () (tptp.rel_s4 @t267 @t266)) % 0.43/0.63 (define @t324 () (not @t323)) % 0.43/0.63 (define @t325 () (or @t324 @t322 @t321)) % 0.43/0.63 (define @t326 () (@list true)) % 0.43/0.63 (define @t327 () (@list @t325)) % 0.43/0.63 (define @t328 () (not (tptp.bomb @t265 @t108))) % 0.43/0.63 (define @t329 () (tptp.defused @t265 @t108)) % 0.43/0.63 (define @t330 () (not (tptp.rel_s4 @t266 @t108))) % 0.43/0.63 (define @t331 () (forall @t115 (or (not (tptp.exists_in_world @t109 @t266)) (not (forall @t113 (or @t330 @t329 @t328 @t110)))))) % 0.43/0.63 (define @t332 () (not @t331)) % 0.43/0.63 (define @t333 () (or @t324 @t322 @t332)) % 0.43/0.63 (define @t334 () (@quantifiers_skolemize @t331 0)) % 0.43/0.63 (define @t335 () (forall @t113 (or @t330 @t329 @t328 (not (tptp.h @t334 @t108))))) % 0.43/0.63 (define @t336 () (not @t335)) % 0.43/0.63 (define @t337 () (tptp.exists_in_world @t334 @t266)) % 0.43/0.63 (define @t338 () (not @t337)) % 0.43/0.63 (define @t339 () (or @t338 @t336)) % 0.43/0.63 (define @t340 () (@list @t339)) % 0.43/0.63 (define @t341 () (@list @t266)) % 0.43/0.63 (define @t342 () (tptp.h @t334 @t266)) % 0.43/0.63 (define @t343 () (and @t319 @t317 @t342)) % 0.43/0.63 (define @t344 () (or @t338 @t343)) % 0.43/0.63 (define @t345 () (@list false false)) % 0.43/0.63 (define @t346 () (@list false)) % 0.43/0.63 (define @t347 () (and @t319 @t317 (tptp.h @t265 @t266))) % 0.43/0.63 (define @t348 () (or @t322 @t347)) % 0.43/0.63 (define @t349 () (not @t347)) % 0.43/0.63 (define @t350 () (@list @t347)) % 0.43/0.63 (define @t351 () (not @t342)) % 0.43/0.63 (define @t352 () (not @t317)) % 0.43/0.63 (define @t353 () (tptp.rel_s4 @t266 @t266)) % 0.43/0.63 (define @t354 () (not @t353)) % 0.43/0.63 (define @t355 () (or @t354 @t318 @t352 @t351)) % 0.43/0.63 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.43/0.63 (assume @p2 (forall @t6 (exists @t5 @t4))) % 0.43/0.63 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 0.43/0.63 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 0.43/0.63 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 0.43/0.63 (assume @p6 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mexists_ind (lambda (@list @t10 @t9) (_ (_ tptp.bomb @t10) @t9)))))) % 0.43/0.63 (assume @p7 (_ tptp.mvalid (_ tptp.mexists_ind (lambda (@list @t12 @t9) (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t14 (_ (_ (_ tptp.mimplies (_ @t13 (_ tptp.h @t12))) (_ tptp.mbox_s4 @t11)) @t9)))) @t9))))) % 0.43/0.63 (assume @p8 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind @t21)))) % 0.43/0.63 (assume @p9 @t24) % 0.43/0.63 (assume @p10 true) % 0.43/0.63 (step @p11 (= tptp.meq_prop @t27) :rule refl :args (@t27)) % 0.43/0.63 (step @p12 (= tptp.mnot @t32) :rule refl :args (@t32)) % 0.43/0.63 (step @p13 (= tptp.mor @t35) :rule refl :args (@t35)) % 0.43/0.63 (step @p14 (= tptp.mbox @t38) :rule refl :args (@t38)) % 0.43/0.63 (step @p15 (= tptp.mforall_prop @t42) :rule refl :args (@t42)) % 0.43/0.63 (step @p16 (= tptp.mtrue @t44) :rule refl :args (@t44)) % 0.43/0.63 (step @p17 (= tptp.mand @t49) :rule refl :args (@t49)) % 0.43/0.63 (step @p18 (= tptp.mimplies @t50) :rule refl :args (@t50)) % 0.43/0.63 (step @p19 (= tptp.mimplied @t51) :rule refl :args (@t51)) % 0.43/0.63 (step @p20 (= tptp.mequiv @t52) :rule refl :args (@t52)) % 0.43/0.63 (step @p21 (= tptp.mxor @t53) :rule refl :args (@t53)) % 0.43/0.63 (step @p22 (= tptp.mdia @t54) :rule refl :args (@t54)) % 0.43/0.63 (step @p23 (= tptp.mforall_ind @t60) :rule refl :args (@t60)) % 0.43/0.63 (step @p24 (= tptp.mexists_ind @t63) :rule refl :args (@t63)) % 0.43/0.63 (step @p25 (= tptp.mexists_prop @t64) :rule refl :args (@t64)) % 0.43/0.63 (step @p26 (= tptp.mreflexive @t71) :rule refl :args (@t71)) % 0.43/0.63 (step @p27 (= tptp.msymmetric @t75) :rule refl :args (@t75)) % 0.43/0.63 (step @p28 (= tptp.mserial @t77) :rule refl :args (@t77)) % 0.43/0.63 (step @p29 (= tptp.mtransitive @t82) :rule refl :args (@t82)) % 0.43/0.63 (step @p30 (= tptp.meuclidean @t84) :rule refl :args (@t84)) % 0.43/0.63 (step @p31 (= tptp.mpartially_functional @t86) :rule refl :args (@t86)) % 0.43/0.63 (step @p32 (= tptp.mfunctional @t88) :rule refl :args (@t88)) % 0.43/0.63 (step @p33 (= tptp.mweakly_dense @t91) :rule refl :args (@t91)) % 0.43/0.63 (step @p34 (= tptp.mweakly_connected @t92) :rule refl :args (@t92)) % 0.43/0.63 (step @p35 (= tptp.mweakly_directed @t93) :rule refl :args (@t93)) % 0.43/0.63 (step @p36 (= tptp.mvalid @t96) :rule refl :args (@t96)) % 0.43/0.63 (step @p37 (= tptp.msatisfiable @t97) :rule refl :args (@t97)) % 0.43/0.63 (step @p38 (= tptp.mcountersatisfiable @t98) :rule refl :args (@t98)) % 0.43/0.63 (step @p39 (= tptp.minvalid @t99) :rule refl :args (@t99)) % 0.43/0.63 (step @p40 (= tptp.mbox_s4 @t104) :rule refl :args (@t104)) % 0.43/0.63 (step @p41 (= tptp.mdia_s4 @t105) :rule refl :args (@t105)) % 0.43/0.63 (step @p42 :rule beta-reduce :args ((= (_ (lambda @t70 (forall @t68 @t107)) tptp.rel_s4) @t106))) % 0.43/0.63 (step @p43 :rule refl :args (tptp.rel_s4)) % 0.43/0.63 (step @p44 :rule refl :args (@t107)) % 0.43/0.63 (step @p45 :rule refl :args (@t67)) % 0.43/0.63 (step @p46 :rule cong :premises (@p45 @p44) :args ((= @t67 @t107))) % 0.43/0.63 (step @p47 :rule symm :premises (@p46)) % 0.43/0.63 (step @p48 :rule eq_resolve :premises (@p45 @p47)) % 0.43/0.63 (step @p49 :rule cong :premises (@p48) :args (@t69)) % 0.43/0.63 (step @p50 :rule cong :premises (@p49) :args (@t71)) % 0.43/0.63 (step @p51 :rule trans :premises (@p26 @p50)) % 0.43/0.63 (step @p52 :rule ho_cong :premises (@p51 @p43)) % 0.43/0.63 (step @p53 :rule trans :premises (@p52 @p42)) % 0.43/0.63 (step @p54 :rule eq_resolve :premises (@p3 @p53)) % 0.43/0.63 (step @p55 :rule quant-merge-prenex :args ((= (forall @t43 @t122) (forall (@list @t7 @t1 @t111) @t120)))) % 0.43/0.63 (step @p56 :rule beta-reduce :args ((= @t124 @t122))) % 0.43/0.63 (step @p57 :rule cong :premises (@p56) :args (@t125)) % 0.43/0.63 (step @p58 :rule trans :premises (@p57 @p55)) % 0.43/0.63 (step @p59 :rule beta-reduce :args ((= (_ @t127 @t123) @t125))) % 0.43/0.63 (step @p60 :rule trans :premises (@p59 @p58)) % 0.43/0.63 (step @p61 :rule aci_norm :args ((= @t129 @t120))) % 0.43/0.63 (step @p62 :rule cong :premises (@p61) :args (@t130)) % 0.43/0.63 (step @p63 :rule quant-merge-prenex :args ((= (forall @t6 @t132) @t130))) % 0.43/0.63 (step @p64 :rule