%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN397^7 : TPTP v9.2.1. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:08:48 AM UTC 2026 % Result : Theorem 1.42s 1.63s % Output : Proof 1.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN397^7 : TPTP v9.2.1. Released v5.5.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n016.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 23:27:09 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 1.42/1.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.42/1.63 % SZS status Theorem % 1.42/1.63 % SZS output start Proof % 1.42/1.63 ( % 1.42/1.63 (declare-sort $$unsorted 0) % 1.42/1.63 (declare-sort tptp.mu 0) % 1.42/1.63 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 1.42/1.63 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 1.42/1.63 (declare-const tptp.f (-> tptp.mu $$unsorted Bool)) % 1.42/1.63 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 1.42/1.63 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 1.42/1.63 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 1.42/1.63 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 1.42/1.63 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 1.42/1.63 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 1.42/1.63 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 1.42/1.63 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 1.42/1.63 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 1.42/1.63 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 1.42/1.63 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 1.42/1.63 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 1.42/1.63 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 1.42/1.63 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.exists_in_world _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 1.42/1.63 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 1.42/1.63 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 1.42/1.63 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 1.42/1.63 (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)))))))) % 1.42/1.63 (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)))))))) % 1.42/1.63 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 1.42/1.63 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 1.42/1.63 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 1.42/1.63 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 1.42/1.63 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 1.42/1.63 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 1.42/1.63 (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))))))))))))) % 1.42/1.63 (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)))))) % 1.42/1.63 (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)))))) % 1.42/1.63 (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))))))) % 1.42/1.63 (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))))))) % 1.42/1.63 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 1.42/1.63 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 1.42/1.63 (define @t1 () (@var "V" $$unsorted)) % 1.42/1.63 (define @t2 () (@var "X" tptp.mu)) % 1.42/1.63 (define @t3 () (_ tptp.exists_in_world @t2)) % 1.42/1.63 (define @t4 () (_ @t3 @t1)) % 1.42/1.63 (define @t5 () (@list @t2)) % 1.42/1.63 (define @t6 () (@list @t1)) % 1.42/1.63 (define @t7 () (@var "W" $$unsorted)) % 1.42/1.63 (define @t8 () (_ @t3 @t7)) % 1.42/1.63 (define @t9 () (_ (_ tptp.rel_s4 @t1) @t7)) % 1.42/1.63 (define @t10 () (and @t4 @t9)) % 1.42/1.63 (define @t11 () (@list @t2 @t1 @t7)) % 1.42/1.63 (define @t12 () (forall @t11 (=> @t10 @t8))) % 1.42/1.63 (define @t13 () (@var "__flatten_var_0" $$unsorted)) % 1.42/1.63 (define @t14 () (_ tptp.f @t2)) % 1.42/1.63 (define @t15 () (@list @t2 @t13)) % 1.42/1.63 (define @t16 () (lambda @t15 (_ (_ tptp.mbox_s4 @t14) @t13))) % 1.42/1.63 (define @t17 () (_ tptp.mbox_s4 (_ tptp.mnot (_ tptp.mexists_ind @t16)))) % 1.42/1.63 (define @t18 () (@var "Y" tptp.mu)) % 1.42/1.63 (define @t19 () (_ tptp.f @t18)) % 1.42/1.63 (define @t20 () (@list @t18 @t13)) % 1.42/1.63 (define @t21 () (lambda @t20 (_ (_ tptp.mbox_s4 (_ tptp.mnot (_ tptp.mbox_s4 @t19))) @t13))) % 1.42/1.63 (define @t22 () (_ tptp.mbox_s4 (_ tptp.mforall_ind @t21))) % 1.42/1.63 (define @t23 () (not (_ tptp.mvalid (_ (_ tptp.mand (_ tptp.mbox_s4 (_ (_ tptp.mimplies @t17) @t22))) (_ tptp.mbox_s4 (_ (_ tptp.mimplies @t22) @t17)))))) % 1.42/1.63 (define @t24 () (@var "Y" (-> $$unsorted Bool))) % 1.42/1.63 (define @t25 () (@var "X" (-> $$unsorted Bool))) % 1.42/1.63 (define @t26 () (lambda (@list @t25 @t24 @t7) (= (_ @t25 @t7) (_ @t24 @t7)))) % 1.42/1.63 (define @t27 () (@var "Phi" (-> $$unsorted Bool))) % 1.42/1.63 (define @t28 () (_ @t27 @t7)) % 1.42/1.63 (define @t29 () (not @t28)) % 1.42/1.63 (define @t30 () (@list @t27 @t7)) % 1.42/1.63 (define @t31 () (lambda @t30 @t29)) % 1.42/1.63 (define @t32 () (@var "Psi" (-> $$unsorted Bool))) % 1.42/1.63 (define @t33 () (_ @t32 @t7)) % 1.42/1.63 (define @t34 () (lambda (@list @t27 @t32 @t7) (or @t28 @t33))) % 1.42/1.63 (define @t35 () (_ @t27 @t1)) % 1.42/1.63 (define @t36 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 1.42/1.63 (define @t37 () (lambda (@list @t36 @t27 @t7) (forall @t6 (or (not (_ (_ @t36 @t7) @t1)) @t35)))) % 1.42/1.63 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 1.42/1.63 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 1.42/1.63 (define @t40 () (_ @t39 @t38)) % 1.42/1.63 (define @t41 () (lambda (@list @t39 @t7) (forall (@list @t38) (_ @t40 @t7)))) % 1.42/1.63 (define @t42 () (@list @t7)) % 1.42/1.63 (define @t43 () (lambda @t42 true)) % 1.42/1.63 (define @t44 () (_ tptp.mnot @t32)) % 1.42/1.63 (define @t45 () (_ tptp.mnot @t27)) % 1.42/1.63 (define @t46 () (_ tptp.mor @t45)) % 1.42/1.63 (define @t47 () (@list @t27 @t32 @t13)) % 1.42/1.63 (define @t48 () (lambda @t47 (_ (_ tptp.mnot (_ @t46 @t44)) @t13))) % 1.42/1.63 (define @t49 () (lambda @t47 (_ (_ @t46 @t32) @t13))) % 1.42/1.63 (define @t50 () (lambda @t47 (_ (_ (_ tptp.mor @t44) @t27) @t13))) % 1.42/1.63 (define @t51 () (lambda @t47 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t27) @t32)) (_ (_ tptp.mimplies @t32) @t27)) @t13))) % 1.42/1.63 (define @t52 () (lambda @t47 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t27) @t32)) @t13))) % 1.42/1.63 (define @t53 () (lambda (@list @t36 @t27 @t13) (_ (_ tptp.mnot (_ (_ tptp.mbox @t36) @t45)) @t13))) % 1.42/1.63 (define @t54 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 1.42/1.63 (define @t55 () (_ @t54 @t2)) % 1.42/1.63 (define @t56 () (_ @t55 @t7)) % 1.42/1.63 (define @t57 () (forall @t5 (=> @t8 @t56))) % 1.42/1.63 (define @t58 () (@list @t54 @t7)) % 1.42/1.63 (define @t59 () (lambda @t58 @t57)) % 1.42/1.63 (define @t60 () (lambda @t15 (_ (_ tptp.mnot @t55) @t13))) % 1.42/1.63 (define @t61 () (@list @t54 @t13)) % 1.42/1.63 (define @t62 () (lambda @t61 (_ (_ tptp.mnot (_ tptp.mforall_ind @t60)) @t13))) % 1.42/1.63 (define @t63 () (lambda (@list @t39 @t13) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t13) (_ (_ tptp.mnot @t40) @t13)))) @t13))) % 1.42/1.63 (define @t64 () (@var "S" $$unsorted)) % 1.42/1.63 (define @t65 () (_ @t36 @t64)) % 1.42/1.63 (define @t66 () (_ @t65 @t64)) % 1.42/1.63 (define @t67 () (@list @t64)) % 1.42/1.63 (define @t68 () (forall @t67 @t66)) % 1.42/1.63 (define @t69 () (@list @t36)) % 1.42/1.63 (define @t70 () (lambda @t69 @t68)) % 1.42/1.63 (define @t71 () (@var "T" $$unsorted)) % 1.42/1.63 (define @t72 () (_ @t36 @t71)) % 1.42/1.63 (define @t73 () (_ @t65 @t71)) % 1.42/1.63 (define @t74 () (lambda @t69 (forall (@list @t64 @t71) (=> @t73 (_ @t72 @t64))))) % 1.42/1.63 (define @t75 () (@list @t71)) % 1.42/1.63 (define @t76 () (lambda @t69 (forall @t67 (exists @t75 @t73)))) % 1.42/1.63 (define @t77 () (@var "U" $$unsorted)) % 1.42/1.63 (define @t78 () (_ @t65 @t77)) % 1.42/1.63 (define @t79 () (_ @t72 @t77)) % 1.42/1.63 (define @t80 () (and @t73 @t79)) % 1.42/1.63 (define @t81 () (@list @t64 @t71 @t77)) % 1.42/1.63 (define @t82 () (forall @t81 (=> @t80 @t78))) % 1.42/1.63 (define @t83 () (lambda @t69 @t82)) % 1.42/1.63 (define @t84 () (and @t73 @t78)) % 1.42/1.63 (define @t85 () (lambda @t69 (forall @t81 (=> @t84 @t79)))) % 1.42/1.63 (define @t86 () (= @t71 @t77)) % 1.42/1.63 (define @t87 () (lambda @t69 (forall @t81 (=> @t84 @t86)))) % 1.42/1.63 (define @t88 () (@list @t77)) % 1.42/1.63 (define @t89 () (lambda @t69 (forall @t67 (exists @t75 (and @t73 (forall @t88 (=> @t78 @t86))))))) % 1.42/1.63 (define @t90 () (_ @t36 @t77)) % 1.42/1.63 (define @t91 () (_ @t90 @t71)) % 1.42/1.63 (define @t92 () (lambda @t69 (forall @t81 (=> @t73 (exists @t88 (and @t78 @t91)))))) % 1.42/1.63 (define @t93 () (lambda @t69 (forall @t81 (=> @t84 (or @t79 @t86 @t91))))) % 1.42/1.63 (define @t94 () (lambda @t69 (forall @t81 (=> @t84 (exists @t6 (and (_ @t72 @t1) (_ @t90 @t1))))))) % 1.42/1.63 (define @t95 () (forall @t42 @t28)) % 1.42/1.63 (define @t96 () (@list @t27)) % 1.42/1.63 (define @t97 () (lambda @t96 @t95)) % 1.42/1.63 (define @t98 () (lambda @t96 (exists @t42 @t28))) % 1.42/1.63 (define @t99 () (lambda @t96 (exists @t42 @t29))) % 1.42/1.63 (define @t100 () (lambda @t96 (forall @t42 @t29))) % 1.42/1.63 (define @t101 () (_ (_ tptp.rel_s4 @t7) @t1)) % 1.42/1.63 (define @t102 () (not @t101)) % 1.42/1.63 (define @t103 () (or @t102 @t35)) % 1.42/1.63 (define @t104 () (forall @t6 @t103)) % 1.42/1.63 (define @t105 () (lambda @t30 @t104)) % 1.42/1.63 (define @t106 () (lambda (@list @t27 @t13) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t45)) @t13))) % 1.42/1.63 (define @t107 () (@var "BOUND_VARIABLE_8528" $$unsorted)) % 1.42/1.63 (define @t108 () (@var "BOUND_VARIABLE_8550" tptp.mu)) % 1.42/1.63 (define @t109 () (tptp.f @t108 @t107)) % 1.42/1.63 (define @t110 () (@var "BOUND_VARIABLE_8707" $$unsorted)) % 1.42/1.63 (define @t111 () (@list @t107)) % 1.42/1.63 (define @t112 () (not (forall @t111 (or (not (tptp.rel_s4 @t110 @t107)) @t109)))) % 1.42/1.63 (define @t113 () (not (tptp.exists_in_world @t108 @t110))) % 1.42/1.63 (define @t114 () (@var "BOUND_VARIABLE_8597" $$unsorted)) % 1.42/1.63 (define @t115 () (@var "BOUND_VARIABLE_8740" tptp.mu)) % 1.42/1.63 (define @t116 () (@var "BOUND_VARIABLE_8742" $$unsorted)) % 