%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET925^7 : 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 : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:48:59 AM UTC 2026 % Result : Theorem 0.50s 0.70s % Output : Proof 0.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SET925^7 : TPTP v9.2.1. Released v5.5.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n008.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 16:18:03 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.50/0.70 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.50/0.70 % SZS status Theorem % 0.50/0.70 % SZS output start Proof % 0.50/0.70 ( % 0.50/0.70 (declare-sort tptp.mu 0) % 0.50/0.70 (declare-sort $$unsorted 0) % 0.50/0.70 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 0.50/0.70 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.50/0.70 (declare-const tptp.in (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.50/0.70 (declare-const tptp.empty (-> tptp.mu $$unsorted Bool)) % 0.50/0.70 (declare-const tptp.qmltpeq (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.50/0.70 (declare-const tptp.set_difference (-> tptp.mu tptp.mu tptp.mu)) % 0.50/0.70 (declare-const tptp.empty_set tptp.mu) % 0.50/0.70 (declare-const tptp.singleton (-> tptp.mu tptp.mu)) % 0.50/0.70 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.50/0.70 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.50/0.70 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.50/0.70 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.50/0.70 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.50/0.70 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.50/0.70 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.50/0.70 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.50/0.70 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.50/0.70 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.50/0.70 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.50/0.70 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.50/0.70 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.50/0.70 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.exists_in_world _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.50/0.70 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.50/0.70 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.50/0.70 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.50/0.70 (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)))))))) % 0.50/0.70 (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)))))))) % 0.50/0.70 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.50/0.70 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.50/0.70 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.50/0.70 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.50/0.70 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.50/0.70 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.50/0.70 (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))))))))))))) % 0.50/0.70 (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)))))) % 0.50/0.70 (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)))))) % 0.50/0.70 (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))))))) % 0.50/0.70 (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))))))) % 0.50/0.70 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.50/0.70 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.50/0.70 (define @t1 () (@var "V" $$unsorted)) % 0.50/0.70 (define @t2 () (@var "X" tptp.mu)) % 0.50/0.70 (define @t3 () (_ tptp.exists_in_world @t2)) % 0.50/0.70 (define @t4 () (_ @t3 @t1)) % 0.50/0.70 (define @t5 () (@list @t2)) % 0.50/0.70 (define @t6 () (@list @t1)) % 0.50/0.70 (define @t7 () (@var "W" $$unsorted)) % 0.50/0.70 (define @t8 () (_ @t3 @t7)) % 0.50/0.70 (define @t9 () (@var "V1" tptp.mu)) % 0.50/0.70 (define @t10 () (@var "V2" tptp.mu)) % 0.50/0.70 (define @t11 () (@var "__flatten_var_0" $$unsorted)) % 0.50/0.70 (define @t12 () (_ tptp.qmltpeq @t2)) % 0.50/0.70 (define @t13 () (@list @t2 @t11)) % 0.50/0.70 (define @t14 () (@var "Y" tptp.mu)) % 0.50/0.70 (define @t15 () (_ tptp.qmltpeq @t14)) % 0.50/0.70 (define @t16 () (_ tptp.mbox_s4 (_ @t12 @t14))) % 0.50/0.70 (define @t17 () (@list @t14 @t11)) % 0.50/0.70 (define @t18 () (@var "Z" tptp.mu)) % 0.50/0.70 (define @t19 () (@var "C" tptp.mu)) % 0.50/0.70 (define @t20 () (@var "B" tptp.mu)) % 0.50/0.70 (define @t21 () (@var "A" tptp.mu)) % 0.50/0.70 (define @t22 () (_ tptp.mbox_s4 (_ (_ tptp.qmltpeq @t21) @t20))) % 0.50/0.70 (define @t23 () (_ tptp.mimplies @t22)) % 0.50/0.70 (define @t24 () (@list @t19 @t11)) % 0.50/0.70 (define @t25 () (@list @t20 @t11)) % 0.50/0.70 (define @t26 () (@list @t21 @t11)) % 0.50/0.70 (define @t27 () (_ tptp.set_difference @t19)) % 0.50/0.70 (define @t28 () (_ tptp.singleton @t21)) % 0.50/0.70 (define @t29 () (_ tptp.mbox_s4 (_ tptp.empty @t21))) % 0.50/0.70 (define @t30 () (_ tptp.mand @t22)) % 0.50/0.70 (define @t31 () (_ tptp.in @t20)) % 0.50/0.70 (define @t32 () (_ tptp.in @t21)) % 0.50/0.70 (define @t33 () (_ tptp.in @t19)) % 0.50/0.70 (define @t34 () (_ @t32 @t20)) % 0.50/0.70 (define @t35 () (_ tptp.mbox_s4 @t34)) % 0.50/0.70 (define @t36 () (_ tptp.mimplies @t35)) % 0.50/0.70 (define @t37 () (_ (_ tptp.set_difference @t28) @t20)) % 0.50/0.70 (define @t38 () (_ (_ tptp.qmltpeq @t37) tptp.empty_set)) % 0.50/0.70 (define @t39 () (_ tptp.mbox_s4 @t38)) % 0.50/0.70 (define @t40 () (lambda @t25 (_ (_ (_ tptp.mand (_ tptp.mbox_s4 (_ (_ tptp.mimplies @t39) @t35))) (_ tptp.mbox_s4 (_ @t36 @t39))) @t11))) % 0.50/0.70 (define @t41 () (lambda @t26 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind @t40)) @t11))) % 