%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET926^7 : 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 : n009.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 08:49:00 AM UTC 2026 % Result : Theorem 0.37s 0.60s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET926^7 : TPTP v9.2.1. Released v5.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n009.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 16:17:59 EDT 2026 % 0.18/0.34 % CPUTime : % 0.31/0.51 %----Proving TH0 % 0.37/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.60 % SZS status Theorem % 0.37/0.60 % SZS output start Proof % 0.37/0.60 ( % 0.37/0.60 (declare-sort tptp.mu 0) % 0.37/0.60 (declare-sort $$unsorted 0) % 0.37/0.60 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.in (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.empty (-> tptp.mu $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.qmltpeq (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.set_difference (-> tptp.mu tptp.mu tptp.mu)) % 0.37/0.60 (declare-const tptp.empty_set tptp.mu) % 0.37/0.60 (declare-const tptp.singleton (-> tptp.mu tptp.mu)) % 0.37/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.37/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.60 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.37/0.60 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.37/0.60 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.37/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.37/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.37/0.60 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.37/0.60 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.exists_in_world _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.60 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.37/0.60 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.37/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.37/0.60 (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)))))))) % 0.37/0.60 (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)))))))) % 0.37/0.60 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.37/0.60 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.37/0.60 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.37/0.60 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.37/0.60 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.37/0.60 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.37/0.60 (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))))))))))))) % 0.37/0.60 (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)))))) % 0.37/0.60 (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)))))) % 0.37/0.60 (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))))))) % 0.37/0.60 (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))))))) % 0.37/0.60 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.37/0.60 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.37/0.60 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.60 (define @t2 () (@var "X" tptp.mu)) % 0.37/0.60 (define @t3 () (_ tptp.exists_in_world @t2)) % 0.37/0.60 (define @t4 () (_ @t3 @t1)) % 0.37/0.60 (define @t5 () (@list @t2)) % 0.37/0.60 (define @t6 () (@list @t1)) % 0.37/0.60 (define @t7 () (@var "W" $$unsorted)) % 0.37/0.60 (define @t8 () (_ @t3 @t7)) % 0.37/0.60 (define @t9 () (@var "V1" tptp.mu)) % 0.37/0.60 (define @t10 () (@var "V2" tptp.mu)) % 0.37/0.60 (define @t11 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.60 (define @t12 () (_ tptp.qmltpeq @t2)) % 0.37/0.60 (define @t13 () (@list @t2 @t11)) % 0.37/0.60 (define @t14 () (@var "Y" tptp.mu)) % 0.37/0.60 (define @t15 () (_ tptp.qmltpeq @t14)) % 0.37/0.60 (define @t16 () (_ @t12 @t14)) % 0.37/0.60 (define @t17 () (@list @t14 @t11)) % 0.37/0.60 (define @t18 () (@var "Z" tptp.mu)) % 0.37/0.60 (define @t19 () (@var "C" tptp.mu)) % 0.37/0.60 (define @t20 () (@var "B" tptp.mu)) % 0.37/0.60 (define @t21 () (@var "A" tptp.mu)) % 0.37/0.60 (define @t22 () (_ (_ tptp.qmltpeq @t21) @t20)) % 0.37/0.60 (define @t23 () (_ tptp.mimplies @t22)) % 0.37/0.60 (define @t24 () (@list @t19 @t11)) % 0.37/0.60 (define @t25 () (@list @t20 @t11)) % 0.37/0.60 (define @t26 () (@list @t21 @t11)) % 0.37/0.60 (define @t27 () (_ tptp.set_difference @t19)) % 0.37/0.60 (define @t28 () (_ tptp.singleton @t21)) % 0.37/0.60 (define @t29 () (_ tptp.empty @t21)) % 0.37/0.60 (define @t30 () (_ tptp.mand @t22)) % 0.37/0.60 (define @t31 () (_ tptp.in @t20)) % 0.37/0.60 (define @t32 () (_ tptp.in @t21)) % 0.37/0.60 (define @t33 () (_ tptp.in @t19)) % 0.37/0.60 (define @t34 () (_ @t32 @t20)) % 0.37/0.60 (define @t35 () (_ tptp.set_difference @t28)) % 0.37/0.60 (define @t36 () (_ tptp.qmltpeq (_ @t35 @t20))) % 0.37/0.60 (define @t37 () (_ @t36 @t28)) % 0.37/0.60 (define @t38 () (lambda @t25 (_ (_ (_ tptp.mequiv @t37) (_ tptp.mnot @t34)) @t11))) % 0.37/0.60 (define @t39 () (lambda @t26 (_ (_ tptp.mforall_ind @t38) @t11))) % 0.37/0.60 (define @t40 () (_ @t36 tptp.empty_set)) % 0.37/0.60 (define @t41 () (lambda @t25 (_ (_ (_ tptp.mequiv @t40) @t34) @t11))) % 0.37/0.60 (define @t42 () (lambda @t26 (_ (_ tptp.mforall_ind @t41) @t11))) % 0.37/0.60 (define @t43 () (lambda @t25 (_ (_ (_ tptp.mor @t40) @t37) @t11))) % 0.37/0.60 (define @t44 () (lambda @t26 (_ (_ tptp.mforall_ind @t43) @t11))) % 0.37/0.60 (define @t45 () (not (_ tptp.mvalid (_ tptp.mforall_ind @t44)))) % 0.37/0.60 (define @t46 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.60 (define @t47 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.60 (define @t48 () (lambda (@list @t47 @t46 @t7) (= (_ @t47 @t7) (_ @t46 @t7)))) % 0.37/0.60 (define @t49 () (@var "Phi" (-> $$unsorted Bool))) % 0.37/0.60 (define @t50 () (_ @t49 @t7)) % 0.37/0.60 (define @t51 () (not @t50)) % 0.37/0.60 (define @t52 () (@list @t49 @t7)) % 0.37/0.60 (define @t53 () (lambda @t52 @t51)) % 0.37/0.60 (define @t54 () (@var "Psi" (-> $$unsorted Bool))) % 0.37/0.60 (define @t55 () (_ @t54 @t7)) % 0.37/0.60 (define @t56 () (lambda (@list @t49 @t54 @t7) (or @t50 @t55))) % 0.37/0.60 (define @t57 () (_ @t49 @t1)) % 0.37/0.60 (define @t58 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.60 (define @t59 () (lambda (@list @t58 @t49 @t7) (forall @t6 (or (not (_ (_ @t58 @t7) @t1)) @t57)))) % 0.37/0.60 (define @t60 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.60 (define @t61 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.37/0.60 (define @t62 () (_ @t61 @t60)) % 0.37/0.60 (define @t63 () (lambda (@list @t61 @t7) (forall (@list @t60) (_ @t62 @t7)))) % 0.37/0.60 (define @t64 () (@list @t7)) % 0.37/0.60 (define @t65 () (lambda @t64 true)) % 0.37/0.60 (define @t66 () (_ tptp.mnot @t54)) % 0.37/0.60 (define @t67 () (_ tptp.mnot @t49)) % 0.37/0.60 (define @t68 () (_ tptp.mor @t67)) % 0.37/0.60 (define @t69 () (@list @t49 @t54 @t11)) % 0.37/0.60 (define @t70 () (lambda @t69 (_ (_ tptp.mnot (_ @t68 @t66)) @t11))) % 0.37/0.60 (define @t71 () (lambda @t69 (_ (_ @t68 @t54) @t11))) % 0.37/0.60 (define @t72 () (lambda @t69 (_ (_ (_ tptp.mor @t66) @t49) @t11))) % 0.37/0.60 (define @t73 () (lambda @t69 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t49) @t54)) (_ (_ tptp.mimplies @t54) @t49)) @t11))) % 0.37/0.60 (define @t74 () (lambda @t69 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t49) @t54)) @t11))) % 0.37/0.60 (define @t75 () (lambda (@list @t58 @t49 @t11) (_ (_ tptp.mnot (_ (_ tptp.mbox @t58) @t67)) @t11))) % 0.37/0.60 (define @t76 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.37/0.60 (define @t77 () (_ @t76 @t2)) % 0.37/0.60 (define @t78 () (_ @t77 @t7)) % 0.37/0.60 (define @t79 () (forall @t5 (=> @t8 @t78))) % 0.37/0.60 (define @t80 () (@list @t76 @t7)) % 0.37/0.60 (define @t81 () (lambda @t80 @t79)) % 0.37/0.60 (define @t82 () (lambda (@list @t76 @t11) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda @t13 (_ (_ tptp.mnot @t77) @t11)))) @t11))) % 0.37/0.60 (define @t83 () (lambda (@list @t61 @t11) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t60 @t11) (_ (_ tptp.mnot @t62) @t11)))) @t11))) % 0.37/0.60 (define @t84 () (@var "S" $$unsorted)) % 0.37/0.60 (define @t85 () (_ @t58 @t84)) % 0.37/0.60 (define @t86 () (@list @t84)) % 0.37/0.60 (define @t87 () (@list @t58)) % 0.37/0.60 (define @t88 () (lambda @t87 (forall @t86 (_ @t85 @t84)))) % 0.37/0.60 (define @t89 () (@var "T" $$unsorted)) % 0.37/0.60 (define @t90 () (_ @t58 @t89)) % 0.37/0.60 (define @t91 () (_ @t85 @t89)) % 0.37/0.60 (define @t92 () (lambda @t87 (forall (@list @t84 @t89) (=> @t91 (_ @t90 @t84))))) % 0.37/0.60 (define @t93 () (@list @t89)) % 0.37/0.60 (define @t94 () (lambda @t87 (forall @t86 (exists @t93 @t91)))) % 0.37/0.60 (define @t95 () (@var "U" $$unsorted)) % 0.37/0.60 (define @t96 () (_ @t85 @t95)) % 0.37/0.60 (define @t97 () (_ @t90 @t95)) % 0.37/0.60 (define @t98 () (@list @t84 @t89 @t95)) % 0.37/0.60 (define @t99 () (lambda @t87 (forall @t98 (=> (and @t91 @t97) @t96)))) % 0.37/0.60 (define @t100 () (and @t91 @t96)) % 0.37/0.60 (define @t101 () (lambda @t87 (forall @t98 (=> @t100 @t97)))) % 0.37/0.60 (define @t102 () (= @t89 @t95)) % 0.37/0.60 (define @t103 () (lambda @t87 (forall @t98 (=> @t100 @t102)))) % 0.37/0.60 (define @t104 () (@list @t95)) % 0.37/0.60 (define @t105 () (lambda @t87 (forall @t86 (exists @t93 (and @t91 (forall @t104 (=> @t96 @t102))))))) % 0.37/0.60 (define @t106 () (_ @t58 @t95)) % 0.37/0.60 (define @t107 () (_ @t106 @t89)) % 0.37/0.60 (define @t108 () (lambda @t87 (forall @t98 (=> @t91 (exists @t104 (and @t96 @t107)))))) % 0.37/0.60 (define @t109 () (lambda @t87 (forall @t98 (=> @t100 (or @t97 @t102 @t107))))) % 0.37/0.60 (define @t110 () (lambda @t87 (forall @t98 (=> @t100 (exists @t6 (and (_ @t90 @t1) (_ @t106 @t1))))))) % 0.37/0.60 (define @t111 () (forall @t64 @t50)) % 0.37/0.60 (define @t112 () (@list @t49)) % 0.37/0.60 (define @t113 () (lambda @t112 @t111)) % 0.37/0.60 (define @t114 () (lambda @t112 (exists @t64 @t50))) % 0.37/0.60 (define @t115 () (lambda @t112 (exists @t64 @t51))) % 0.37/0.60 (define @t116 () (lambda @t112 (forall @t64 @t51))) % 0.37/0.60 (define @t117 () (lambda @t52 (forall @t6 (or (not (_ (_ tptp.rel_s4 @t7) @t1)) @t57)))) % 0.37/0.60 (define @t118 () (lambda (@list @t49 @t11) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t67)) @t11))) % 0.37/0.60 (define @t119 () (tptp.singleton @t2)) % 0.37/0.60 (define @t120 () (@var "BOUND_VARIABLE_10349" tptp.mu)) % 0.37/0.60 (define @t121 () (tptp.set_difference @t119 @t120)) % 0.37/0.60 (define @t122 () (tptp.qmltpeq @t121 @t119 @t7)) % 0.37/0.60 (define @t123 () (tptp.qmltpeq @t121 tptp.empty_set @t7)) % 0.37/0.60 (define @t124 () (not (tptp.exists_in_world @t120 @t7))) % 0.37/0.60 (define @t125 () (tptp.exists_in_world @t2 @t7)) % 0.37/0.60 (define @t126 () (not @t125)) % 0.37/0.60 (define @t127 () (or @t126 @t124 @t123 @t122)) % 0.37/0.60 (define @t128 () (forall (@list @t7 @t2 @t120) @t127)) % 0.37/0.60 (define @t129 () (@list @t2 @t120)) % 0.37/0.60 (define @t130 () (forall @t129 @t127)) % 0.37/0.60 (define @t131 () (lambda @t64 @t130)) % 0.37/0.60 (define @t132 () (_ @t131 @t7)) % 0.37/0.60 (define @t133 () (forall @t64 @t132)) % 0.37/0.60 (define @t134 () (_ @t49 @t7)) % 0.37/0.60 (define @t135 () (lambda @t112 (forall @t64 @t134))) % 0.37/0.60 (define @t136 () (or @t124 @t123 @t122)) % 0.37/0.60 (define @t137 () (or @t126 @t136)) % 0.37/0.60 (define @t138 () (forall @t129 @t137)) % 0.37/0.60 (define @t139 () (@list @t120)) % 0.37/0.60 (define @t140 () (forall @t139 @t137)) % 0.37/0.60 (define @t141 () (forall @t139 @t136)) % 0.37/0.60 (define @t142 () (@var "BOUND_VARIABLE_10328" tptp.mu)) % 0.37/0.60 (define @t143 () (@list @t142)) % 0.37/0.60 (define @t144 () (or @t126 @t141)) % 0.37/0.60 (define @t145 () (tptp.set_difference @t119 @t142)) % 0.37/0.60 (define @t146 () (@list @t142)) % 0.37/0.60 (define @t147 () (forall @t146 (or (not (tptp.exists_in_world @t142 @t7)) (tptp.qmltpeq @t145 tptp.empty_set @t7) (tptp.qmltpeq @t145 @t119 @t7)))) % 0.37/0.60 (define @t148 () (tptp.singleton @t21)) % 0.37/0.60 (define @t149 () (tptp.set_difference @t148 @t142)) % 0.37/0.60 (define @t150 () (tptp.set_difference @t148 @t2)) % 0.37/0.60 (define @t151 () (tptp.qmltpeq @t150 @t148 @t11)) % 0.37/0.60 (define @t152 () (tptp.qmltpeq @t150 tptp.empty_set @t11)) % 0.37/0.60 (define @t153 () (not (tptp.exists_in_world @t2 @t11))) % 0.37/0.60 (define @t154 () (forall @t5 (or @t153 @t152 @t151))) % 0.37/0.60 (define @t155 () (@list @t2)) % 0.37/0.60 (define @t156 () (lambda @t26 @t154)) % 0.37/0.60 (define @t157 () (or @t126 (_ @t156 @t2 @t7))) % 0.37/0.60 (define @t158 () (forall @t5 @t157)) % 0.37/0.60 (define @t159 () (lambda @t64 @t158)) % 0.37/0.60 (define @t160 () (_ @t76 @t2 @t7)) % 0.37/0.60 (define @t161 () (lambda @t80 (forall @t5 (or @t126 @t160)))) % 0.37/0.60 (define @t162 () (tptp.qmltpeq @t150 @t148 @t7)) % 0.37/0.60 (define @t163 () (tptp.qmltpeq @t150 tptp.empty_set @t7)) % 0.37/0.60 (define @t164 () (_ @t35 @t2)) % 0.37/0.60 (define @t165 () (_ tptp.qmltpeq @t150)) % 0.37/0.60 (define @t166 () (_ tptp.qmltpeq @t164)) % 0.37/0.60 (define @t167 () (_ (_ @t166 @t28) @t7)) % 0.37/0.60 (define @t168 () (_ (_ @t166 tptp.empty_set) @t7)) % 0.37/0.60 (define @t169 () (or @t126 @t168 @t167)) % 0.37/0.60 (define @t170 () (or @t168 @t167)) % 0.37/0.60 (define @t171 () (_ @t37 @t11)) % 0.37/0.60 (define @t172 () (_ @t40 @t11)) % 0.37/0.60 (define @t173 () (or @t172 @t171)) % 0.37/0.60 (define @t174 () (lambda @t25 @t173)) % 0.37/0.60 (define @t175 () (_ @t174 @t2 @t7)) % 0.37/0.60 (define @t176 () (or @t126 @t175)) % 0.37/0.60 (define @t177 () (forall @t5 @t176)) % 0.37/0.60 (define @t178 () (lambda @t64 @t177)) % 0.37/0.60 (define @t179 () (_ @t40 @t7)) % 0.37/0.60 (define @t180 () (lambda @t64 (or @t179 (_ @t37 @t7)))) % 0.37/0.60 (define @t181 () (@list @t54 @t7)) % 0.37/0.60 (define @t182 () (lambda @t181 (or @t179 @t55))) % 0.37/0.60 (define @t183 () (_ @t56 @t40)) % 0.37/0.60 (define @t184 () (lambda @t25 (_ (_ @t183 @t37) @t11))) % 0.37/0.60 (define @t185 () (lambda @t26 (_ (_ @t161 @t184) @t11))) % 0.37/0.60 (define @t186 () (not @t8)) % 0.37/0.60 (define @t187 () (or @t186 @t78)) % 0.37/0.60 (define @t188 () (@quantifiers_skolemize @t128 0)) % 0.37/0.60 (define @t189 () (@quantifiers_skolemize @t128 1)) % 0.37/0.60 (define @t190 () (tptp.singleton @t189)) % 0.37/0.60 (define @t191 () (@quantifiers_skolemize @t128 2)) % 0.37/0.60 (define @t192 () (tptp.set_difference @t190 @t191)) % 0.37/0.60 (define @t193 () (tptp.qmltpeq @t192 @t190 @t188)) % 0.37/0.60 (define @t194 () (tptp.qmltpeq @t192 tptp.empty_set @t188)) % 0.37/0.60 (define @t195 () (tptp.exists_in_world @t191 @t188)) % 0.37/0.60 (define @t196 () (not @t195)) % 0.37/0.60 (define @t197 () (tptp.exists_in_world @t189 @t188)) % 0.37/0.60 (define @t198 () (not @t197)) % 0.37/0.60 (define @t199 () (or @t198 @t196 @t194 @t193)) % 0.37/0.60 (define @t200 () (not @t194)) % 0.37/0.60 (define @t201 () (@list true)) % 0.37/0.60 (define @t202 () (@list @t199)) % 0.37/0.60 (define @t203 () (@var "BOUND_VARIABLE_10202" tptp.mu)) % 0.37/0.60 (define @t204 () (tptp.qmltpeq (tptp.set_difference @t119 @t203) tptp.empty_set @t7)) % 0.37/0.60 (define @t205 () (tptp.in @t2 @t203 @t7)) % 0.37/0.60 (define @t206 () (and (or (not @t204) @t205) (or (not @t205) @t204))) % 0.37/0.60 (define @t207 () (not (tptp.exists_in_world @t203 @t7))) % 0.37/0.60 (define @t208 () (or @t126 @t207 @t206)) % 0.37/0.60 (define @t209 () (@list @t2 @t203)) % 0.37/0.60 (define @t210 () (forall @t209 @t208)) % 0.37/0.60 (define @t211 () (lambda @t64 @t210)) % 0.37/0.60 (define @t212 () (_ @t211 @t7)) % 0.37/0.60 (define @t213 () (forall @t64 @t212)) % 0.37/0.60 (define @t214 () (or @t207 @t206)) % 0.37/0.60 (define @t215 () (or @t126 @t214)) % 0.37/0.60 (define @t216 () (forall @t209 @t215)) % 0.37/0.60 (define @t217 () (@list @t203)) % 0.37/0.60 (define @t218 () (forall @t217 @t215)) % 0.37/0.60 (define @t219 () (forall @t217 @t214)) % 0.37/0.60 (define @t220 () (@var "BOUND_VARIABLE_10171" tptp.mu)) % 0.37/0.60 (define @t221 () (@list @t220)) % 0.37/0.60 (define @t222 () (or @t126 @t219)) % 0.37/0.60 (define @t223 () (tptp.qmltpeq (tptp.set_difference @t119 @t220) tptp.empty_set @t7)) % 0.37/0.60 (define @t224 () (tptp.in @t2 @t220 @t7)) % 0.37/0.60 (define @t225 () (@list @t220)) % 0.37/0.60 (define @t226 () (forall @t225 (or (not (tptp.exists_in_world @t220 @t7)) (and (or (not @t223) @t224) (or (not @t224) @t223))))) % 0.37/0.60 (define @t227 () (tptp.qmltpeq (tptp.set_difference @t148 @t220) tptp.empty_set @t11)) % 0.37/0.60 (define @t228 () (tptp.in @t21 @t220 @t11)) % 0.37/0.60 (define @t229 () (tptp.in @t21 @t2 @t11)) % 0.37/0.60 (define @t230 () (not @t229)) % 0.37/0.60 (define @t231 () (forall @t5 (or @t153 (and (or (not @t152) @t229) (or @t230 @t152))))) % 0.37/0.60 (define @t232 () (lambda @t26 @t231)) % 0.37/0.60 (define @t233 () (or @t126 (_ @t232 @t2 @t7))) % 0.37/0.60 (define @t234 () (forall @t5 @t233)) % 0.37/0.60 (define @t235 () (lambda @t64 @t234)) % 0.37/0.60 (define @t236 () (tptp.in @t21 @t2 @t7)) % 0.37/0.60 (define @t237 () (not @t236)) % 0.37/0.60 (define @t238 () (_ (_ @t32 @t2) @t7)) % 0.37/0.60 (define @t239 () (not @t238)) % 0.37/0.60 (define @t240 () (or @t239 @t168)) % 0.37/0.60 (define @t241 () (not @t168)) % 0.37/0.60 (define @t242 () (or @t241 @t238)) % 0.37/0.60 (define @t243 () (and @t242 @t240)) % 0.37/0.60 (define @t244 () (or @t126 @t243)) % 0.37/0.60 (define @t245 () (not @t240)) % 0.37/0.60 (define @t246 () (not @t242)) % 0.37/0.60 (define @t247 () (not (or @t246 @t245))) % 0.37/0.60 (define @t248 () (or @t126 @t247)) % 0.37/0.60 (define @t249 () (_ @t34 @t11)) % 0.37/0.60 (define @t250 () (not @t249)) % 0.37/0.60 (define @t251 () (not @t172)) % 0.37/0.60 (define @t252 () (not (or (not (or @t251 @t249)) (not (or @t250 @t172))))) % 0.37/0.60 (define @t253 () (lambda @t25 @t252)) % 0.37/0.60 (define @t254 () (_ @t253 @t2 @t7)) % 0.37/0.60 (define @t255 () (or @t126 @t254)) % 0.37/0.60 (define @t256 () (forall @t5 @t255)) % 0.37/0.60 (define @t257 () (lambda @t64 @t256)) % 0.37/0.60 (define @t258 () (@list @t11)) % 0.37/0.60 (define @t259 () (lambda @t258 @t252)) % 0.37/0.60 (define @t260 () (_ @t54 @t11)) % 0.37/0.60 (define @t261 () (not @t260)) % 0.37/0.60 (define @t262 () (@list @t54 @t11)) % 0.37/0.60 (define @t263 () (lambda @t262 (not (or (not (or @t251 @t260)) (not (or @t261 @t172)))))) % 0.37/0.60 (define @t264 () (_ @t49 @t11)) % 0.37/0.60 (define @t265 () (or @t261 @t264)) % 0.37/0.60 (define @t266 () (not @t264)) % 0.37/0.60 (define @t267 () (or @t266 @t260)) % 0.37/0.60 (define @t268 () (not @t267)) % 0.37/0.60 (define @t269 () (not (or @t268 (not @t265)))) % 0.37/0.60 (define @t270 () (lambda @t69 @t269)) % 0.37/0.60 (define @t271 () (_ @t270 @t40)) % 0.37/0.60 (define @t272 () (lambda @t25 (_ (_ @t271 @t34) @t11))) % 0.37/0.60 (define @t273 () (lambda @t258 @t265)) % 0.37/0.60 (define @t274 () (_ @t273 @t11)) % 0.37/0.60 (define @t275 () (not @t274)) % 0.37/0.60 (define @t276 () (or @t268 @t275)) % 0.37/0.60 (define @t277 () (not @t276)) % 0.37/0.60 (define @t278 () (lambda @t258 @t277)) % 0.37/0.60 (define @t279 () (@var "BOUND_VARIABLE_7630" (-> $$unsorted Bool))) % 0.37/0.60 (define @t280 () (not (_ @t279 @t11))) % 0.37/0.60 (define @t281 () (@list @t279 @t11)) % 0.37/0.60 (define @t282 () (@var "BOUND_VARIABLE_7650" (-> $$unsorted Bool))) % 0.37/0.60 (define @t283 () (_ @t282 @t11)) % 0.37/0.60 (define @t284 () (lambda (@list @t282 @t11) (or @t261 @t283))) % 0.37/0.60 (define @t285 () (lambda @t69 @t267)) % 0.37/0.60 (define @t286 () (@list @t54)) % 0.37/0.60 (define @t287 () (lambda @t258 @t267)) % 0.37/0.60 (define @t288 () (_ @t287 @t11)) % 0.37/0.60 (define @t289 () (not @t288)) % 0.37/0.60 (define @t290 () (or @t289 @t280)) % 0.37/0.60 (define @t291 () (not @t290)) % 0.37/0.60 (define @t292 () (lambda @t281 @t291)) % 0.37/0.60 (define @t293 () (not (or @t266 @t261))) % 0.37/0.60 (define @t294 () (lambda @t69 @t293)) % 0.37/0.60 (define @t295 () (lambda @t262 @t267)) % 0.37/0.60 (define @t296 () (or @t51 @t55)) % 0.37/0.60 (define @t297 () (lambda @t64 @t296)) % 0.37/0.60 (define @t298 () (lambda @t181 @t296)) % 0.37/0.60 (define @t299 () (lambda @t64 @t51)) % 0.37/0.60 (define @t300 () (_ @t299 @t7)) % 0.37/0.60 (define @t301 () (or @t300 @t55)) % 0.37/0.60 (define @t302 () (lambda @t181 @t301)) % 0.37/0.60 (define @t303 () (not @t55)) % 0.37/0.60 (define @t304 () (or @t51 @t303)) % 0.37/0.60 (define @t305 () (lambda @t64 @t304)) % 0.37/0.60 (define @t306 () (_ @t305 @t7)) % 0.37/0.60 (define @t307 () (not @t306)) % 0.37/0.60 (define @t308 () (lambda @t64 @t307)) % 0.37/0.60 (define @t309 () (lambda @t64 @t303)) % 0.37/0.60 (define @t310 () (_ @t309 @t7)) % 0.37/0.60 (define @t311 () (or @t51 @t310)) % 0.37/0.60 (define @t312 () (lambda @t64 @t311)) % 0.37/0.60 (define @t313 () (@list @t188 @t189 @t191)) % 0.37/0.60 (define @t314 () (tptp.in @t189 @t191 @t188)) % 0.37/0.60 (define @t315 () (not @t314)) % 0.37/0.60 (define @t316 () (or @t315 @t194)) % 0.37/0.60 (define @t317 () (and (or @t200 @t314) @t316)) % 0.37/0.60 (define @t318 () (or @t198 @t196 @t317)) % 0.37/0.60 (define @t319 () (@list false false false)) % 0.37/0.60 (define @t320 () (@list false)) % 0.37/0.60 (define @t321 () (@var "BOUND_VARIABLE_10072" tptp.mu)) % 0.37/0.60 (define @t322 () (tptp.qmltpeq (tptp.set_difference @t119 @t321) @t119 @t7)) % 0.37/0.60 (define @t323 () (tptp.in @t2 @t321 @t7)) % 0.37/0.60 (define @t324 () (and (or (not @t322) (not @t323)) (or @t323 @t322))) % 0.37/0.60 (define @t325 () (not (tptp.exists_in_world @t321 @t7))) % 0.37/0.60 (define @t326 () (or @t126 @t325 @t324)) % 0.37/0.60 (define @t327 () (@list @t2 @t321)) % 0.37/0.60 (define @t328 () (forall @t327 @t326)) % 0.37/0.60 (define @t329 () (lambda @t64 @t328)) % 0.37/0.60 (define @t330 () (_ @t329 @t7)) % 0.37/0.60 (define @t331 () (forall @t64 @t330)) % 0.37/0.60 (define @t332 () (or @t325 @t324)) % 0.37/0.60 (define @t333 () (or @t126 @t332)) % 0.37/0.60 (define @t334 () (forall @t327 @t333)) % 0.37/0.60 (define @t335 () (@list @t321)) % 0.37/0.60 (define @t336 () (forall @t335 @t333)) % 0.37/0.60 (define @t337 () (forall @t335 @t332)) % 0.37/0.60 (define @t338 () (@var "BOUND_VARIABLE_10041" tptp.mu)) % 0.37/0.60 (define @t339 () (@list @t338)) % 0.37/0.60 (define @t340 () (or @t126 @t337)) % 0.37/0.60 (define @t341 () (tptp.qmltpeq (tptp.set_difference @t119 @t338) @t119 @t7)) % 0.37/0.60 (define @t342 () (tptp.in @t2 @t338 @t7)) % 0.37/0.60 (define @t343 () (@list @t338)) % 0.37/0.60 (define @t344 () (forall @t343 (or (not (tptp.exists_in_world @t338 @t7)) (and (or (not @t341) (not @t342)) (or @t342 @t341))))) % 0.37/0.60 (define @t345 () (tptp.qmltpeq (tptp.set_difference @t148 @t338) @t148 @t11)) % 0.37/0.60 (define @t346 () (tptp.in @t21 @t338 @t11)) % 0.37/0.60 (define @t347 () (forall @t5 (or @t153 (and (or (not @t151) @t230) (or @t229 @t151))))) % 0.37/0.60 (define @t348 () (lambda @t26 @t347)) % 0.37/0.60 (define @t349 () (or @t126 (_ @t348 @t2 @t7))) % 0.37/0.60 (define @t350 () (forall @t5 @t349)) % 0.37/0.60 (define @t351 () (lambda @t64 @t350)) % 0.37/0.60 (define @t352 () (or @t238 @t167)) % 0.37/0.60 (define @t353 () (not @t167)) % 0.37/0.60 (define @t354 () (or @t353 @t239)) % 0.37/0.60 (define @t355 () (and @t354 @t352)) % 0.37/0.60 (define @t356 () (or @t126 @t355)) % 0.37/0.60 (define @t357 () (not @t352)) % 0.37/0.60 (define @t358 () (not @t354)) % 0.37/0.60 (define @t359 () (not (or @t358 @t357))) % 0.37/0.60 (define @t360 () (or @t126 @t359)) % 0.37/0.60 (define @t361 () (not @t171)) % 0.37/0.60 (define @t362 () (not (or (not (or @t361 @t250)) (not (or @t249 @t171))))) % 0.37/0.60 (define @t363 () (lambda @t25 @t362)) % 0.37/0.60 (define @t364 () (_ @t363 @t2 @t7)) % 0.37/0.60 (define @t365 () (or @t126 @t364)) % 0.37/0.60 (define @t366 () (forall @t5 @t365)) % 0.37/0.60 (define @t367 () (lambda @t64 @t366)) % 0.37/0.60 (define @t368 () (lambda @t64 (not (_ @t34 @t7)))) % 0.37/0.60 (define @t369 () (_ @t368 @t11)) % 0.37/0.60 (define @t370 () (not @t369)) % 0.37/0.60 (define @t371 () (or @t370 @t171)) % 0.37/0.60 (define @t372 () (not @t371)) % 0.37/0.60 (define @t373 () (or @t361 @t369)) % 0.37/0.60 (define @t374 () (not @t373)) % 0.37/0.60 (define @t375 () (or @t374 @t372)) % 0.37/0.60 (define @t376 () (not @t375)) % 0.37/0.60 (define @t377 () (lambda @t258 @t376)) % 0.37/0.60 (define @t378 () (lambda @t262 (not (or (not (or @t361 @t260)) (not (or @t261 @t171)))))) % 0.37/0.60 (define @t379 () (_ @t53 @t34)) % 0.37/0.60 (define @t380 () (_ @t270 @t37)) % 0.37/0.60 (define @t381 () (lambda @t25 (_ (_ @t380 @t379) @t11))) % 0.37/0.60 (define @t382 () (or @t314 @t193)) % 0.37/0.60 (define @t383 () (not @t193)) % 0.37/0.60 (define @t384 () (and (or @t383 @t315) @t382)) % 0.37/0.60 (define @t385 () (or @t198 @t196 @t384)) % 0.37/0.60 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.37/0.60 (assume @p2 (forall @t6 (exists @t5 @t4))) % 0.37/0.60 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 0.37/0.60 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 0.37/0.60 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 0.37/0.60 (assume @p6 (forall @t6 (_ (_ tptp.exists_in_world tptp.empty_set) @t1))) % 0.37/0.60 (assume @p7 (forall (@list @t1 @t9) (_ (_ tptp.exists_in_world (_ tptp.singleton @t9)) @t1))) % 0.37/0.60 (assume @p8 (forall (@list @t1 @t10 @t9) (_ (_ tptp.exists_in_world (_ (_ tptp.set_difference @t10) @t9)) @t1))) % 0.37/0.60 (assume @p9 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t13 (_ (_ @t12 @t2) @t11))))) % 0.37/0.60 (assume @p10 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t13 (_ (_ tptp.mforall_ind (lambda @t17 (_ (_ (_ tptp.mimplies @t16) (_ @t15 @t2)) @t11))) @t11))))) % 0.37/0.60 (assume @p11 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t13 (_ (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda (@list @t18 @t11) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t16) (_ @t15 @t18))) (_ @t12 @t18)) @t11))) @t11))) @t11))))) % 0.37/0.60 (assume @p12 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mforall_ind (lambda @t24 (_ (_ @t23 (_ (_ tptp.qmltpeq (_ (_ tptp.set_difference @t21) @t19)) (_ (_ tptp.set_difference @t20) @t19))) @t11))) @t11))) @t11))))) % 0.37/0.60 (assume @p13 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mforall_ind (lambda @t24 (_ (_ @t23 (_ (_ tptp.qmltpeq (_ @t27 @t21)) (_ @t27 @t20))) @t11))) @t11))) @t11))))) % 0.37/0.60 (assume @p14 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mforall_ind (lambda @t25 (_ (_ @t23 (_ (_ tptp.qmltpeq @t28) (_ tptp.singleton @t20))) @t11))) @t11))))) % 0.37/0.60 (assume @p15 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mforall_ind (lambda @t25 (_ (_ (_ tptp.mimplies (_ @t30 @t29)) (_ tptp.empty @t20)) @t11))) @t11))))) % 0.37/0.60 (assume @p16 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mforall_ind (lambda @t24 (_ (_ (_ tptp.mimplies (_ @t30 (_ @t32 @t19))) (_ @t31 @t19)) @t11))) @t11))) @t11))))) % 0.37/0.60 (assume @p17 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mforall_ind (lambda @t25 (_ (_ tptp.mforall_ind (lambda @t24 (_ (_ (_ tptp.mimplies (_ @t30 (_ @t33 @t21))) (_ @t33 @t20)) @t11))) @t11))) @t11))))) % 