alpha_equiv :args (@t133 (@list @t111) @t134)) % 0.43/0.63 (step @p65 :rule refl :args (@t119)) % 0.43/0.63 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t135)) % 0.43/0.63 (step @p67 :rule quant-miniscope-or :args ((= @t132 @t135))) % 0.43/0.63 (step @p68 :rule trans :premises (@p67 @p66)) % 0.43/0.63 (step @p69 :rule symm :premises (@p68)) % 0.43/0.63 (step @p70 :rule cong :premises (@p69) :args ((forall @t6 (or @t119 @t139)))) % 0.43/0.63 (step @p71 :rule trans :premises (@p70 @p63)) % 0.43/0.63 (step @p72 :rule trans :premises (@p71 @p62)) % 0.43/0.63 (step @p73 :rule beta-reduce :args ((= (_ (lambda @t43 (forall @t5 (or @t142 (not (forall @t115 (or @t140 (not (forall @t113 (or (not (tptp.rel_s4 @t7 @t108)) @t137 @t136 @t110))))))))) @t1) @t139))) % 0.43/0.63 (step @p74 :rule refl :args (@t1)) % 0.43/0.63 (step @p75 :rule alpha_equiv :args (@t147 (@list @t1) (@list @t108))) % 0.43/0.63 (step @p76 :rule cong :premises (@p75) :args (@t148)) % 0.43/0.63 (step @p77 :rule refl :args (@t140)) % 0.43/0.63 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t149)) % 0.43/0.63 (step @p79 :rule cong :premises (@p78) :args (@t150)) % 0.43/0.63 (step @p80 :rule cong :premises (@p79) :args (@t151)) % 0.43/0.63 (step @p81 :rule refl :args (@t142)) % 0.43/0.63 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t152)) % 0.43/0.63 (step @p83 :rule cong :premises (@p82) :args (@t153)) % 0.43/0.63 (step @p84 :rule cong :premises (@p83) :args (@t154)) % 0.43/0.63 (step @p85 :rule ho_cong :premises (@p84 @p74)) % 0.43/0.63 (step @p86 :rule trans :premises (@p85 @p73)) % 0.43/0.63 (step @p87 :rule refl :args (@t119)) % 0.43/0.63 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t155)) % 0.43/0.63 (step @p89 :rule cong :premises (@p88) :args (@t156)) % 0.43/0.63 (step @p90 :rule trans :premises (@p89 @p72)) % 0.43/0.63 (step @p91 :rule cong :premises (@p90) :args (@t157)) % 0.43/0.63 (step @p92 :rule beta-reduce :args ((= (_ @t159 @t154) @t157))) % 0.43/0.63 (step @p93 :rule trans :premises (@p92 @p91)) % 0.43/0.63 (step @p94 :rule beta-reduce :args ((= @t165 @t151))) % 0.43/0.63 (step @p95 :rule refl :args (@t142)) % 0.43/0.63 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t166)) % 0.43/0.63 (step @p97 :rule cong :premises (@p96) :args (@t167)) % 0.43/0.63 (step @p98 :rule cong :premises (@p97) :args (@t168)) % 0.43/0.63 (step @p99 :rule beta-reduce :args ((= (_ @t170 @t164) @t168))) % 0.43/0.63 (step @p100 :rule trans :premises (@p99 @p98)) % 0.43/0.63 (step @p101 :rule beta-reduce :args ((= (_ (lambda @t171 @t163) @t9) @t163))) % 0.43/0.63 (step @p102 :rule refl :args (@t9)) % 0.43/0.63 (step @p103 :rule beta-reduce :args ((= @t176 @t161))) % 0.43/0.63 (step @p104 :rule cong :premises (@p103) :args (@t177)) % 0.43/0.63 (step @p105 :rule refl :args (@t162)) % 0.43/0.63 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t178)) % 0.43/0.63 (step @p107 :rule cong :premises (@p106) :args (@t179)) % 0.43/0.63 (step @p108 :rule cong :premises (@p107) :args (@t180)) % 0.43/0.63 (step @p109 :rule cong :premises (@p108) :args (@t181)) % 0.43/0.63 (step @p110 :rule beta-reduce :args ((= (_ (lambda @t62 (not (forall @t115 (or @t162 (not (_ @t55 @t109 @t9)))))) @t175) @t181))) % 0.43/0.63 (step @p111 :rule trans :premises (@p110 @p109)) % 0.43/0.63 (step @p112 :rule refl :args (@t175)) % 0.43/0.63 (step @p113 :rule alpha_equiv :args (@t182 @t134 (@list @t109))) % 0.43/0.63 (step @p114 :rule cong :premises (@p113) :args (@t183)) % 0.43/0.63 (step @p115 :rule cong :premises (@p114) :args (@t184)) % 0.43/0.63 (step @p116 :rule ho_cong :premises (@p115 @p112)) % 0.43/0.63 (step @p117 :rule trans :premises (@p116 @p111)) % 0.43/0.63 (step @p118 :rule beta-reduce :args ((= (_ (lambda @t43 (forall @t6 (or @t119 @t146 @t145 @t173))) @t9) @t174))) % 0.43/0.63 (step @p119 :rule refl :args (@t172)) % 0.43/0.63 (step @p120 :rule refl :args (@t185)) % 0.43/0.63 (step @p121 :rule cong :premises (@p120 @p119) :args ((= @t185 @t172))) % 0.43/0.63 (step @p122 :rule symm :premises (@p121)) % 0.43/0.63 (step @p123 :rule eq_resolve :premises (@p120 @p122)) % 0.43/0.63 (step @p124 :rule cong :premises (@p123) :args (@t186)) % 0.43/0.63 (step @p125 :rule refl :args (@t144)) % 0.43/0.63 (step @p126 :rule refl :args (@t187)) % 0.43/0.63 (step @p127 :rule cong :premises (@p126 @p125) :args ((= @t187 @t144))) % 0.43/0.63 (step @p128 :rule symm :premises (@p127)) % 0.43/0.63 (step @p129 :rule eq_resolve :premises (@p126 @p128)) % 0.43/0.63 (step @p130 :rule cong :premises (@p129) :args (@t188)) % 0.43/0.63 (step @p131 :rule refl :args (@t146)) % 0.43/0.63 (step @p132 :rule refl :args (@t189)) % 0.43/0.63 (step @p133 :rule cong :premises (@p132 @p131) :args ((= @t189 @t146))) % 0.43/0.63 (step @p134 :rule symm :premises (@p133)) % 0.43/0.63 (step @p135 :rule eq_resolve :premises (@p132 @p134)) % 0.43/0.63 (step @p136 :rule nary_cong :premises (@p65 @p135 @p130 @p124) :args (@t190)) % 0.43/0.63 (step @p137 :rule cong :premises (@p136) :args ((forall @t6 @t190))) % 0.43/0.63 (step @p138 :rule aci_norm :args ((= (or @t119 @t191) @t190))) % 0.43/0.63 (step @p139 :rule beta-reduce :args ((= @t198 @t191))) % 0.43/0.63 (step @p140 :rule nary_cong :premises (@p87 @p139) :args (@t199)) % 0.43/0.63 (step @p141 :rule trans :premises (@p140 @p138)) % 0.43/0.63 (step @p142 :rule cong :premises (@p141) :args (@t200)) % 0.43/0.63 (step @p143 :rule trans :premises (@p142 @p137)) % 0.43/0.63 (step @p144 :rule cong :premises (@p143) :args (@t201)) % 0.43/0.63 (step @p145 :rule beta-reduce :args ((= (_ @t159 @t197) @t201))) % 0.43/0.63 (step @p146 :rule trans :premises (@p145 @p144)) % 0.43/0.63 (step @p147 :rule beta-reduce :args ((= (_ (lambda @t204 @t203) @t15) @t197))) % 0.43/0.63 (step @p148 :rule refl :args (@t15)) % 0.43/0.63 (step @p149 :rule aci_norm :args ((= (or @t205 @t202) @t203))) % 0.43/0.63 (step @p150 :rule refl :args (@t202)) % 0.43/0.63 (step @p151 :rule bool-double-not-elim :args (@t205)) % 0.43/0.63 (step @p152 :rule beta-reduce :args ((= @t208 @t206))) % 0.43/0.63 (step @p153 :rule cong :premises (@p152) :args (@t209)) % 0.43/0.63 (step @p154 :rule trans :premises (@p153 @p151)) % 0.43/0.63 (step @p155 :rule nary_cong :premises (@p154 @p150) :args (@t210)) % 0.43/0.63 (step @p156 :rule trans :premises (@p155 @p149)) % 0.43/0.63 (step @p157 :rule cong :premises (@p156) :args (@t211)) % 0.43/0.63 (step @p158 :rule beta-reduce :args ((= (_ @t214 @t207) @t211))) % 0.43/0.63 (step @p159 :rule trans :premises (@p158 @p157)) % 0.43/0.63 (step @p160 :rule beta-reduce :args ((= (_ @t216 @t17) @t207))) % 0.43/0.63 (step @p161 :rule refl :args (@t17)) % 0.43/0.63 (step @p162 :rule beta-reduce :args ((= @t218 @t216))) % 0.43/0.63 (step @p163 :rule ho_cong :premises (@p162 @p161)) % 0.43/0.63 (step @p164 :rule trans :premises (@p163 @p160)) % 0.43/0.63 (step @p165 :rule refl :args (@t214)) % 0.43/0.63 (step @p166 :rule ho_cong :premises (@p165 @p164)) % 0.43/0.63 (step @p167 :rule trans :premises (@p166 @p159)) % 0.43/0.63 (step @p168 :rule ho_cong :premises (@p167 @p148)) % 0.43/0.63 (step @p169 :rule trans :premises (@p168 @p147)) % 0.43/0.63 (step @p170 :rule refl :args (@t159)) % 0.43/0.63 (step @p171 :rule ho_cong :premises (@p170 @p169)) % 0.43/0.63 (step @p172 :rule trans :premises (@p171 @p146)) % 0.43/0.63 (step @p173 :rule ho_cong :premises (@p172 @p102)) % 0.43/0.63 (step @p174 :rule trans :premises (@p173 @p118)) % 0.43/0.63 (step @p175 :rule cong :premises (@p174) :args (@t220)) % 0.43/0.63 (step @p176 :rule refl :args (@t184)) % 0.43/0.63 (step @p177 :rule ho_cong :premises (@p176 @p175)) % 0.43/0.63 (step @p178 :rule trans :premises (@p177 @p117)) % 0.43/0.63 (step @p179 :rule ho_cong :premises (@p178 @p102)) % 0.43/0.63 (step @p180 :rule trans :premises (@p179 @p101)) % 0.43/0.63 (step @p181 :rule cong :premises (@p180) :args ((lambda @t14 (_ (_ @t184 @t220) @t9)))) % 0.43/0.63 (step @p182 :rule refl :args (@t170)) % 0.43/0.63 (step @p183 :rule ho_cong :premises (@p182 @p181)) % 0.43/0.63 (step @p184 :rule trans :premises (@p183 @p100)) % 0.43/0.63 (step @p185 :rule ho_cong :premises (@p170 @p184)) % 0.43/0.63 (step @p186 :rule trans :premises (@p185 @p93)) % 0.43/0.63 (step @p187 :rule refl :args (@t127)) % 0.43/0.63 (step @p188 :rule ho_cong :premises (@p187 @p186)) % 0.43/0.63 (step @p189 :rule trans :premises (@p188 @p60)) % 0.43/0.63 (step @p190 :rule refl :args (@t11)) % 0.43/0.63 (step @p191 :rule beta-reduce :args ((= (_ (lambda @t43 (not @t222)) @t9) @t217))) % 0.43/0.63 (step @p192 :rule beta-reduce :args ((= @t224 @t222))) % 0.43/0.63 (step @p193 :rule cong :premises (@p192) :args (@t225)) % 0.43/0.63 (step @p194 :rule cong :premises (@p193) :args (@t226)) % 0.43/0.63 (step @p195 :rule beta-reduce :args ((= (_ @t32 @t223) @t226))) % 0.43/0.63 (step @p196 :rule trans :premises (@p195 @p194)) % 0.43/0.63 (step @p197 :rule beta-reduce :args ((= @t228 @t221))) % 0.43/0.63 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((or @t339 (not @t336)))) % 0.43/0.64 (step @p466 :rule cnf_or_neg :args (@t339 1)) % 0.43/0.64 (step @p467 :rule eq_resolve :premises (@p466 @p465)) % 0.43/0.64 (step @p468 :rule reordering :premises (@p467) :args ((or @t335 @t339))) % 0.43/0.64 (step @p469 :rule chain_m_resolution :premises (@p468 @p462) :args (@t335 @t326 @t340)) % 0.43/0.64 (step @p470 :rule instantiate :premises (@p469) :args (@t341)) % 0.43/0.64 (step @p471 :rule bool-double-not-elim :args (@t320)) % 0.43/0.64 (step @p472 :rule nary_cong :premises (@p447 @p471) :args ((or @t325 (not @t321)))) % 