0.50/0.70 (define @t42 () (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind @t41)))) % 0.50/0.70 (define @t43 () (not @t42)) % 0.50/0.70 (define @t44 () (@var "Y" (-> $$unsorted Bool))) % 0.50/0.70 (define @t45 () (@var "X" (-> $$unsorted Bool))) % 0.50/0.70 (define @t46 () (lambda (@list @t45 @t44 @t7) (= (_ @t45 @t7) (_ @t44 @t7)))) % 0.50/0.70 (define @t47 () (@var "Phi" (-> $$unsorted Bool))) % 0.50/0.70 (define @t48 () (_ @t47 @t7)) % 0.50/0.70 (define @t49 () (not @t48)) % 0.50/0.70 (define @t50 () (@list @t47 @t7)) % 0.50/0.70 (define @t51 () (lambda @t50 @t49)) % 0.50/0.70 (define @t52 () (@var "Psi" (-> $$unsorted Bool))) % 0.50/0.70 (define @t53 () (_ @t52 @t7)) % 0.50/0.70 (define @t54 () (lambda (@list @t47 @t52 @t7) (or @t48 @t53))) % 0.50/0.70 (define @t55 () (_ @t47 @t1)) % 0.50/0.70 (define @t56 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.50/0.70 (define @t57 () (lambda (@list @t56 @t47 @t7) (forall @t6 (or (not (_ (_ @t56 @t7) @t1)) @t55)))) % 0.50/0.70 (define @t58 () (@var "P" (-> $$unsorted Bool))) % 0.50/0.70 (define @t59 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.50/0.70 (define @t60 () (_ @t59 @t58)) % 0.50/0.70 (define @t61 () (lambda (@list @t59 @t7) (forall (@list @t58) (_ @t60 @t7)))) % 0.50/0.70 (define @t62 () (@list @t7)) % 0.50/0.70 (define @t63 () (lambda @t62 true)) % 0.50/0.70 (define @t64 () (_ tptp.mnot @t52)) % 0.50/0.70 (define @t65 () (_ tptp.mnot @t47)) % 0.50/0.70 (define @t66 () (_ tptp.mor @t65)) % 0.50/0.70 (define @t67 () (@list @t47 @t52 @t11)) % 0.50/0.70 (define @t68 () (lambda @t67 (_ (_ tptp.mnot (_ @t66 @t64)) @t11))) % 0.50/0.70 (define @t69 () (lambda @t67 (_ (_ @t66 @t52) @t11))) % 0.50/0.70 (define @t70 () (lambda @t67 (_ (_ (_ tptp.mor @t64) @t47) @t11))) % 0.50/0.70 (define @t71 () (lambda @t67 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t47) @t52)) (_ (_ tptp.mimplies @t52) @t47)) @t11))) % 0.50/0.70 (define @t72 () (lambda @t67 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t47) @t52)) @t11))) % 0.50/0.70 (define @t73 () (lambda (@list @t56 @t47 @t11) (_ (_ tptp.mnot (_ (_ tptp.mbox @t56) @t65)) @t11))) % 0.50/0.70 (define @t74 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.50/0.70 (define @t75 () (_ @t74 @t2)) % 0.50/0.70 (define @t76 () (_ @t75 @t7)) % 0.50/0.70 (define @t77 () (forall @t5 (=> @t8 @t76))) % 0.50/0.70 (define @t78 () (@list @t74 @t7)) % 0.50/0.70 (define @t79 () (lambda @t78 @t77)) % 0.50/0.70 (define @t80 () (lambda (@list @t74 @t11) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda @t13 (_ (_ tptp.mnot @t75) @t11)))) @t11))) % 0.50/0.70 (define @t81 () (lambda (@list @t59 @t11) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t58 @t11) (_ (_ tptp.mnot @t60) @t11)))) @t11))) % 0.50/0.70 (define @t82 () (@var "S" $$unsorted)) % 0.50/0.70 (define @t83 () (_ @t56 @t82)) % 0.50/0.70 (define @t84 () (@list @t82)) % 0.50/0.70 (define @t85 () (@list @t56)) % 0.50/0.70 (define @t86 () (lambda @t85 (forall @t84 (_ @t83 @t82)))) % 0.50/0.70 (define @t87 () (@var "T" $$unsorted)) % 0.50/0.70 (define @t88 () (_ @t56 @t87)) % 0.50/0.70 (define @t89 () (_ @t83 @t87)) % 0.50/0.70 (define @t90 () (lambda @t85 (forall (@list @t82 @t87) (=> @t89 (_ @t88 @t82))))) % 0.50/0.70 (define @t91 () (@list @t87)) % 0.50/0.70 (define @t92 () (lambda @t85 (forall @t84 (exists @t91 @t89)))) % 0.50/0.70 (define @t93 () (@var "U" $$unsorted)) % 0.50/0.70 (define @t94 () (_ @t83 @t93)) % 0.50/0.70 (define @t95 () (_ @t88 @t93)) % 0.50/0.70 (define @t96 () (@list @t82 @t87 @t93)) % 0.50/0.70 (define @t97 () (lambda @t85 (forall @t96 (=> (and @t89 @t95) @t94)))) % 0.50/0.70 (define @t98 () (and @t89 @t94)) % 0.50/0.70 (define @t99 () (lambda @t85 (forall @t96 (=> @t98 @t95)))) % 0.50/0.70 (define @t100 () (= @t87 @t93)) % 0.50/0.70 (define @t101 () (lambda @t85 (forall @t96 (=> @t98 @t100)))) % 0.50/0.70 (define @t102 () (@list @t93)) % 0.50/0.70 (define @t103 () (lambda @t85 (forall @t84 (exists @t91 (and @t89 (forall @t102 (=> @t94 @t100))))))) % 0.50/0.70 (define @t104 () (_ @t56 @t93)) % 0.50/0.70 (define @t105 () (_ @t104 @t87)) % 0.50/0.70 (define @t106 () (lambda @t85 (forall @t96 (=> @t89 (exists @t102 (and @t94 @t105)))))) % 0.50/0.70 (define @t107 () (lambda @t85 (forall @t96 (=> @t98 (or @t95 @t100 @t105))))) % 0.50/0.70 (define @t108 () (lambda @t85 (forall @t96 (=> @t98 (exists @t6 (and (_ @t88 @t1) (_ @t104 @t1))))))) % 0.50/0.70 (define @t109 () (forall @t62 @t48)) % 0.50/0.70 (define @t110 () (@list @t47)) % 0.50/0.70 (define @t111 () (lambda @t110 @t109)) % 0.50/0.70 (define @t112 () (lambda @t110 (exists @t62 @t48))) % 0.50/0.70 (define @t113 () (lambda @t110 (exists @t62 @t49))) % 0.50/0.70 (define @t114 () (lambda @t110 (forall @t62 @t49))) % 0.50/0.70 (define @t115 () (_ (_ tptp.rel_s4 @t7) @t1)) % 0.50/0.70 (define @t116 () (not @t115)) % 0.50/0.70 (define @t117 () (or @t116 @t55)) % 0.50/0.70 (define @t118 () (forall @t6 @t117)) % 0.50/0.70 (define @t119 () (lambda @t50 @t118)) % 0.50/0.70 (define @t120 () (lambda (@list @t47 @t11) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t65)) @t11))) % 0.50/0.70 (define @t121 () (@var "BOUND_VARIABLE_12761" $$unsorted)) % 0.50/0.70 (define @t122 () (@var "BOUND_VARIABLE_12753" tptp.mu)) % 0.50/0.70 (define @t123 () (@var "BOUND_VARIABLE_12749" tptp.mu)) % 0.50/0.70 (define @t124 () (tptp.set_difference (tptp.singleton @t123) @t122)) % 0.50/0.70 (define @t125 () (@var "BOUND_VARIABLE_12759" $$unsorted)) % 0.50/0.70 (define @t126 () (@var "BOUND_VARIABLE_12484" $$unsorted)) % 0.50/0.70 (define @t127 () (@list @t126)) % 0.50/0.70 (define @t128 () (@var "BOUND_VARIABLE_12751" $$unsorted)) % 0.50/0.70 (define @t129 () (@var "BOUND_VARIABLE_12757" $$unsorted)) % 0.50/0.70 (define @t130 () (@var "BOUND_VARIABLE_12755" $$unsorted)) % 0.50/0.70 (define @t131 () (@var "BOUND_VARIABLE_12417" $$unsorted)) % 0.50/0.70 (define @t132 () (@list @t131)) % 0.50/0.70 (define @t133 () (and (or (not (tptp.rel_s4 @t128 @t130)) (not (forall @t132 (or (not (tptp.rel_s4 @t130 @t131)) (tptp.qmltpeq @t124 tptp.empty_set @t131)))) (not (tptp.rel_s4 @t130 @t129)) (tptp.in @t123 @t122 @t129)) (or (not (tptp.rel_s4 @t128 @t125)) (not (forall @t127 (or (not (tptp.rel_s4 @t125 @t126)) (tptp.in @t123 @t122 @t126)))) (not (tptp.rel_s4 @t125 @t121)) (tptp.qmltpeq @t124 tptp.empty_set @t121)))) % 0.50/0.70 (define @t134 () (not (tptp.exists_in_world @t122 @t128))) % 0.50/0.70 (define @t135 () (not (tptp.rel_s4 @t1 @t128))) % 0.50/0.70 (define @t136 () (not (tptp.exists_in_world @t123 @t1))) % 0.50/0.70 (define @t137 () (tptp.rel_s4 @t7 @t1)) % 0.50/0.70 (define @t138 () (not @t137)) % 0.50/0.70 (define @t139 () (or @t138 @t136 @t135 @t134 @t133)) % 0.50/0.70 (define @t140 () (@list @t1 @t123 @t128 @t122 @t130 @t129 @t125 @t121)) % 0.50/0.70 (define @t141 () (forall @t140 @t139)) % 0.50/0.70 (define @t142 () (lambda @t62 @t141)) % 0.50/0.70 (define @t143 () (_ @t142 @t7)) % 0.50/0.70 (define @t144 () (forall @t62 @t143)) % 0.50/0.70 (define @t145 () (_ @t47 @t7)) % 0.50/0.70 (define @t146 () (lambda @t110 (forall @t62 @t145))) % 0.50/0.70 (define @t147 () (or @t136 @t135 @t134 @t133)) % 0.50/0.70 (define @t148 () (or @t138 @t147)) % 0.50/0.70 (define @t149 () (forall @t140 @t148)) % 0.50/0.70 (define @t150 () (@list @t123 @t128 @t122 @t130 @t129 @t125 @t121)) % 0.50/0.70 (define @t151 () (forall @t150 @t148)) % 0.50/0.70 (define @t152 () (forall @t150 @t147)) % 0.50/0.70 (define @t153 () (@var "BOUND_VARIABLE_12699" $$unsorted)) % 0.50/0.70 (define @t154 () (@var "BOUND_VARIABLE_12697" $$unsorted)) % 0.50/0.70 (define @t155 () (@var "BOUND_VARIABLE_12695" $$unsorted)) % 0.50/0.70 (define @t156 () (@var "BOUND_VARIABLE_12693" $$unsorted)) % 0.50/0.70 (define @t157 () (@var "BOUND_VARIABLE_12691" tptp.mu)) % 0.50/0.70 (define @t158 () (@var "BOUND_VARIABLE_12689" $$unsorted)) % 0.50/0.70 (define @t159 () (or @t138 @t152)) % 0.50/0.70 (define @t160 () (tptp.singleton @t2)) % 0.50/0.70 (define @t161 () (tptp.set_difference @t160 @t157)) % 0.50/0.70 (define @t162 () (and (or (not (tptp.rel_s4 @t158 @t156)) (not (forall @t132 (or (not (tptp.rel_s4 @t156 @t131)) (tptp.qmltpeq @t161 tptp.empty_set @t131)))) (not (tptp.rel_s4 @t156 @t155)) (tptp.in @t2 @t157 @t155)) (or (not (tptp.rel_s4 @t158 @t154)) (not (forall @t127 (or (not (tptp.rel_s4 @t154 @t126)) (tptp.in @t2 @t157 @t126)))) (not (tptp.rel_s4 @t154 @t153)) (tptp.qmltpeq @t161 tptp.empty_set @t153)))) % 0.50/0.70 (define @t163 () (not (tptp.exists_in_world @t157 @t158))) % 0.50/0.70 (define @t164 () (not (tptp.exists_in_world @t2 @t1))) % 0.50/0.70 (define @t165 () (@list @t2 @t158 @t157 @t156 @t155 @t154 @t153)) % 0.50/0.70 (define @t166 () (forall @t165 (or @t164 (not (tptp.rel_s4 @t1 @t158)) @t163 @t162))) % 0.50/0.70 (define @t167 () (not (tptp.rel_s4 @t7 @t158))) % 0.50/0.70 (define @t168 () (tptp.exists_in_world @t2 @t7)) % 0.50/0.70 (define @t169 () (not @t168)) % 0.50/0.70 (define @t170 () (or @t169 @t167 @t163 @t162)) % 0.50/0.70 (define @t171 () (lambda @t62 (forall @t165 @t170))) % 0.50/0.70 (define @t172 () (_ @t171 @t1)) % 0.50/0.70 (define @t173 () (or @t138 @t172)) % 0.50/0.70 (define @t174 () (forall @t6 @t173)) % 0.50/0.70 (define @t175 () (lambda @t62 @t174)) % 0.50/0.70 (define @t176 () (_ @t47 @t1)) % 0.50/0.70 (define @t177 () (lambda @t50 (forall @t6 (or @t138 @t176)))) % 0.50/0.70 (define @t178 () (or @t167 @t163 @t162)) % 0.50/0.70 (define @t179 () (or @t169 @t178)) % 0.50/0.70 (define @t180 () (forall @t165 @t179)) % 0.50/0.70 (define @t181 () (@list @t158 @t157 @t156 @t155 @t154 @t153)) % 0.50/0.70 (define @t182 () (forall @t181 @t179)) % 0.50/0.70 (define @t183 () (forall @t181 @t178)) % 0.50/0.70 (define @t184 () (@var "BOUND_VARIABLE_12624" $$unsorted)) % 0.50/0.70 (define @t185 () (@var "BOUND_VARIABLE_12622" $$unsorted)) % 0.50/0.70 (define @t186 () (@var "BOUND_VARIABLE_12620" $$unsorted)) % 0.50/0.70 (define @t187 () (@var "BOUND_VARIABLE_12618" $$unsorted)) % 0.50/0.70 (define @t188 () (@var "BOUND_VARIABLE_12616" tptp.mu)) % 0.50/0.70 (define @t189 () (or @t169 @t183)) % 0.50/0.70 (define @t190 () (tptp.set_difference @t160 @t188)) % 0.50/0.70 (define @t191 () (not (tptp.rel_s4 @t185 @t184))) % 0.50/0.70 (define @t192 () (not (tptp.rel_s4 @t185 @t126))) % 0.50/0.70 (define @t193 () (not (tptp.rel_s4 @t1 @t185))) % 0.50/0.70 (define @t194 () (not (tptp.rel_s4 @t187 @t186))) % 0.50/0.70 (define @t195 () (not (tptp.rel_s4 @t187 @t131))) % 0.50/0.70 (define @t196 () (not (tptp.rel_s4 @t1 @t187))) % 0.50/0.70 (define @t197 () (not (tptp.exists_in_world @t188 @t1))) % 0.50/0.70 (define @t198 () (@list @t1 @t188 @t187 @t186 @t185 @t184)) % 0.50/0.70 (define @t199 () (forall @t198 (or @t138 @t197 (and (or @t196 (not (forall @t132 (or @t195 (tptp.qmltpeq @t190 tptp.empty_set @t131)))) @t194 (tptp.in @t2 @t188 @t186)) (or @t193 (not (forall @t127 (or @t192 (tptp.in @t2 @t188 @t126)))) @t191 (tptp.qmltpeq @t190 tptp.empty_set @t184)))))) % 0.50/0.70 (define @t200 () (tptp.singleton @t21)) % 0.50/0.70 (define @t201 () (tptp.set_difference @t200 @t188)) % 0.50/0.70 (define @t202 () (and (or @t196 (not (forall @t132 (or @t195 (tptp.qmltpeq @t201 tptp.empty_set @t131)))) @t194 (tptp.in @t21 @t188 @t186)) (or @t193 (not (forall @t127 (or @t192 (tptp.in @t21 @t188 @t126)))) @t191 (tptp.qmltpeq @t201 tptp.empty_set @t184)))) % 0.50/0.70 (define @t203 () (not (tptp.rel_s4 @t11 @t1))) % 0.50/0.70 (define @t204 () (forall @t198 (or @t203 @t197 @t202))) % 0.50/0.70 (define @t205 () (lambda @t26 @t204)) % 0.50/0.70 (define @t206 () (_ @t205 @t2 @t7)) % 0.50/0.70 (define @t207 () (or @t169 @t206)) % 0.50/0.70 (define @t208 () (forall @t5 @t207)) % 0.50/0.70 (define @t209 () (lambda @t62 @t208)) % 0.50/0.70 (define @t210 () (_ @t74 @t2 @t7)) % 0.50/0.70 (define @t211 () (lambda @t78 (forall @t5 (or @t169 @t210)))) % 0.50/0.70 (define @t212 () (or @t138 @t197 @t202)) % 0.50/0.70 (define @t213 () (or @t197 @t202)) % 0.50/0.70 (define @t214 () (or @t138 @t213)) % 0.50/0.70 (define @t215 () (forall @t198 @t214)) % 0.50/0.70 (define @t216 () (@list @t188 @t187 @t186 @t185 @t184)) % 0.50/0.70 (define @t217 () (forall @t216 @t214)) % 0.50/0.70 (define @t218 () (forall @t216 @t213)) % 0.50/0.70 (define @t219 () (@var "BOUND_VARIABLE_12582" $$unsorted)) % 0.50/0.70 (define @t220 () (@var "BOUND_VARIABLE_12580" $$unsorted)) % 0.50/0.70 (define @t221 () (@var "BOUND_VARIABLE_12567" $$unsorted)) % 0.50/0.70 (define @t222 () (@var "BOUND_VARIABLE_12565" $$unsorted)) % 0.50/0.70 (define @t223 () (or @t138 @t218)) % 0.50/0.70 (define @t224 () (tptp.set_difference @t200 @t2)) % 0.50/0.70 (define @t225 () (tptp.qmltpeq @t224 tptp.empty_set @t219)) % 0.50/0.70 (define @t226 () (not (tptp.rel_s4 @t220 @t219))) % 0.50/0.70 (define @t227 () (tptp.in @t21 @t2 @t126)) % 0.50/0.70 (define @t228 () (not (forall @t127 (or (not (tptp.rel_s4 @t220 @t126)) @t227)))) % 0.50/0.70 (define @t229 () (tptp.in @t21 @t2 @t221)) % 0.50/0.70 (define @t230 () (not (tptp.rel_s4 @t222 @t221))) % 0.50/0.70 (define @t231 () (tptp.qmltpeq @t224 tptp.empty_set @t131)) % 0.50/0.70 (define @t232 () (not (forall @t132 (or (not (tptp.rel_s4 @t222 @t131)) @t231)))) % 0.50/0.70 (define @t233 () (@list @t2 @t222 @t221 @t220 @t219)) % 0.50/0.70 (define @t234 () (forall @t233 (or @t164 (and (or (not (tptp.rel_s4 @t1 @t222)) @t232 @t230 @t229) (or (not (tptp.rel_s4 @t1 @t220)) @t228 @t226 @t225))))) % 0.50/0.70 (define @t235 () (or (not (tptp.rel_s4 @t7 @t220)) @t228 @t226 @t225)) % 0.50/0.70 (define @t236 () (or (not (tptp.rel_s4 @t7 @t222)) @t232 @t230 @t229)) % 0.50/0.70 (define @t237 () (and @t236 @t235)) % 0.50/0.70 (define @t238 () (or @t169 @t237)) % 0.50/0.70 (define @t239 () (forall @t233 @t238)) % 0.50/0.70 (define @t240 () (lambda @t62 @t239)) % 0.50/0.70 (define @t241 () (_ @t240 @t1)) % 0.50/0.70 (define @t242 () (or @t138 @t241)) % 0.50/0.70 (define @t243 () (forall @t6 @t242)) % 0.50/0.70 (define @t244 () (lambda @t62 @t243)) % 0.50/0.70 (define @t245 () (@list @t222 @t221 @t220 @t219)) % 0.50/0.70 (define @t246 () (forall @t245 @t238)) % 0.50/0.70 (define @t247 () (forall (@list @t220 @t219) @t235)) % 0.50/0.70 (define @t248 () (@var "BOUND_VARIABLE_12509" $$unsorted)) % 0.50/0.70 (define @t249 () (forall @t245 @t235)) % 0.50/0.70 (define @t250 () (forall (@list @t222 @t221) @t236)) % 0.50/0.70 (define @t251 () (@var "BOUND_VARIABLE_12442" $$unsorted)) % 0.50/0.70 (define @t252 () (forall @t245 @t236)) % 0.50/0.70 (define @t253 () (and @t252 @t249)) % 0.50/0.70 (define @t254 () (forall @t245 @t237)) % 0.50/0.70 (define @t255 () (or @t169 @t254)) % 0.50/0.70 (define @t256 () (not (tptp.rel_s4 @t1 @t248))) % 0.50/0.70 (define @t257 () (not (tptp.rel_s4 @t1 @t126))) % 0.50/0.70 (define @t258 () (@list @t1 @t248)) % 0.50/0.70 (define @t259 () (forall @t258 (or @t138 (not (forall @t127 (or @t257 @t227))) @t256 (tptp.qmltpeq @t224 tptp.empty_set @t248)))) % 0.50/0.70 (define @t260 () (not (tptp.rel_s4 @t1 @t251))) % 0.50/0.70 (define @t261 () (not (tptp.rel_s4 @t1 @t131))) % 0.50/0.70 (define @t262 () (@list @t1 @t251)) % 0.50/0.70 (define @t263 () (forall @t262 (or @t138 (not (forall @t132 (or @t261 @t231))) @t260 (tptp.in @t21 @t2 @t251)))) % 0.50/0.70 (define @t264 () (not @t259)) % 0.50/0.70 (define @t265 () (not @t263)) % 0.50/0.70 (define @t266 () (not (or @t265 @t264))) % 0.50/0.70 (define @t267 () (or @t169 @t266)) % 0.50/0.70 (define @t268 () (tptp.set_difference @t200 @t20)) % 0.50/0.70 (define @t269 () (tptp.qmltpeq @t268 tptp.empty_set @t248)) % 0.50/0.70 (define @t270 () (tptp.in @t21 @t20 @t126)) % 0.50/0.70 (define @t271 () (not (forall @t127 (or @t257 @t270)))) % 0.50/0.70 (define @t272 () (forall @t258 (or @t203 @t271 @t256 @t269))) % 0.50/0.70 (define @t273 () (tptp.in @t21 @t20 @t251)) % 0.50/0.70 (define @t274 () (tptp.qmltpeq @t268 tptp.empty_set @t131)) % 0.50/0.70 (define @t275 () (not (forall @t132 (or @t261 @t274)))) % 0.50/0.70 (define @t276 () (forall @t262 (or @t203 @t275 @t260 @t273))) % 0.50/0.70 (define @t277 () (not @t276)) % 0.50/0.70 (define @t278 () (not (or @t277 (not @t272)))) % 0.50/0.70 (define @t279 () (lambda @t25 @t278)) % 0.50/0.70 (define @t280 () (_ @t279 @t2 @t7)) % 0.50/0.70 (define @t281 () (or @t169 @t280)) % 0.50/0.70 (define @t282 () (forall @t5 @t281)) % 0.50/0.70 (define @t283 () (lambda @t62 @t282)) % 0.50/0.70 (define @t284 () (@list @t11)) % 0.50/0.70 (define @t285 () (or @t138 @t271 @t256 @t269)) % 0.50/0.70 (define @t286 () (lambda @t62 (forall @t258 @t285))) % 0.50/0.70 (define @t287 () (_ @t286 @t11)) % 0.50/0.70 (define @t288 () (not @t287)) % 0.50/0.70 (define @t289 () (or @t277 @t288)) % 0.50/0.70 (define @t290 () (not @t289)) % 0.50/0.70 (define @t291 () (lambda @t284 @t290)) % 0.50/0.70 (define @t292 () (_ @t52 @t11)) % 0.50/0.70 (define @t293 () (not @t292)) % 0.50/0.70 (define @t294 () (@list @t52 @t11)) % 0.50/0.70 (define @t295 () (or @t256 @t269)) % 0.50/0.70 (define @t296 () (or @t138 @t271 @t295)) % 0.50/0.70 (define @t297 () (forall @t258 @t296)) % 0.50/0.70 (define @t298 () (@list @t248)) % 0.50/0.70 (define @t299 () (forall @t298 @t296)) % 0.50/0.70 (define @t300 () (forall @t298 @t295)) % 0.50/0.70 (define @t301 () (@var "BOUND_VARIABLE_12476" $$unsorted)) % 0.50/0.70 (define @t302 () (@list @t301)) % 0.50/0.70 (define @t303 () (or @t138 @t271 @t300)) % 0.50/0.70 (define @t304 () (tptp.qmltpeq @t268 tptp.empty_set @t301)) % 0.50/0.70 (define @t305 () (@list @t301)) % 0.50/0.70 (define @t306 () (forall @t305 (or (not (tptp.rel_s4 @t1 @t301)) @t304))) % 0.50/0.70 (define @t307 () (or @t138 @t271 @t306)) % 0.50/0.70 (define @t308 () (or @t271 @t306)) % 0.50/0.70 (define @t309 () (tptp.qmltpeq @t268 tptp.empty_set @t1)) % 0.50/0.70 (define @t310 () (forall @t6 (or @t203 @t309))) % 0.50/0.70 (define @t311 () (@list @t1)) % 0.50/0.70 (define @t312 () (tptp.in @t21 @t20 @t1)) % 0.50/0.70 (define @t313 () (forall @t6 (or @t203 @t312))) % 0.50/0.70 (define @t314 () (not @t313)) % 0.50/0.70 (define @t315 () (or @t314 @t310)) % 0.50/0.70 (define @t316 () (lambda @t284 @t315)) % 0.50/0.70 (define @t317 () (or @t138 (_ @t316 @t1))) % 0.50/0.70 (define @t318 () (forall @t6 @t317)) % 0.50/0.70 (define @t319 () (lambda @t62 @t318)) % 0.50/0.70 (define @t320 () (lambda @t62 (forall @t6 (or @t138 @t309)))) % 0.50/0.70 (define @t321 () (_ @t320 @t11)) % 0.50/0.70 (define @t322 () (or @t314 @t321)) % 0.50/0.70 (define @t323 () (lambda @t284 @t322)) % 0.50/0.70 (define @t324 () (_ @t38 @t1)) % 0.50/0.70 (define @t325 () (or @t138 @t324)) % 0.50/0.70 (define @t326 () (_ @t38 @t1)) % 0.50/0.70 (define @t327 () (or @t138 @t326)) % 0.50/0.70 (define @t328 () (forall @t6 @t327)) % 0.50/0.70 (define @t329 () (lambda @t62 @t328)) % 0.50/0.70 (define @t330 () (_ @t177 @t38)) % 0.50/0.70 (define @t331 () (lambda @t62 (forall @t6 (or @t138 @t312)))) % 0.50/0.70 (define @t332 () (_ @t331 @t11)) % 0.50/0.70 (define @t333 () (not @t332)) % 0.50/0.70 (define @t334 () (or @t333 @t292)) % 0.50/0.70 (define @t335 () (lambda @t294 @t334)) % 0.50/0.70 (define @t336 () (not (_ @t47 @t11))) % 0.50/0.70 (define @t337 () (or @t336 @t292)) % 0.50/0.70 (define @t338 () (lambda @t67 @t337)) % 0.50/0.70 (define @t339 () (_ @t34 @t1)) % 0.50/0.70 (define @t340 () (or @t138 @t339)) % 0.50/0.70 (define @t341 () (_ @t34 @t1)) % 0.50/0.70 (define @t342 () (or @t138 @t341)) % 0.50/0.70 (define @t343 () (forall @t6 @t342)) % 0.50/0.70 (define @t344 () (lambda @t62 @t343)) % 0.50/0.70 (define @t345 () (_ @t177 @t34)) % 0.50/0.70 (define @t346 () (or @t138 @t275 @t260 @t273)) % 0.50/0.70 (define @t347 () (lambda @t62 (forall @t262 @t346))) % 0.50/0.70 (define @t348 () (_ @t347 @t11)) % 0.50/0.70 (define @t349 () (not @t348)) % 0.50/0.70 (define @t350 () (or @t349 @t293)) % 0.50/0.70 (define @t351 () (not @t350)) % 0.50/0.70 (define @t352 () (lambda @t294 @t351)) % 0.50/0.70 (define @t353 () (not (or @t336 @t293))) % 0.50/0.70 (define @t354 () (lambda @t67 @t353)) % 0.50/0.70 (define @t355 () (or @t260 @t273)) % 0.50/0.70 (define @t356 () (or @t138 @t275 @t355)) % 0.50/0.70 (define @t357 () (forall @t262 @t356)) % 0.50/0.70 (define @t358 () (@list @t251)) % 0.50/0.70 (define @t359 () (forall @t358 @t356)) % 0.50/0.70 (define @t360 () (forall @t358 @t355)) % 0.50/0.70 (define @t361 () (@var "BOUND_VARIABLE_12409" $$unsorted)) % 0.50/0.70 (define @t362 () (@list @t361)) % 0.50/0.70 (define @t363 () (or @t138 @t275 @t360)) % 0.50/0.70 (define @t364 () (tptp.in @t21 @t20 @t361)) % 0.50/0.70 (define @t365 () (@list @t361)) % 0.50/0.70 (define @t366 () (forall @t365 (or (not (tptp.rel_s4 @t1 @t361)) @t364))) % 0.50/0.70 (define @t367 () (or @t138 @t275 @t366)) % 0.50/0.70 (define @t368 () (or @t275 @t366)) % 0.50/0.70 (define @t369 () (not @t310)) % 0.50/0.70 (define @t370 () (or @t369 @t313)) % 0.50/0.70 (define @t371 () (lambda @t284 @t370)) % 0.50/0.70 (define @t372 () (or @t138 (_ @t371 @t1))) % 0.50/0.70 (define @t373 () (forall @t6 @t372)) % 0.50/0.70 (define @t374 () (lambda @t62 @t373)) % 0.50/0.70 (define @t375 () (or @t369 @t332)) % 0.50/0.70 (define @t376 () (lambda @t284 @t375)) % 0.50/0.70 (define @t377 () (not @t321)) % 0.50/0.70 (define @t378 () (or @t377 @t292)) % 0.50/0.70 (define @t379 () (lambda @t294 @t378)) % 0.50/0.70 (define @t380 () (lambda @t25 (_ (_ (_ @t354 (_ @t177 (_ (_ @t338 @t330) @t345))) (_ @t177 (_ (_ @t338 @t345) @t330))) @t11))) % 0.50/0.70 (define @t381 () (lambda @t26 (_ (_ @t177 (_ @t211 @t380)) @t11))) % 0.50/0.70 (define @t382 () (or @t49 @t53)) % 0.50/0.70 (define @t383 () (lambda @t62 @t382)) % 0.50/0.70 (define @t384 () (@list @t52 @t7)) % 0.50/0.70 (define @t385 () (lambda @t384 @t382)) % 0.50/0.70 (define @t386 () (lambda @t62 @t49)) % 0.50/0.70 (define @t387 () (_ @t386 @t7)) % 0.50/0.70 (define @t388 () (or @t387 @t53)) % 0.50/0.70 (define @t389 () (lambda @t384 @t388)) % 0.50/0.70 (define @t390 () (not @t53)) % 0.50/0.70 (define @t391 () (or @t49 @t390)) % 0.50/0.70 (define @t392 () (lambda @t62 @t391)) % 0.50/0.70 (define @t393 () (_ @t392 @t7)) % 0.50/0.70 (define @t394 () (not @t393)) % 0.50/0.70 (define @t395 () (lambda @t62 @t394)) % 0.50/0.70 (define @t396 () (lambda @t62 @t390)) % 0.50/0.70 (define @t397 () (_ @t396 @t7)) % 0.50/0.70 (define @t398 () (or @t49 @t397)) % 0.50/0.70 (define @t399 () (lambda @t62 @t398)) % 0.50/0.70 (define @t400 () (not @t8)) % 0.50/0.70 (define @t401 () (or @t400 @t76)) % 0.50/0.70 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.50/0.70 (assume @p2 (forall @t6 (exists @t5 @t4))) % 0.50/0.70 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 0.50/0.70 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 0.50/0.70 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 0.50/0.70 (assume @p6 (forall @t6 (_ (_ tptp.exists_in_world tptp.empty_set) @t1))) % 0.50/0.70 (assume @p7 (forall (@list @t1 @t9) (_ (_ tptp.exists_in_world (_ tptp.singleton @t9)) @t1))) % 0.50/0.70 (assume @p8 (forall (@list @t1 @t10 @t9) (_ (_ tptp.exists_in_world (_ (_ tptp.set_difference @t10) @t9)) @t1))) % 0.50/0.70 (assume @p9 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t13 (_ (_ tptp.mbox_s4 (_ @t12 @t2)) @t11)))))) % 0.50/0.70 (assume @p10 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t13 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mbox_s4 (_ (_ tptp.mimplies @t16) (_ tptp.mbox_s4 (_ @t15 @t2)))) @t11)))) @t11)))))) % 0.50/0.70 (assume @p11 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t13 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda (@list @t18 @t11) (_ (_ tptp.mbox_s4 (_ (_ tptp.mimplies (_ (_ tptp.mand @t16) (_ tptp.mbox_s4 (_ @t15 @t18)))) (_ tptp.mbox_s4 (_ @t12 @t18)))) @t11)))) @t11)))) @t11)))))) % 0.50/0.70 (assume @p12 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t24 (_ (_ tptp.mbox_s4 (_ @t23 (_ tptp.mbox_s4 (_ (_ tptp.qmltpeq (_ (_ tptp.set_difference @t21) @t19)) (_ (_ tptp.set_difference @t20) @t19))))) @t11)))) @t11)))) @t11)))))) % 0.50/0.70 (assume @p13 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t24 (_ (_ tptp.mbox_s4 (_ @t23 (_ tptp.mbox_s4 (_ (_ tptp.qmltpeq (_ @t27 @t21)) (_ @t27 @t20))))) @t11)))) @t11)))) @t11)))))) % 0.50/0.70 (assume @p14 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mbox_s4 (_ @t23 (_ tptp.mbox_s4 (_ (_ tptp.qmltpeq @t28) (_ tptp.singleton @t20))))) @t11)))) @t11)))))) % 0.50/0.70 (assume @p15 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mbox_s4 (_ (_ tptp.mimplies (_ @t30 @t29)) (_ tptp.mbox_s4 (_ tptp.empty @t20)))) @t11)))) @t11)))))) % 0.50/0.70 (assume @p16 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t24 (_ (_ tptp.mbox_s4 (_ (_ tptp.mimplies (_ @t30 (_ tptp.mbox_s4 (_ @t32 @t19)))) (_ tptp.mbox_s4 (_ @t31 @t19)))) @t11)))) @t11)))) @t11)))))) % 0.50/0.70 (assume @p17 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t24 (_ (_ tptp.mbox_s4 (_ (_ tptp.mimplies (_ @t30 (_ tptp.mbox_s4 (_ @t33 @t21)))) (_ tptp.mbox_s4 (_ @t33 @t20)))) @t11)))) @t11)))) @t11)))))) % 0.50/0.70 (assume @p18 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mbox_s4 (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mbox_s4 (_ @t36 (_ tptp.mbox_s4 (_ tptp.mnot (_ tptp.mbox_s4 (_ @t31 @t21)))))) @t11)))) @t11)))))) % 0.50/0.70 (assume @p19 (_ tptp.mvalid (_ tptp.mbox_s4 (_ tptp.empty tptp.empty_set)))) % 0.50/0.70 (assume @p20 (_ tptp.mvalid (_ tptp.mexists_ind (lambda @t26 (_ @t29 @t11))))) % 0.50/0.70 (assume @p21 (_ tptp.mvalid (_ tptp.mexists_ind (lambda @t26 (_ (_ tptp.mbox_s4 (_ tptp.mnot @t29)) @t11))))) % 0.50/0.70 (assume @p22 @t42) % 0.50/0.70 (assume @p23 @t43) % 0.50/0.70 (assume @p24 true) % 0.50/0.70 (step @p25 (= tptp.meq_prop @t46) :rule refl :args (@t46)) % 0.50/0.70 (step @p26 (= tptp.mnot @t51) :rule refl :args (@t51)) % 0.50/0.70 (step @p27 (= tptp.mor @t54) :rule refl :args (@t54)) % 0.50/0.70 (step @p28 (= tptp.mbox @t57) :rule refl :args (@t57)) % 0.50/0.70 (step @p29 (= tptp.mforall_prop @t61) :rule refl :args (@t61)) % 0.50/0.70 (step @p30 (= tptp.mtrue @t63) :rule refl :args (@t63)) % 0.50/0.70 (step @p31 (= tptp.mand @t68) :rule refl :args (@t68)) % 0.50/0.70 (step @p32 (= tptp.mimplies @t69) :rule refl :args (@t69)) % 0.50/0.70 (step @p33 (= tptp.mimplied @t70) :rule refl :args (@t70)) % 0.50/0.70 (step @p34 (= tptp.mequiv @t71) :rule refl :args (@t71)) % 0.50/0.70 (step @p35 (= tptp.mxor @t72) :rule refl :args (@t72)) % 0.50/0.70 (step @p36 (= tptp.mdia @t73) :rule refl :args (@t73)) % 0.50/0.70 (step @p37 (= tptp.mforall_ind @t79) :rule refl :args (@t79)) % 0.50/0.70 (step @p38 (= tptp.mexists_ind @t80) :rule refl :args (@t80)) % 0.50/0.70 (step @p39 (= tptp.mexists_prop @t81) :rule refl :args (@t81)) % 0.50/0.70 (step @p40 (= tptp.mreflexive @t86) :rule refl :args (@t86)) % 0.50/0.70 (step @p41 (= tptp.msymmetric @t90) :rule refl :args (@t90)) % 0.50/0.70 (step @p42 (= tptp.mserial @t92) :rule refl :args (@t92)) % 0.50/0.70 (step @p43 (= tptp.mtransitive @t97) :rule refl :args (@t97)) % 0.50/0.70 (step @p44 (= tptp.meuclidean @t99) :rule refl :args (@t99)) % 0.50/0.70 (step @p45 (= tptp.mpartially_functional @t101) :rule refl :args (@t101)) % 0.50/0.70 (step @p46 (= tptp.mfunctional @t103) :rule refl :args (@t103)) % 0.50/0.70 (step @p47 (= tptp.mweakly_dense @t106) :rule refl :args (@t106)) % 0.50/0.70 (step @p48 (= tptp.mweakly_connected @t107) :rule refl :args (@t107)) % 0.50/0.70 (step @p49 (= tptp.mweakly_directed @t108) :rule refl :args (@t108)) % 0.50/0.70 (step @p50 (= tptp.mvalid @t111) :rule refl :args (@t111)) % 0.50/0.70 (step @p51 (= tptp.msatisfiable @t112) :rule refl :args (@t112)) % 0.50/0.70 (step @p52 (= tptp.mcountersatisfiable @t113) :rule refl :args (@t113)) % 0.50/0.70 (step @p53 (= tptp.minvalid @t114) :rule refl :args (@t114)) % 0.50/0.70 (step @p54 (= tptp.mbox_s4 @t119) :rule refl :args (@t119)) % 0.50/0.70 (step @p55 (= tptp.mdia_s4 @t120) :rule refl :args (@t120)) % 0.50/0.70 (step @p56 :rule quant-merge-prenex :args ((= (forall @t62 @t141) (forall (@list @t7 @t1 @t123 @t128 @t122 @t130 @t129 @t125 @t121) @t139)))) % 0.50/0.70 (step @p57 :rule beta-reduce :args ((= @t143 @t141))) % 0.50/0.70 (step @p58 :rule cong :premises (@p57) :args (@t144)) % 0.50/0.70 (step @p59 :rule trans :premises (@p58 @p56)) % 0.50/0.70 (step @p60 :rule beta-reduce :args ((= (_ @t146 @t142) @t144))) % 0.50/0.70 (step @p61 :rule trans :premises (@p60 @p59)) % 0.50/0.70 (step @p62 :rule aci_norm :args ((= @t148 @t139))) % 0.50/0.70 (step @p63 :rule cong :premises (@p62) :args (@t149)) % 0.50/0.70 (step @p64 :rule