1.42/1.63 (define @t117 () (@list @t114)) % 1.42/1.63 (define @t118 () (not (forall @t117 (or (not (tptp.rel_s4 @t116 @t114)) (tptp.f @t115 @t114))))) % 1.42/1.63 (define @t119 () (@var "BOUND_VARIABLE_8738" $$unsorted)) % 1.42/1.63 (define @t120 () (not (tptp.rel_s4 @t119 @t116))) % 1.42/1.63 (define @t121 () (not (tptp.exists_in_world @t115 @t119))) % 1.42/1.63 (define @t122 () (not (tptp.rel_s4 @t1 @t119))) % 1.42/1.63 (define @t123 () (@list @t110 @t108)) % 1.42/1.63 (define @t124 () (not (forall @t123 (or (not (tptp.rel_s4 @t1 @t110)) @t113 @t112)))) % 1.42/1.63 (define @t125 () (@var "BOUND_VARIABLE_8879" $$unsorted)) % 1.42/1.63 (define @t126 () (or (not (tptp.rel_s4 @t125 @t1)) @t124 @t122 @t121 @t120 @t118)) % 1.42/1.63 (define @t127 () (forall (@list @t125 @t1 @t119 @t115 @t116) @t126)) % 1.42/1.63 (define @t128 () (@quantifiers_skolemize @t127 1)) % 1.42/1.63 (define @t129 () (forall @t123 (or (not (tptp.rel_s4 @t128 @t110)) @t113 @t112))) % 1.42/1.63 (define @t130 () (@quantifiers_skolemize @t127 3)) % 1.42/1.63 (define @t131 () (@quantifiers_skolemize @t127 4)) % 1.42/1.63 (define @t132 () (forall @t117 (or (not (tptp.rel_s4 @t131 @t114)) (tptp.f @t130 @t114)))) % 1.42/1.63 (define @t133 () (not @t132)) % 1.42/1.63 (define @t134 () (@quantifiers_skolemize @t127 2)) % 1.42/1.63 (define @t135 () (tptp.rel_s4 @t134 @t131)) % 1.42/1.63 (define @t136 () (not @t135)) % 1.42/1.63 (define @t137 () (tptp.exists_in_world @t130 @t134)) % 1.42/1.63 (define @t138 () (not @t137)) % 1.42/1.63 (define @t139 () (tptp.rel_s4 @t128 @t134)) % 1.42/1.63 (define @t140 () (not @t139)) % 1.42/1.63 (define @t141 () (not @t129)) % 1.42/1.63 (define @t142 () (or (not (tptp.rel_s4 (@quantifiers_skolemize @t127 0) @t128)) @t141 @t140 @t138 @t136 @t133)) % 1.42/1.63 (define @t143 () (forall @t111 (or (not (tptp.rel_s4 @t131 @t107)) (tptp.f @t130 @t107)))) % 1.42/1.63 (define @t144 () (not @t143)) % 1.42/1.63 (define @t145 () (tptp.exists_in_world @t130 @t131)) % 1.42/1.63 (define @t146 () (not @t145)) % 1.42/1.63 (define @t147 () (tptp.rel_s4 @t128 @t131)) % 1.42/1.63 (define @t148 () (not @t147)) % 1.42/1.63 (define @t149 () (or @t148 @t146 @t144)) % 1.42/1.63 (define @t150 () (_ @t36 @t64 @t77)) % 1.42/1.63 (define @t151 () (_ @t36 @t71 @t77)) % 1.42/1.63 (define @t152 () (_ @t36 @t64 @t71)) % 1.42/1.63 (define @t153 () (not @t79)) % 1.42/1.63 (define @t154 () (not @t73)) % 1.42/1.63 (define @t155 () (or @t154 @t153 @t78)) % 1.42/1.63 (define @t156 () (or @t140 @t136 @t147)) % 1.42/1.63 (define @t157 () (tptp.exists_in_world @t2 @t7)) % 1.42/1.63 (define @t158 () (tptp.rel_s4 @t1 @t7)) % 1.42/1.63 (define @t159 () (not @t9)) % 1.42/1.63 (define @t160 () (tptp.exists_in_world @t2 @t1)) % 1.42/1.63 (define @t161 () (not @t4)) % 1.42/1.63 (define @t162 () (or @t161 @t159 @t8)) % 1.42/1.63 (define @t163 () (or @t138 @t136 @t145)) % 1.42/1.63 (define @t164 () (@list @t114)) % 1.42/1.63 (define @t165 () (@list @t107)) % 1.42/1.63 (define @t166 () (not @t142)) % 1.42/1.63 (define @t167 () (not @t127)) % 1.42/1.63 (define @t168 () (@list false)) % 1.42/1.63 (define @t169 () (@var "BOUND_VARIABLE_8837" tptp.mu)) % 1.42/1.63 (define @t170 () (@var "BOUND_VARIABLE_8835" $$unsorted)) % 1.42/1.63 (define @t171 () (not (forall @t111 (or (not (tptp.rel_s4 @t170 @t107)) (tptp.f @t169 @t107))))) % 1.42/1.63 (define @t172 () (not (tptp.exists_in_world @t169 @t170))) % 1.42/1.63 (define @t173 () (not (tptp.rel_s4 @t1 @t170))) % 1.42/1.63 (define @t174 () (@var "BOUND_VARIABLE_8661" tptp.mu)) % 1.42/1.63 (define @t175 () (@var "BOUND_VARIABLE_8663" $$unsorted)) % 1.42/1.63 (define @t176 () (not (forall @t117 (or (not (tptp.rel_s4 @t175 @t114)) (tptp.f @t174 @t114))))) % 1.42/1.63 (define @t177 () (@var "BOUND_VARIABLE_8807" $$unsorted)) % 1.42/1.63 (define @t178 () (not (tptp.rel_s4 @t177 @t175))) % 1.42/1.63 (define @t179 () (not (tptp.exists_in_world @t174 @t177))) % 1.42/1.63 (define @t180 () (@list @t177 @t174 @t175)) % 1.42/1.63 (define @t181 () (not (forall @t180 (or (not (tptp.rel_s4 @t1 @t177)) @t179 @t178 @t176)))) % 1.42/1.63 (define @t182 () (@var "BOUND_VARIABLE_8887" $$unsorted)) % 1.42/1.63 (define @t183 () (or (not (tptp.rel_s4 @t182 @t1)) @t181 @t173 @t172 @t171)) % 1.42/1.63 (define @t184 () (forall (@list @t182 @t1 @t170 @t169) @t183)) % 1.42/1.63 (define @t185 () (@list @t1 @t170 @t169)) % 1.42/1.63 (define @t186 () (forall (@list @t182) (forall @t185 @t183))) % 1.42/1.63 (define @t187 () (@list @t1 @t119 @t115 @t116)) % 1.42/1.63 (define @t188 () (forall (@list @t125) (forall @t187 @t126))) % 1.42/1.63 (define @t189 () (tptp.rel_s4 @t7 @t1)) % 1.42/1.63 (define @t190 () (not @t189)) % 1.42/1.63 (define @t191 () (or @t190 @t181 @t173 @t172 @t171)) % 1.42/1.63 (define @t192 () (forall @t185 @t191)) % 1.42/1.63 (define @t193 () (forall @t42 @t192)) % 1.42/1.63 (define @t194 () (@list @t7)) % 1.42/1.63 (define @t195 () (or @t190 @t124 @t122 @t121 @t120 @t118)) % 1.42/1.63 (define @t196 () (forall @t187 @t195)) % 1.42/1.63 (define @t197 () (forall @t42 @t196)) % 1.42/1.63 (define @t198 () (and @t197 @t193)) % 1.42/1.63 (define @t199 () (not @t192)) % 1.42/1.63 (define @t200 () (not @t196)) % 1.42/1.63 (define @t201 () (not (or @t200 @t199))) % 1.42/1.63 (define @t202 () (not (tptp.rel_s4 @t13 @t1))) % 1.42/1.63 (define @t203 () (forall @t185 (or @t202 @t181 @t173 @t172 @t171))) % 1.42/1.63 (define @t204 () (forall @t187 (or @t202 @t124 @t122 @t121 @t120 @t118))) % 1.42/1.63 (define @t205 () (not @t204)) % 1.42/1.63 (define @t206 () (@list @t13)) % 1.42/1.63 (define @t207 () (lambda @t206 (not (or @t205 (not @t203))))) % 1.42/1.63 (define @t208 () (_ @t207 @t7)) % 1.42/1.63 (define @t209 () (forall @t42 @t208)) % 1.42/1.63 (define @t210 () (_ @t27 @t7)) % 1.42/1.63 (define @t211 () (lambda @t96 (forall @t42 @t210))) % 1.42/1.63 (define @t212 () (lambda @t42 @t192)) % 1.42/1.63 (define @t213 () (_ @t212 @t13)) % 1.42/1.63 (define @t214 () (not @t213)) % 1.42/1.63 (define @t215 () (or @t205 @t214)) % 1.42/1.63 (define @t216 () (not @t215)) % 1.42/1.63 (define @t217 () (lambda @t206 @t216)) % 1.42/1.63 (define @t218 () (_ @t32 @t13)) % 1.42/1.63 (define @t219 () (not @t218)) % 1.42/1.63 (define @t220 () (@list @t32 @t13)) % 1.42/1.63 (define @t221 () (or @t173 @t172 @t171)) % 1.42/1.63 (define @t222 () (or @t190 @t181 @t221)) % 1.42/1.63 (define @t223 () (forall @t185 @t222)) % 1.42/1.63 (define @t224 () (@list @t170 @t169)) % 1.42/1.63 (define @t225 () (forall @t224 @t222)) % 1.42/1.63 (define @t226 () (forall @t224 @t221)) % 1.42/1.63 (define @t227 () (@var "BOUND_VARIABLE_8793" $$unsorted)) % 1.42/1.63 (define @t228 () (or @t190 @t181 @t226)) % 1.42/1.63 (define @t229 () (not (forall @t111 (or (not (tptp.rel_s4 @t227 @t107)) @t109)))) % 1.42/1.63 (define @t230 () (not (tptp.exists_in_world @t108 @t227))) % 1.42/1.63 (define @t231 () (@list @t227 @t108)) % 1.42/1.63 (define @t232 () (forall @t231 (or (not (tptp.rel_s4 @t1 @t227)) @t230 @t229))) % 1.42/1.63 (define @t233 () (or @t190 @t181 @t232)) % 1.42/1.63 (define @t234 () (or @t181 @t232)) % 1.42/1.63 (define @t235 () (not (tptp.rel_s4 @t1 @t107))) % 1.42/1.63 (define @t236 () (not (forall @t111 (or @t235 @t109)))) % 1.42/1.63 (define @t237 () (not (tptp.exists_in_world @t108 @t1))) % 1.42/1.63 (define @t238 () (@list @t1 @t108)) % 1.42/1.63 (define @t239 () (forall @t238 (or @t202 @t237 @t236))) % 1.42/1.63 (define @t240 () (@list @t1)) % 1.42/1.63 (define @t241 () (not (tptp.rel_s4 @t1 @t175))) % 1.42/1.63 (define @t242 () (not (tptp.exists_in_world @t174 @t1))) % 1.42/1.63 (define @t243 () (@list @t1 @t174 @t175)) % 1.42/1.63 (define @t244 () (forall @t243 (or @t202 @t242 @t241 @t176))) % 1.42/1.63 (define @t245 () (not @t244)) % 1.42/1.63 (define @t246 () (or @t245 @t239)) % 1.42/1.63 (define @t247 () (lambda @t206 @t246)) % 1.42/1.63 (define @t248 () (or @t190 (_ @t247 @t1))) % 1.42/1.63 (define @t249 () (forall @t6 @t248)) % 1.42/1.63 (define @t250 () (lambda @t42 @t249)) % 1.42/1.63 (define @t251 () (_ @t27 @t1)) % 1.42/1.63 (define @t252 () (lambda @t30 (forall @t6 (or @t190 @t251)))) % 1.42/1.63 (define @t253 () (or @t190 @t237 @t236)) % 1.42/1.63 (define @t254 () (lambda @t42 (forall @t238 @t253))) % 1.42/1.63 (define @t255 () (_ @t254 @t13)) % 1.42/1.63 (define @t256 () (or @t245 @t255)) % 1.42/1.63 (define @t257 () (lambda @t206 @t256)) % 1.42/1.63 (define @t258 () (or @t237 @t236)) % 1.42/1.63 (define @t259 () (or @t190 @t258)) % 1.42/1.63 (define @t260 () (forall @t238 @t259)) % 1.42/1.63 (define @t261 () (@list @t108)) % 1.42/1.63 (define @t262 () (forall @t261 @t259)) % 1.42/1.63 (define @t263 () (forall @t261 @t258)) % 1.42/1.63 (define @t264 () (or @t190 @t263)) % 1.42/1.63 (define @t265 () (tptp.f @t2 @t107)) % 1.42/1.63 (define @t266 () (not @t160)) % 1.42/1.63 (define @t267 () (forall @t5 (or @t266 (not (forall @t111 (or @t235 @t265)))))) % 1.42/1.63 (define @t268 () (not @t157)) % 1.42/1.63 (define @t269 () (tptp.f @t2 @t1)) % 1.42/1.63 (define @t270 () (forall @t6 (or @t190 @t269))) % 1.42/1.63 (define @t271 () (not @t270)) % 1.42/1.63 (define @t272 () (or @t268 @t271)) % 1.42/1.63 (define @t273 () (forall @t5 @t272)) % 1.42/1.63 (define @t274 () (lambda @t42 @t273)) % 1.42/1.63 (define @t275 () (or @t190 (_ @t274 @t1))) % 1.42/1.63 (define @t276 () (forall @t6 @t275)) % 1.42/1.63 (define @t277 () (lambda @t42 @t276)) % 1.42/1.63 (define @t278 () (forall @t6 (or @t202 @t269))) % 1.42/1.63 (define @t279 () (not (tptp.exists_in_world @t2 @t13))) % 1.42/1.63 (define @t280 () (lambda @t206 (not (forall @t5 (or @t279 (not @t278)))))) % 1.42/1.63 (define @t281 () (_ @t280 @t7)) % 1.42/1.63 (define @t282 () (not @t281)) % 1.42/1.63 (define @t283 () (lambda @t42 @t282)) % 1.42/1.63 (define @t284 () (lambda @t15 @t278)) % 1.42/1.63 (define @t285 () (_ @t284 @t2 @t13)) % 1.42/1.63 (define @t286 () (not @t285)) % 1.42/1.63 (define @t287 () (or @t279 @t286)) % 1.42/1.63 (define @t288 () (forall @t5 @t287)) % 1.42/1.63 (define @t289 () (not @t288)) % 1.42/1.63 (define @t290 () (lambda @t206 @t289)) % 1.42/1.63 (define @t291 () (not (forall @t5 (or @t279 (not (_ @t54 @t2 @t13)))))) % 1.42/1.63 (define @t292 () (lambda @t61 @t291)) % 1.42/1.63 (define @t293 () (_ @t14 @t1)) % 1.42/1.63 (define @t294 () (or @t190 @t293)) % 1.42/1.63 (define @t295 () (_ @t14 @t1)) % 1.42/1.63 (define @t296 () (or @t190 @t295)) % 1.42/1.63 (define @t297 () (forall @t6 @t296)) % 1.42/1.63 (define @t298 () (lambda @t42 @t297)) % 1.42/1.63 (define @t299 () (_ @t252 @t14)) % 1.42/1.63 (define @t300 () (lambda @t15 (_ @t299 @t13))) % 1.42/1.63 (define @t301 () (or @t190 @t242 @t241 @t176)) % 1.42/1.63 (define @t302 () (lambda @t42 (forall @t243 @t301))) % 1.42/1.63 (define @t303 () (_ @t302 @t13)) % 1.42/1.63 (define @t304 () (not @t303)) % 1.42/1.63 (define @t305 () (or @t304 @t218)) % 1.42/1.63 (define @t306 () (lambda @t220 @t305)) % 1.42/1.63 (define @t307 () (not (_ @t27 @t13))) % 1.42/1.63 (define @t308 () (or @t307 @t218)) % 1.42/1.63 (define @t309 () (lambda @t47 @t308)) % 1.42/1.63 (define @t310 () (or @t242 @t241 @t176)) % 1.42/1.63 (define @t311 () (or @t190 @t310)) % 1.42/1.63 (define @t312 () (forall @t243 @t311)) % 1.42/1.63 (define @t313 () (@list @t174 @t175)) % 1.42/1.63 (define @t314 () (forall @t313 @t311)) % 1.42/1.63 (define @t315 () (forall @t313 @t310)) % 1.42/1.63 (define @t316 () (@var "BOUND_VARIABLE_8634" $$unsorted)) % 1.42/1.63 (define @t317 () (or @t190 @t315)) % 1.42/1.63 (define @t318 () (tptp.f @t2 @t114)) % 1.42/1.63 (define @t319 () (not (forall @t117 (or (not (tptp.rel_s4 @t316 @t114)) @t318)))) % 1.42/1.63 (define @t320 () (@list @t2 @t316)) % 1.42/1.63 (define @t321 () (forall @t320 (or @t266 (not (tptp.rel_s4 @t1 @t316)) @t319))) % 1.42/1.63 (define @t322 () (not (tptp.rel_s4 @t7 @t316))) % 1.42/1.63 (define @t323 () (or @t268 @t322 @t319)) % 1.42/1.63 (define @t324 () (lambda @t42 (forall @t320 @t323))) % 1.42/1.63 (define @t325 () (_ @t324 @t1)) % 1.42/1.63 (define @t326 () (or @t190 @t325)) % 1.42/1.63 (define @t327 () (forall @t6 @t326)) % 1.42/1.63 (define @t328 () (lambda @t42 @t327)) % 1.42/1.63 (define @t329 () (or @t322 @t319)) % 1.42/1.63 (define @t330 () (or @t268 @t329)) % 1.42/1.63 (define @t331 () (forall @t320 @t330)) % 1.42/1.63 (define @t332 () (@list @t316)) % 1.42/1.63 (define @t333 () (forall @t332 @t330)) % 1.42/1.63 (define @t334 () (forall @t332 @t329)) % 1.42/1.63 (define @t335 () (or @t268 @t334)) % 1.42/1.63 (define @t336 () (not (tptp.rel_s4 @t1 @t114))) % 1.42/1.63 (define @t337 () (forall @t6 (or @t190 (not (forall @t117 (or @t336 @t318)))))) % 1.42/1.63 (define @t338 () (tptp.f @t18 @t114)) % 1.42/1.63 (define @t339 () (not (forall @t117 (or @t336 @t338)))) % 1.42/1.63 (define @t340 () (forall @t6 (or @t202 @t339))) % 1.42/1.63 (define @t341 () (lambda @t20 @t340)) % 1.42/1.63 (define @t342 () (_ @t341 @t2 @t7)) % 1.42/1.63 (define @t343 () (or @t268 @t342)) % 1.42/1.63 (define @t344 () (forall @t5 @t343)) % 1.42/1.63 (define @t345 () (lambda @t42 @t344)) % 1.42/1.63 (define @t346 () (_ @t54 @t2 @t7)) % 1.42/1.63 (define @t347 () (lambda @t58 (forall @t5 (or @t268 @t346)))) % 1.42/1.63 (define @t348 () (tptp.f @t18 @t1)) % 1.42/1.63 (define @t349 () (forall @t6 (or @t190 @t348))) % 1.42/1.63 (define @t350 () (not @t349)) % 1.42/1.63 (define @t351 () (lambda @t42 @t350)) % 1.42/1.63 (define @t352 () (or @t190 (_ @t351 @t1))) % 1.42/1.63 (define @t353 () (forall @t6 @t352)) % 1.42/1.63 (define @t354 () (lambda @t42 @t353)) % 1.42/1.63 (define @t355 () (lambda @t42 @t349)) % 1.42/1.63 (define @t356 () (_ @t355 @t7)) % 1.42/1.63 (define @t357 () (not @t356)) % 1.42/1.63 (define @t358 () (lambda @t42 @t357)) % 1.42/1.63 (define @t359 () (_ @t19 @t1)) % 1.42/1.63 (define @t360 () (or @t190 @t359)) % 1.42/1.63 (define @t361 () (_ @t19 @t1)) % 1.42/1.63 (define @t362 () (or @t190 @t361)) % 1.42/1.63 (define @t363 () (forall @t6 @t362)) % 1.42/1.63 (define @t364 () (lambda @t42 @t363)) % 1.42/1.63 (define @t365 () (_ @t252 @t19)) % 1.42/1.63 (define @t366 () (lambda @t20 (_ (_ @t252 (_ @t31 @t365)) @t13))) % 1.42/1.63 (define @t367 () (lambda @t42 @t196)) % 1.42/1.63 (define @t368 () (_ @t367 @t13)) % 1.42/1.63 (define @t369 () (not @t368)) % 1.42/1.63 (define @t370 () (or @t369 @t219)) % 1.42/1.63 (define @t371 () (not @t370)) % 1.42/1.63 (define @t372 () (lambda @t220 @t371)) % 1.42/1.63 (define @t373 () (not (or @t307 @t219))) % 1.42/1.63 (define @t374 () (lambda @t47 @t373)) % 1.42/1.63 (define @t375 () (or @t122 @t121 @t120 @t118)) % 1.42/1.63 (define @t376 () (or @t190 @t124 @t375)) % 1.42/1.63 (define @t377 () (forall @t187 @t376)) % 1.42/1.63 (define @t378 () (@list @t119 @t115 @t116)) % 1.42/1.64 (define @t379 () (forall @t378 @t376)) % 1.42/1.64 (define @t380 () (forall @t378 @t375)) % 1.42/1.64 (define @t381 () (@var "BOUND_VARIABLE_8696" $$unsorted)) % 1.42/1.64 (define @t382 () (or @t190 @t124 @t380)) % 1.42/1.64 (define @t383 () (not (tptp.rel_s4 @t381 @t175))) % 1.42/1.64 (define @t384 () (not (tptp.exists_in_world @t174 @t381))) % 1.42/1.64 (define @t385 () (@list @t381 @t174 @t175)) % 1.42/1.64 (define @t386 () (forall @t385 (or (not (tptp.rel_s4 @t1 @t381)) @t384 @t383 @t176))) % 1.42/1.64 (define @t387 () (or @t190 @t124 @t386)) % 1.42/1.64 (define @t388 () (or @t124 @t386)) % 1.42/1.64 (define @t389 () (not @t239)) % 1.42/1.64 (define @t390 () (or @t389 @t244)) % 1.42/1.64 (define @t391 () (lambda @t206 @t390)) % 1.42/1.64 (define @t392 () (or @t190 (_ @t391 @t1))) % 1.42/1.64 (define @t393 () (forall @t6 @t392)) % 1.42/1.64 (define @t394 () (lambda @t42 @t393)) % 1.42/1.64 (define @t395 () (or @t389 @t303)) % 1.42/1.64 (define @t396 () (lambda @t206 @t395)) % 1.42/1.64 (define @t397 () (not @t255)) % 1.42/1.64 (define @t398 () (or @t397 @t218)) % 1.42/1.64 (define @t399 () (lambda @t220 @t398)) % 1.42/1.64 (define @t400 () (_ @t252 (_ @t31 (_ @t292 @t300)))) % 1.42/1.64 (define @t401 () (_ @t252 (_ @t347 @t366))) % 1.42/1.64 (define @t402 () (forall @t5 (or @t268 (not @t346)))) % 1.42/1.64 (define @t403 () (lambda @t42 @t402)) % 1.42/1.64 (define @t404 () (_ @t403 @t7)) % 1.42/1.64 (define @t405 () (not @t404)) % 1.42/1.64 (define @t406 () (lambda @t42 @t405)) % 1.42/1.64 (define @t407 () (not @t56)) % 1.42/1.64 (define @t408 () (or @t268 @t407)) % 1.42/1.64 (define @t409 () (not (_ @t55 @t13))) % 1.42/1.64 (define @t410 () (lambda @t15 @t409)) % 1.42/1.64 (define @t411 () (_ @t410 @t2 @t7)) % 1.42/1.64 (define @t412 () (or @t268 @t411)) % 1.42/1.64 (define @t413 () (forall @t5 @t412)) % 1.42/1.64 (define @t414 () (lambda @t42 @t413)) % 1.42/1.64 (define @t415 () (lambda @t42 @t407)) % 1.42/1.64 (define @t416 () (_ @t31 @t55)) % 1.42/1.64 (define @t417 () (not @t8)) % 1.42/1.64 (define @t418 () (or @t417 @t56)) % 1.42/1.64 (define @t419 () (or @t29 @t33)) % 1.42/1.64 (define @t420 () (lambda @t42 @t419)) % 1.42/1.64 (define @t421 () (@list @t32 @t7)) % 1.42/1.64 (define @t422 () (lambda @t421 @t419)) % 1.42/1.64 (define @t423 () (lambda @t42 @t29)) % 1.42/1.64 (define @t424 () (_ @t423 @t7)) % 1.42/1.64 (define @t425 () (or @t424 @t33)) % 1.42/1.64 (define @t426 () (lambda @t421 @t425)) % 1.42/1.64 (define @t427 () (not @t33)) % 1.42/1.64 (define @t428 () (or @t29 @t427)) % 1.42/1.64 (define @t429 () (lambda @t42 @t428)) % 1.42/1.64 (define @t430 () (_ @t429 @t7)) % 1.42/1.64 (define @t431 () (not @t430)) % 1.42/1.64 (define @t432 () (lambda @t42 @t431)) % 1.42/1.64 (define @t433 () (lambda @t42 @t427)) % 1.42/1.64 (define @t434 () (_ @t433 @t7)) % 1.42/1.64 (define @t435 () (or @t29 @t434)) % 1.42/1.64 (define @t436 () (lambda @t42 @t435)) % 1.42/1.64 (define @t437 () (not @t184)) % 1.42/1.64 (define @t438 () (@quantifiers_skolemize @t184 3)) % 1.42/1.64 (define @t439 () (@quantifiers_skolemize @t184 2)) % 1.42/1.64 (define @t440 () (forall @t111 (or (not (tptp.rel_s4 @t439 @t107)) (tptp.f @t438 @t107)))) % 1.42/1.64 (define @t441 () (not @t440)) % 1.42/1.64 (define @t442 () (tptp.exists_in_world @t438 @t439)) % 1.42/1.64 (define @t443 () (not @t442)) % 1.42/1.64 (define @t444 () (@quantifiers_skolemize @t184 1)) % 1.42/1.64 (define @t445 () (tptp.rel_s4 @t444 @t439)) % 1.42/1.64 (define @t446 () (not @t445)) % 1.42/1.64 (define @t447 () (forall @t180 (or (not (tptp.rel_s4 @t444 @t177)) @t179 @t178 @t176))) % 1.42/1.64 (define @t448 () (not @t447)) % 1.42/1.64 (define @t449 () (or (not (tptp.rel_s4 (@quantifiers_skolemize @t184 0) @t444)) @t448 @t446 @t443 @t441)) % 1.42/1.64 (define @t450 () (not @t449)) % 1.42/1.64 (define @t451 () (@list true)) % 1.42/1.64 (define @t452 () (@list @t449)) % 1.42/1.64 (define @t453 () (forall @t117 (or (not (tptp.rel_s4 @t439 @t114)) (tptp.f @t438 @t114)))) % 1.42/1.64 (define @t454 () (not @t453)) % 1.42/1.64 (define @t455 () (tptp.rel_s4 @t439 @t439)) % 1.42/1.64 (define @t456 () (not @t455)) % 1.42/1.64 (define @t457 () (or @t446 @t443 @t456 @t454)) % 1.42/1.64 (define @t458 () (_ @t36 @t64 @t64)) % 1.42/1.64 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 1.42/1.64 (assume @p2 (forall @t6 (exists @t5 @t4))) % 1.42/1.64 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 1.42/1.64 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 1.42/1.64 (assume @p5 @t12) % 1.42/1.64 (assume @p6 @t23) % 1.42/1.64 (assume @p7 true) % 1.42/1.64 (step @p8 (= tptp.meq_prop @t26) :rule refl :args (@t26)) % 1.42/1.64 (step @p9 (= tptp.mnot @t31) :rule refl :args (@t31)) % 1.42/1.64 (step @p10 (= tptp.mor @t34) :rule refl :args (@t34)) % 1.42/1.64 (step @p11 (= tptp.mbox @t37) :rule refl :args (@t37)) % 1.42/1.64 (step @p12 (= tptp.mforall_prop @t41) :rule refl :args (@t41)) % 1.42/1.64 (step @p13 (= tptp.mtrue @t43) :rule refl :args (@t43)) % 1.42/1.64 (step @p14 (= tptp.mand @t48) :rule refl :args (@t48)) % 1.42/1.64 (step @p15 (= tptp.mimplies @t49) :rule refl :args (@t49)) % 1.42/1.64 (step @p16 (= tptp.mimplied @t50) :rule refl :args (@t50)) % 1.42/1.64 (step @p17 (= tptp.mequiv @t51) :rule refl :args (@t51)) % 1.42/1.64 (step @p18 (= tptp.mxor @t52) :rule refl :args (@t52)) % 1.42/1.64 (step @p19 (= tptp.mdia @t53) :rule refl :args (@t53)) % 1.42/1.64 (step @p20 (= tptp.mforall_ind @t59) :rule refl :args (@t59)) % 1.42/1.64 (step @p21 (= tptp.mexists_ind @t62) :rule refl :args (@t62)) % 1.42/1.64 (step @p22 (= tptp.mexists_prop @t63) :rule refl :args (@t63)) % 1.42/1.64 (step @p23 (= tptp.mreflexive @t70) :rule refl :args (@t70)) % 1.42/1.64 (step @p24 (= tptp.msymmetric @t74) :rule refl :args (@t74)) % 1.42/1.64 (step @p25 (= tptp.mserial @t76) :rule refl :args (@t76)) % 1.42/1.64 (step @p26 (= tptp.mtransitive @t83) :rule refl :args (@t83)) % 1.42/1.64 (step @p27 (= tptp.meuclidean @t85) :rule refl :args (@t85)) % 1.42/1.64 (step @p28 (= tptp.mpartially_functional @t87) :rule refl :args (@t87)) % 1.42/1.64 (step @p29 (= tptp.mfunctional @t89) :rule refl :args (@t89)) % 1.42/1.64 (step @p30 (= tptp.mweakly_dense @t92) :rule refl :args (@t92)) % 1.42/1.64 (step @p31 (= tptp.mweakly_connected @t93) :rule refl :args (@t93)) % 1.42/1.64 (step @p32 (= tptp.mweakly_directed @t94) :rule refl :args (@t94)) % 1.42/1.64 (step @p33 (= tptp.mvalid @t97) :rule refl :args (@t97)) % 1.42/1.64 (step @p34 (= tptp.msatisfiable @t98) :rule refl :args (@t98)) % 1.42/1.64 (step @p35 (= tptp.mcountersatisfiable @t99) :rule refl :args (@t99)) % 1.42/1.64 (step @p36 (= tptp.minvalid @t100) :rule refl :args (@t100)) % 1.42/1.64 (step @p37 (= tptp.mbox_s4 @t105) :rule refl :args (@t105)) % 1.42/1.64 (step @p38 (= tptp.mdia_s4 @t106) :rule refl :args (@t106)) % 1.42/1.64 (step @p39 :rule bool-double-not-elim :args (@t129)) % 1.42/1.64 (step @p40 :rule refl :args (@t142)) % 1.42/1.64 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or @t142 (not @t141)))) % 1.42/1.64 (step @p42 :rule cnf_or_neg :args (@t142 1)) % 1.42/1.64 (step @p43 :rule eq_resolve :premises (@p42 @p41)) % 1.42/1.64 (step @p44 :rule reordering :premises (@p43) :args ((or @t129 @t142))) % 1.42/1.64 (step @p45 :rule bool-double-not-elim :args (@t139)) % 1.42/1.64 (step @p46 :rule nary_cong :premises (@p40 @p45) :args ((or @t142 (not @t140)))) % 1.42/1.64 (step @p47 :rule cnf_or_neg :args (@t142 2)) % 1.42/1.64 (step @p48 :rule eq_resolve :premises (@p47 @p46)) % 1.42/1.64 (step @p49 :rule reordering :premises (@p48) :args ((or @t139 @t142))) % 1.42/1.64 (step @p50 :rule bool-double-not-elim :args (@t137)) % 1.42/1.64 (step @p51 :rule nary_cong :premises (@p40 @p50) :args ((or @t142 (not @t138)))) % 1.42/1.64 (step @p52 :rule cnf_or_neg :args (@t142 3)) % 1.42/1.64 (step @p53 :rule eq_resolve :premises (@p52 @p51)) % 1.42/1.64 (step @p54 :rule reordering :premises (@p53) :args ((or @t137 @t142))) % 1.42/1.64 (step @p55 :rule bool-double-not-elim :args (@t135)) % 1.42/1.64 (step @p56 :rule nary_cong :premises (@p40 @p55) :args ((or @t142 (not @t136)))) % 1.42/1.64 (step @p57 :rule cnf_or_neg :args (@t142 4)) % 1.42/1.64 (step @p58 :rule eq_resolve :premises (@p57 @p56)) % 1.42/1.64 (step @p59 :rule reordering :premises (@p58) :args ((or @t135 @t142))) % 1.42/1.64 (step @p60 :rule bool-double-not-elim :args (@t132)) % 1.42/1.64 (step @p61 :rule nary_cong :premises (@p40 @p60) :args ((or @t142 (not @t133)))) % 1.42/1.64 (step @p62 :rule cnf_or_neg :args (@t142 5)) % 1.42/1.64 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 1.42/1.64 (step @p64 :rule reordering :premises (@p63) :args ((or @t132 @t142))) % 1.42/1.64 (assume-push @p657 @t129) % 1.42/1.64 (step @p66 :rule instantiate :premises (@p657) :args ((@list @t131 @t130))) % 1.42/1.64 (step-pop @p658 :rule scope :premises (@p66)) % 1.42/1.64 (step @p67 :rule process_scope :premises (@p658) :args (@t149)) % 1.42/1.64 (step @p69 :rule implies_elim :premises (@p67)) % 1.42/1.64 (step @p70 :rule beta-reduce :args ((= (_ (lambda @t69 (forall @t81 (or (not @t152) (not @t151) @t150))) tptp.rel_s4) (forall @t81 (or (not (tptp.rel_s4 @t64 @t71)) (not (tptp.rel_s4 @t71 @t77)) (tptp.rel_s4 @t64 @t77)))))) % 1.42/1.64 (step @p71 :rule refl :args (tptp.rel_s4)) % 1.42/1.64 (step @p72 :rule refl :args (@t150)) % 1.42/1.64 (step @p73 :rule refl :args (@t78)) % 1.42/1.64 (step @p74 :rule cong :premises (@p73 @p72) :args ((= @t78 @t150))) % 1.42/1.64 (step @p75 :rule symm :premises (@p74)) % 1.42/1.64 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 1.42/1.64 (step @p77 :rule refl :args (@t151)) % 1.42/1.64 (step @p78 :rule refl :args (@t79)) % 1.42/1.64 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t79 @t151))) % 1.42/1.64 (step @p80 :rule symm :premises (@p79)) % 1.42/1.64 (step @p81 :rule eq_resolve :premises (@p78 @p80)) % 1.42/1.64 (step @p82 :rule cong :premises (@p81) :args (@t153)) % 1.42/1.64 (step @p83 :rule refl :args (@t152)) % 1.42/1.64 (step @p84 :rule refl :args (@t73)) % 1.42/1.64 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t73 @t152))) % 1.42/1.64 (step @p86 :rule symm :premises (@p85)) % 1.42/1.64 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 1.42/1.64 (step @p88 :rule cong :premises (@p87) :args (@t154)) % 1.42/1.64 (step @p89 :rule nary_cong :premises (@p88 @p82 @p76) :args (@t155)) % 1.42/1.64 (step @p90 :rule cong :premises (@p89) :args ((forall @t81 @t155))) % 1.42/1.64 (step @p91 :rule aci_norm :args ((= (or (or @t154 @t153) @t78) @t155))) % 1.42/1.64 (step @p92 :rule bool-and-de-morgan :args (@t73 @t79 true)) % 1.42/1.64 (step @p93 :rule nary_cong :premises (@p92 @p73) :args ((or (not @t80) @t78))) % 1.42/1.64 (step @p94 :rule trans :premises (@p93 @p91)) % 1.42/1.64 (step @p95 :rule bool-impl-elim :args (@t80 @t78)) % 1.42/1.64 (step @p96 :rule trans :premises (@p95 @p94)) % 1.42/1.64 (step @p97 :rule cong :premises (@p96) :args (@t82)) % 1.42/1.64 (step @p98 :rule trans :premises (@p97 @p90)) % 1.42/1.64 (step @p99 :rule cong :premises (@p98) :args (@t83)) % 1.42/1.64 (step @p100 :rule trans :premises (@p26 @p99)) % 1.42/1.64 (step @p101 :rule ho_cong :premises (@p100 @p71)) % 1.42/1.64 (step @p102 :rule trans :premises (@p101 @p70)) % 1.42/1.64 (step @p103 :rule eq_resolve :premises (@p4 @p102)) % 1.42/1.64 (step @p104 :rule instantiate :premises (@p103) :args ((@list @t128 @t134 @t131))) % 1.42/1.64 (step @p105 :rule cnf_or_pos :args (@t156)) % 1.42/1.64 (step @p106 :rule reordering :premises (@p105) :args ((or @t140 @t136 @t147 (not @t156)))) % 1.42/1.64 (step @p107 :rule refl :args (@t157)) % 1.42/1.64 (step @p108 :rule refl :args (@t8)) % 1.42/1.64 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t8 @t157))) % 1.42/1.64 (step @p110 :rule symm :premises (@p109)) % 1.42/1.64 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 1.42/1.64 (step @p112 :rule refl :args (@t158)) % 1.42/1.64 (step @p113 :rule refl :args (@t9)) % 1.42/1.64 (step @p114 :rule cong :premises (@p113 @p112) :args ((= @t9 @t158))) % 1.42/1.64 (step @p115 :rule symm :premises (@p114)) % 1.42/1.64 (step @p116 :rule eq_resolve :premises (@p113 @p115)) % 1.42/1.64 (step @p117 :rule cong :premises (@p116) :args (@t159)) % 1.42/1.64 (step @p118 :rule refl :args (@t160)) % 1.42/1.64 (step @p119 :rule refl :args (@t4)) % 1.42/1.64 (step @p120 :rule cong :premises (@p119 @p118) :args ((= @t4 @t160))) % 1.42/1.64 (step @p121 :rule symm :premises (@p120)) % 1.42/1.64 (step @p122 :rule eq_resolve :premises (@p119 @p121)) % 1.42/1.64 (step @p123 :rule cong :premises (@p122) :args (@t161)) % 1.42/1.64 (step @p124 :rule nary_cong :premises (@p123 @p117 @p111) :args (@t162)) % 1.42/1.64 (step @p125 :rule cong :premises 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:rule eq_resolve :premises (@p616 @p615)) % 1.42/1.64 (step @p618 :rule reordering :premises (@p617) :args ((or @t442 @t449))) % 1.42/1.64 (step @p619 :rule chain_m_resolution :premises (@p618 @p606) :args (@t442 @t451 @t452)) % 1.42/1.64 (step @p620 :rule bool-double-not-elim :args (@t447)) % 1.42/1.64 (step @p621 :rule nary_cong :premises (@p608 @p620) :args ((or @t449 (not @t448)))) % 1.42/1.64 (step @p622 :rule cnf_or_neg :args (@t449 1)) % 1.42/1.64 (step @p623 :rule eq_resolve :premises (@p622 @p621)) % 1.42/1.64 (step @p624 :rule reordering :premises (@p623) :args ((or @t447 @t449))) % 1.42/1.64 (step @p625 :rule chain_m_resolution :premises (@p624 @p606) :args (@t447 @t451 @t452)) % 1.42/1.64 (assume-push @p663 @t447) % 1.42/1.64 (step @p627 :rule instantiate :premises (@p663) :args ((@list @t439 @t438 @t439))) % 1.42/1.64 (step-pop @p664 :rule scope :premises (@p627)) % 1.42/1.64 (step @p628 :rule process_scope :premises (@p664) :args (@t457)) % 1.42/1.64 (step @p630 :rule implies_elim :premises (@p628)) % 1.42/1.64 (step @p631 :rule chain_m_resolution :premises (@p630 @p625) :args (@t457 @t168 (@list @t447))) % 1.42/1.64 (step @p632 :rule beta-reduce :args ((= (_ (lambda @t69 (forall @t67 @t458)) tptp.rel_s4) (forall @t67 (tptp.rel_s4 @t64 @t64))))) % 1.42/1.64 (step @p633 :rule refl :args (@t458)) % 1.42/1.64 (step @p634 :rule refl :args (@t66)) % 1.42/1.64 (step @p635 :rule cong :premises (@p634 @p633) :args ((= @t66 @t458))) % 1.42/1.64 (step @p636 :rule symm :premises (@p635)) % 1.42/1.64 (step @p637 :rule eq_resolve :premises (@p634 @p636)) % 1.42/1.64 (step @p638 :rule cong :premises (@p637) :args (@t68)) % 1.42/1.64 (step @p639 :rule cong :premises (@p638) :args (@t70)) % 1.42/1.64 (step @p640 :rule trans :premises (@p23 @p639)) % 1.42/1.64 (step @p641 :rule ho_cong :premises (@p640 @p71)) % 1.42/1.64 (step @p642 :rule trans :premises (@p641 @p632)) % 1.42/1.64 (step @p643 :rule eq_resolve :premises (@p3 @p642)) % 1.42/1.64 (step @p644 :rule instantiate :premises (@p643) :args ((@list @t439))) % 1.42/1.64 (step @p645 :rule bool-double-not-elim :args (@t440)) % 1.42/1.64 (step @p646 :rule nary_cong :premises (@p608 @p645) :args ((or @t449 (not @t441)))) % 1.42/1.64 (step @p647 :rule cnf_or_neg :args (@t449 4)) % 1.42/1.64 (step @p648 :rule eq_resolve :premises (@p647 @p646)) % 1.42/1.64 (step @p649 :rule reordering :premises (@p648) :args ((or @t440 @t449))) % 1.42/1.64 (step @p650 :rule chain_m_resolution :premises (@p649 @p606) :args (@t440 @t451 @t452)) % 1.42/1.64 (step @p651 :rule alpha_equiv :args (@t440 @t165 @t164)) % 1.42/1.64 (step @p652 :rule equiv_elim1 :premises (@p651)) % 1.42/1.64 (step @p653 :rule chain_m_resolution :premises (@p652 @p650) :args (@t453 @t168 (@list @t440))) % 1.42/1.64 (step @p654 :rule cnf_or_pos :args (@t457)) % 1.42/1.64 (step @p655 :rule reordering :premises (@p654) :args ((or @t446 @t443 @t456 @t454 (not @t457)))) % 1.42/1.64 (step @p656 false :rule chain_m_resolution :premises (@p655 @p653 @p644 @p631 @p619 @p613) :args (false (@list false false false false false) (@list @t453 @t455 @t457 @t442 @t445))) % 1.42/1.64 ) % 1.42/1.64 % SZS output end Proof % 1.42/1.64 % cvc5 exiting %------------------------------------------------------------------------------