0.43/0.64 (step @p473 :rule cnf_or_neg :args (@t325 2)) % 0.43/0.64 (step @p474 :rule eq_resolve :premises (@p473 @p472)) % 0.43/0.64 (step @p475 :rule reordering :premises (@p474) :args ((or @t320 @t325))) % 0.43/0.64 (step @p476 :rule chain_m_resolution :premises (@p475 @p445) :args (@t320 @t326 @t327)) % 0.43/0.64 (step @p477 :rule instantiate :premises (@p476) :args ((@list @t334))) % 0.43/0.64 (step @p478 :rule bool-double-not-elim :args (@t337)) % 0.43/0.64 (step @p479 :rule nary_cong :premises (@p464 @p478) :args ((or @t339 (not @t338)))) % 0.43/0.64 (step @p480 :rule cnf_or_neg :args (@t339 0)) % 0.43/0.64 (step @p481 :rule eq_resolve :premises (@p480 @p479)) % 0.43/0.64 (step @p482 :rule reordering :premises (@p481) :args ((or @t337 @t339))) % 0.43/0.64 (step @p483 :rule chain_m_resolution :premises (@p482 @p462) :args (@t337 @t326 @t340)) % 0.43/0.64 (step @p484 :rule cnf_or_pos :args (@t344)) % 0.43/0.64 (step @p485 :rule reordering :premises (@p484) :args ((or @t338 @t343 (not @t344)))) % 0.43/0.64 (step @p486 :rule chain_m_resolution :premises (@p485 @p483 @p477) :args (@t343 @t345 (@list @t337 @t344))) % 0.43/0.64 (step @p487 :rule cnf_and_pos :args (@t343 2)) % 0.43/0.64 (step @p488 :rule reordering :premises (@p487) :args ((or @t342 (not @t343)))) % 0.43/0.64 (step @p489 :rule chain_m_resolution :premises (@p488 @p486) :args (@t342 @t346 (@list @t343))) % 0.43/0.64 (step @p490 :rule instantiate :premises (@p476) :args ((@list @t265))) % 0.43/0.64 (step @p491 :rule cnf_or_pos :args (@t348)) % 0.43/0.64 (step @p492 :rule reordering :premises (@p491) :args ((or @t322 @t347 (not @t348)))) % 0.43/0.64 (step @p493 :rule chain_m_resolution :premises (@p492 @p452 @p490) :args (@t347 @t345 (@list @t316 @t348))) % 0.43/0.64 (step @p494 :rule cnf_and_pos :args (@t347 1)) % 0.43/0.64 (step @p495 :rule reordering :premises (@p494) :args ((or @t317 @t349))) % 0.43/0.64 (step @p496 :rule chain_m_resolution :premises (@p495 @p493) :args (@t317 @t346 @t350)) % 0.43/0.64 (step @p497 :rule cnf_and_pos :args (@t347 0)) % 0.43/0.64 (step @p498 :rule reordering :premises (@p497) :args ((or @t319 @t349))) % 0.43/0.64 (step @p499 :rule chain_m_resolution :premises (@p498 @p493) :args (@t319 @t346 @t350)) % 0.43/0.64 (step @p500 :rule cnf_or_pos :args (@t355)) % 0.43/0.64 (step @p501 :rule reordering :premises (@p500) :args ((or @t318 @t352 @t354 @t351 (not @t355)))) % 0.43/0.64 (step @p502 :rule chain_m_resolution :premises (@p501 @p499 @p496 @p489 @p470) :args (@t354 (@list true false false false) (@list @t318 @t317 @t342 @t355))) % 0.43/0.64 (assume-push @p509 @t106) % 0.43/0.64 (step @p504 :rule instantiate :premises (@p54) :args (@t341)) % 0.43/0.64 (step-pop @p510 :rule scope :premises (@p504)) % 0.43/0.64 (step @p505 :rule process_scope :premises (@p510) :args (@t353)) % 0.43/0.64 (step @p507 :rule implies_elim :premises (@p505)) % 0.43/0.64 (step @p508 false :rule chain_m_resolution :premises (@p507 @p502 @p54) :args (false (@list true false) (@list @t353 @t106))) % 0.43/0.64 ) % 0.43/0.64 % SZS output end Proof % 0.43/0.64 % cvc5 exiting %------------------------------------------------------------------------------