quant-merge-prenex :args ((= (forall @t6 @t151) @t149))) % 0.50/0.70 (step @p65 :rule alpha_equiv :args (@t152 (@list @t123 @t128 @t122 @t130 @t129 @t125 @t121) (@list @t2 @t158 @t157 @t156 @t155 @t154 @t153))) % 0.50/0.70 (step @p66 :rule refl :args (@t138)) % 0.50/0.70 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t159)) % 0.50/0.70 (step @p68 :rule quant-miniscope-or :args ((= @t151 @t159))) % 0.50/0.70 (step @p69 :rule trans :premises (@p68 @p67)) % 0.50/0.70 (step @p70 :rule symm :premises (@p69)) % 0.50/0.70 (step @p71 :rule cong :premises (@p70) :args ((forall @t6 (or @t138 @t166)))) % 0.50/0.70 (step @p72 :rule trans :premises (@p71 @p64)) % 0.50/0.70 (step @p73 :rule trans :premises (@p72 @p63)) % 0.50/0.70 (step @p74 :rule beta-reduce :args ((= @t172 @t166))) % 0.50/0.70 (step @p75 :rule refl :args (@t138)) % 0.50/0.70 (step @p76 :rule nary_cong :premises (@p75 @p74) :args (@t173)) % 0.50/0.70 (step @p77 :rule cong :premises (@p76) :args (@t174)) % 0.50/0.70 (step @p78 :rule trans :premises (@p77 @p73)) % 0.50/0.70 (step @p79 :rule cong :premises (@p78) :args (@t175)) % 0.50/0.70 (step @p80 :rule beta-reduce :args ((= (_ @t177 @t171) @t175))) % 0.50/0.70 (step @p81 :rule trans :premises (@p80 @p79)) % 0.50/0.70 (step @p82 :rule aci_norm :args ((= @t179 @t170))) % 0.50/0.70 (step @p83 :rule cong :premises (@p82) :args (@t180)) % 0.50/0.70 (step @p84 :rule quant-merge-prenex :args ((= (forall @t5 @t182) @t180))) % 0.50/0.70 (step @p85 :rule alpha_equiv :args (@t183 (@list @t158 @t157 @t156 @t155 @t154 @t153) (@list @t1 @t188 @t187 @t186 @t185 @t184))) % 0.50/0.70 (step @p86 :rule refl :args (@t169)) % 0.50/0.70 (step @p87 :rule nary_cong :premises (@p86 @p85) :args (@t189)) % 0.50/0.70 (step @p88 :rule quant-miniscope-or :args ((= @t182 @t189))) % 0.50/0.70 (step @p89 :rule trans :premises (@p88 @p87)) % 0.50/0.70 (step @p90 :rule symm :premises (@p89)) % 0.50/0.70 (step @p91 :rule cong :premises (@p90) :args ((forall @t5 (or @t169 @t199)))) % 0.50/0.70 (step @p92 :rule trans :premises (@p91 @p84)) % 0.50/0.70 (step @p93 :rule trans :premises (@p92 @p83)) % 0.50/0.70 (step @p94 :rule beta-reduce :args ((= @t206 @t199))) % 0.50/0.70 (step @p95 :rule refl :args (@t169)) % 0.50/0.70 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t207)) % 0.50/0.70 (step @p97 :rule cong :premises (@p96) :args (@t208)) % 0.50/0.70 (step @p98 :rule trans :premises (@p97 @p93)) % 0.50/0.70 (step @p99 :rule cong :premises (@p98) :args (@t209)) % 0.50/0.70 (step @p100 :rule beta-reduce :args ((= (_ @t211 @t205) @t209))) % 0.50/0.70 (step @p101 :rule trans :premises (@p100 @p99)) % 0.50/0.70 (step @p102 :rule beta-reduce :args ((= (_ (lambda @t62 (forall @t198 @t212)) @t11) @t204))) % 0.50/0.70 (step @p103 :rule refl :args (@t11)) % 0.50/0.70 (step @p104 :rule aci_norm :args ((= @t214 @t212))) % 0.50/0.70 (step @p105 :rule cong :premises (@p104) :args (@t215)) % 0.50/0.70 (step @p106 :rule quant-merge-prenex :args ((= (forall @t6 @t217) @t215))) % 0.50/0.71 (step @p107 :rule alpha_equiv :args (@t218 (@list @t188 @t187 @t186 @t185 @t184) (@list @t2 @t222 @t221 @t220 @t219))) % 0.50/0.71 (step @p108 :rule nary_cong :premises (@p66 @p107) :args (@t223)) % 0.50/0.71 (step @p109 :rule quant-miniscope-or :args ((= @t217 @t223))) % 0.50/0.71 (step @p110 :rule trans :premises (@p109 @p108)) % 0.50/0.71 (step @p111 :rule symm :premises (@p110)) % 0.50/0.71 (step @p112 :rule cong :premises (@p111) :args ((forall @t6 (or @t138 @t234)))) % 0.50/0.71 (step @p113 :rule trans :premises (@p112 @p106)) % 0.50/0.71 (step @p114 :rule trans :premises (@p113 @p105)) % 0.50/0.71 (step @p115 :rule beta-reduce :args ((= @t241 @t234))) % 0.50/0.71 (step @p116 :rule nary_cong :premises (@p75 @p115) :args (@t242)) % 0.50/0.71 (step @p117 :rule cong :premises (@p116) :args (@t243)) % 0.50/0.71 (step @p118 :rule trans :premises (@p117 @p114)) % 0.50/0.71 (step @p119 :rule cong :premises (@p118) :args (@t244)) % 0.50/0.71 (step @p120 :rule beta-reduce :args ((= (_ @t177 @t240) @t244))) % 0.50/0.71 (step @p121 :rule trans :premises (@p120 @p119)) % 0.50/0.71 (step @p122 :rule quant-merge-prenex :args ((= (forall @t5 @t246) @t239))) % 0.50/0.71 (step @p123 :rule alpha_equiv :args (@t247 (@list @t220 @t219) (@list @t1 @t248))) % 0.50/0.71 (step @p124 :rule quant-unused-vars :args ((= @t249 @t247))) % 0.50/0.71 (step @p125 :rule trans :premises (@p124 @p123)) % 0.50/0.71 (step @p126 :rule alpha_equiv :args (@t250 (@list @t222 @t221) (@list @t1 @t251))) % 0.50/0.71 (step @p127 :rule quant-unused-vars :args ((= @t252 @t250))) % 0.50/0.71 (step @p128 :rule trans :premises (@p127 @p126)) % 0.50/0.71 (step @p129 :rule nary_cong :premises (@p128 @p125) :args (@t253)) % 0.50/0.71 (step @p130 :rule quant-miniscope-and :args ((= @t254 @t253))) % 0.50/0.71 (step @p131 :rule trans :premises (@p130 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@t385 @t52) @t383))) % 0.50/0.71 (step @p367 :rule refl :args (@t52)) % 0.50/0.71 (step @p368 :rule refl :args (@t53)) % 0.50/0.71 (step @p369 :rule beta-reduce :args ((= @t387 @t49))) % 0.50/0.71 (step @p370 :rule nary_cong :premises (@p369 @p368) :args (@t388)) % 0.50/0.71 (step @p371 :rule cong :premises (@p370) :args (@t389)) % 0.50/0.71 (step @p372 :rule beta-reduce :args ((= (_ @t54 @t386) @t389))) % 0.50/0.71 (step @p373 :rule trans :premises (@p372 @p371)) % 0.50/0.71 (step @p374 :rule beta-reduce :args ((= (_ @t51 @t47) @t386))) % 0.50/0.71 (step @p375 :rule refl :args (@t54)) % 0.50/0.71 (step @p376 :rule ho_cong :premises (@p375 @p374)) % 0.50/0.71 (step @p377 :rule trans :premises (@p376 @p373)) % 0.50/0.71 (step @p378 :rule ho_cong :premises (@p377 @p367)) % 0.50/0.71 (step @p379 :rule trans :premises (@p378 @p366)) % 0.50/0.71 (step @p380 :rule ho_cong :premises (@p379 @p103)) % 0.50/0.71 (step @p381 :rule trans :premises (@p380 @p365)) % 0.50/0.71 (step @p382 :rule refl :args (@t47)) % 0.50/0.71 (step @p383 :rule ho_cong :premises (@p26 @p382)) % 0.50/0.71 (step @p384 :rule ho_cong :premises (@p27 @p383)) % 0.50/0.71 (step @p385 :rule ho_cong :premises (@p384 @p367)) % 0.50/0.71 (step @p386 :rule ho_cong :premises (@p385 @p103)) % 0.50/0.71 (step @p387 :rule trans :premises (@p386 @p381)) % 0.50/0.71 (step @p388 :rule cong :premises (@p387) :args (@t69)) % 0.50/0.71 (step @p389 :rule trans :premises (@p32 @p388)) % 0.50/0.71 (step @p390 :rule ho_cong :premises (@p389 @p364)) % 0.50/0.71 (step @p391 :rule ho_cong :premises (@p390 @p362)) % 0.50/0.71 (step @p392 :rule ho_cong :premises (@p361 @p391)) % 0.50/0.71 (step @p393 :rule ho_cong :premises (@p389 @p362)) % 0.50/0.71 (step @p394 :rule ho_cong :premises (@p393 @p364)) % 0.50/0.71 (step @p395 :rule ho_cong :premises (@p361 @p394)) % 0.50/0.71 (step @p396 :rule beta-reduce :args ((= (_ (lambda @t62 (not @t391)) @t11) @t353))) % 0.50/0.71 (step @p397 :rule beta-reduce :args ((= @t393 @t391))) % 0.50/0.71 (step @p398 :rule cong :premises (@p397) :args (@t394)) % 0.50/0.71 (step @p399 :rule cong :premises (@p398) :args (@t395)) % 0.50/0.71 (step @p400 :rule beta-reduce :args ((= (_ @t51 @t392) @t395))) % 0.50/0.71 (step @p401 :rule trans :premises (@p400 @p399)) % 0.50/0.71 (step @p402 :rule beta-reduce :args ((= @t397 @t390))) % 0.50/0.71 (step @p403 :rule refl :args (@t49)) % 0.50/0.71 (step @p404 :rule nary_cong :premises (@p403 @p402) :args (@t398)) % 0.50/0.71 (step @p405 :rule cong :premises (@p404) :args (@t399)) % 0.50/0.71 (step @p406 :rule beta-reduce :args ((= (_ @t385 @t396) @t399))) % 0.50/0.71 (step @p407 :rule trans :premises (@p406 @p405)) % 0.50/0.71 (step @p408 :rule beta-reduce :args ((= (_ @t51 @t52) @t396))) % 0.50/0.71 (step @p409 :rule ho_cong :premises (@p377 @p408)) % 0.50/0.71 (step @p410 :rule trans :premises (@p409 @p407)) % 0.50/0.71 (step @p411 :rule refl :args (@t51)) % 0.50/0.71 (step @p412 :rule ho_cong :premises (@p411 @p410)) % 0.50/0.71 (step @p413 :rule trans :premises (@p412 @p401)) % 0.50/0.71 (step @p414 :rule ho_cong :premises (@p413 @p103)) % 0.50/0.71 (step @p415 :rule trans :premises (@p414 @p396)) % 0.50/0.71 (step @p416 :rule ho_cong :premises (@p26 @p367)) % 0.50/0.71 (step @p417 :rule ho_cong :premises (@p384 @p416)) % 0.50/0.71 (step @p418 :rule ho_cong :premises (@p26 @p417)) % 0.50/0.71 (step @p419 :rule ho_cong :premises (@p418 @p103)) % 0.50/0.71 (step @p420 :rule trans :premises (@p419 @p415)) % 0.50/0.71 (step @p421 :rule cong :premises (@p420) :args (@t68)) % 0.50/0.71 (step @p422 :rule trans :premises (@p31 @p421)) % 0.50/0.71 (step @p423 :rule ho_cong :premises (@p422 @p395)) % 0.50/0.71 (step @p424 :rule ho_cong :premises (@p423 @p392)) % 0.50/0.71 (step @p425 :rule ho_cong :premises (@p424 @p103)) % 0.50/0.71 (step @p426 :rule cong :premises (@p425) :args (@t40)) % 0.50/0.71 (step @p427 :rule refl :args (@t210)) % 0.50/0.71 (step @p428 :rule refl :args (@t76)) % 0.50/0.71 (step @p429 :rule cong :premises (@p428 @p427) :args ((= @t76 @t210))) % 0.50/0.71 (step @p430 :rule symm :premises (@p429)) % 0.50/0.71 (step @p431 :rule eq_resolve :premises (@p428 @p430)) % 0.50/0.71 (step @p432 :rule refl :args (@t168)) % 0.50/0.71 (step @p433 :rule refl :args (@t8)) % 0.50/0.71 (step @p434 :rule cong :premises (@p433 @p432) :args ((= @t8 @t168))) % 0.50/0.71 (step @p435 :rule symm :premises (@p434)) % 0.50/0.71 (step @p436 :rule eq_resolve :premises (@p433 @p435)) % 0.50/0.71 (step @p437 :rule cong :premises (@p436) :args (@t400)) % 0.50/0.71 (step @p438 :rule nary_cong :premises (@p437 @p431) :args (@t401)) % 0.50/0.71 (step @p439 :rule cong :premises (@p438) :args ((forall @t5 @t401))) % 0.50/0.71 (step @p440 :rule bool-impl-elim :args (@t8 @t76)) % 0.50/0.71 (step @p441 :rule cong :premises (@p440) :args (@t77)) % 0.50/0.71 (step @p442 :rule trans :premises (@p441 @p439)) % 0.50/0.71 (step @p443 :rule cong :premises (@p442) :args (@t79)) % 0.50/0.71 (step @p444 :rule trans :premises (@p37 @p443)) % 0.50/0.71 (step @p445 :rule ho_cong :premises (@p444 @p426)) % 0.50/0.71 (step @p446 :rule ho_cong :premises (@p361 @p445)) % 0.50/0.71 (step @p447 :rule ho_cong :premises (@p446 @p103)) % 0.50/0.71 (step @p448 :rule cong :premises (@p447) :args (@t41)) % 0.50/0.71 (step @p449 :rule ho_cong :premises (@p444 @p448)) % 0.50/0.71 (step @p450 :rule ho_cong :premises (@p361 @p449)) % 0.50/0.71 (step @p451 :rule refl :args (@t145)) % 0.50/0.71 (step @p452 :rule refl :args (@t48)) % 0.50/0.71 (step @p453 :rule cong :premises (@p452 @p451) :args ((= @t48 @t145))) % 0.50/0.71 (step @p454 :rule symm :premises (@p453)) % 0.50/0.71 (step @p455 :rule eq_resolve :premises (@p452 @p454)) % 0.50/0.71 (step @p456 :rule cong :premises (@p455) :args (@t109)) % 0.50/0.71 (step @p457 :rule cong :premises (@p456) :args (@t111)) % 0.50/0.71 (step @p458 :rule trans :premises (@p50 @p457)) % 0.50/0.71 (step @p459 :rule ho_cong :premises (@p458 @p450)) % 0.50/0.71 (step @p460 :rule cong :premises (@p459) :args (@t43)) % 0.50/0.71 (step @p461 :rule trans :premises (@p460 @p345)) % 0.50/0.71 (step @p462 :rule eq_resolve :premises (@p23 @p461)) % 0.50/0.71 (step @p463 :rule trans :premises (@p459 @p344)) % 0.50/0.71 (step @p464 :rule eq_resolve :premises (@p22 @p463)) % 0.50/0.71 (step @p465 false :rule contra :premises (@p464 @p462)) % 0.50/0.71 ) % 0.50/0.71 % SZS output end Proof % 0.50/0.71 % cvc5 exiting %------------------------------------------------------------------------------