0.37/0.60 (assume @p18 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mforall_ind (lambda @t25 (_ (_ (_ tptp.mimplies @t34) (_ tptp.mnot (_ @t31 @t21))) @t11))) @t11))))) % 0.37/0.60 (assume @p19 (_ tptp.mvalid (_ tptp.empty tptp.empty_set))) % 0.37/0.60 (assume @p20 (_ tptp.mvalid (_ tptp.mforall_ind @t39))) % 0.37/0.60 (assume @p21 (_ tptp.mvalid (_ tptp.mforall_ind @t42))) % 0.37/0.60 (assume @p22 (_ tptp.mvalid (_ tptp.mexists_ind (lambda @t26 (_ @t29 @t11))))) % 0.37/0.60 (assume @p23 (_ tptp.mvalid (_ tptp.mexists_ind (lambda @t26 (_ (_ tptp.mnot @t29) @t11))))) % 0.37/0.60 (assume @p24 @t45) % 0.37/0.60 (assume @p25 true) % 0.37/0.60 (step @p26 (= tptp.meq_prop @t48) :rule refl :args (@t48)) % 0.37/0.60 (step @p27 (= tptp.mnot @t53) :rule refl :args (@t53)) % 0.37/0.60 (step @p28 (= tptp.mor @t56) :rule refl :args (@t56)) % 0.37/0.60 (step @p29 (= tptp.mbox @t59) :rule refl :args (@t59)) % 0.37/0.60 (step @p30 (= tptp.mforall_prop @t63) :rule refl :args (@t63)) % 0.37/0.60 (step @p31 (= tptp.mtrue @t65) :rule refl :args (@t65)) % 0.37/0.60 (step @p32 (= tptp.mand @t70) :rule refl :args (@t70)) % 0.37/0.60 (step @p33 (= tptp.mimplies @t71) :rule refl :args (@t71)) % 0.37/0.60 (step @p34 (= tptp.mimplied @t72) :rule refl :args (@t72)) % 0.37/0.60 (step @p35 (= tptp.mequiv @t73) :rule refl :args (@t73)) % 0.37/0.60 (step @p36 (= tptp.mxor @t74) :rule refl :args (@t74)) % 0.37/0.60 (step @p37 (= tptp.mdia @t75) :rule refl :args (@t75)) % 0.37/0.60 (step @p38 (= tptp.mforall_ind @t81) :rule refl :args (@t81)) % 0.37/0.60 (step @p39 (= tptp.mexists_ind @t82) :rule refl :args (@t82)) % 0.37/0.60 (step @p40 (= tptp.mexists_prop @t83) :rule refl :args (@t83)) % 0.37/0.60 (step @p41 (= tptp.mreflexive @t88) :rule refl :args (@t88)) % 0.37/0.60 (step @p42 (= tptp.msymmetric @t92) :rule refl :args (@t92)) % 0.37/0.60 (step @p43 (= tptp.mserial @t94) :rule refl :args (@t94)) % 0.37/0.60 (step @p44 (= tptp.mtransitive @t99) :rule refl :args (@t99)) % 0.37/0.60 (step @p45 (= tptp.meuclidean @t101) :rule refl :args (@t101)) % 0.37/0.60 (step @p46 (= tptp.mpartially_functional @t103) :rule refl :args (@t103)) % 0.37/0.60 (step @p47 (= tptp.mfunctional @t105) :rule refl :args (@t105)) % 0.37/0.60 (step @p48 (= tptp.mweakly_dense @t108) :rule refl :args (@t108)) % 0.37/0.60 (step @p49 (= tptp.mweakly_connected @t109) :rule refl :args (@t109)) % 0.37/0.60 (step @p50 (= tptp.mweakly_directed @t110) :rule refl :args (@t110)) % 0.37/0.60 (step @p51 (= tptp.mvalid @t113) :rule refl :args (@t113)) % 0.37/0.60 (step @p52 (= tptp.msatisfiable @t114) :rule refl :args (@t114)) % 0.37/0.60 (step @p53 (= tptp.mcountersatisfiable @t115) :rule refl :args (@t115)) % 0.37/0.60 (step @p54 (= tptp.minvalid @t116) :rule refl :args (@t116)) % 0.37/0.60 (step @p55 (= tptp.mbox_s4 @t117) :rule refl :args (@t117)) % 0.37/0.60 (step @p56 (= tptp.mdia_s4 @t118) :rule refl :args (@t118)) % 0.37/0.60 (step @p57 :rule quant-merge-prenex :args ((= (forall @t64 @t130) @t128))) % 0.37/0.60 (step @p58 :rule beta-reduce :args ((= @t132 @t130))) % 0.37/0.60 (step @p59 :rule cong :premises (@p58) :args (@t133)) % 0.37/0.60 (step @p60 :rule trans :premises (@p59 @p57)) % 0.37/0.60 (step @p61 :rule beta-reduce :args ((= (_ @t135 @t131) @t133))) % 0.37/0.60 (step @p62 :rule trans :premises (@p61 @p60)) % 0.37/0.60 (step @p63 :rule aci_norm :args ((= @t137 @t127))) % 0.37/0.60 (step @p64 :rule cong :premises (@p63) :args (@t138)) % 0.37/0.60 (step @p65 :rule quant-merge-prenex :args ((= (forall @t5 @t140) @t138))) % 0.37/0.60 (step @p66 :rule alpha_equiv :args (@t141 (@list @t120) @t143)) % 0.37/0.60 (step @p67 :rule refl :args (@t126)) % 0.37/0.60 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t144)) % 0.37/0.60 (step @p69 :rule quant-miniscope-or :args ((= @t140 @t144))) % 0.37/0.60 (step @p70 :rule trans :premises (@p69 @p68)) % 0.37/0.60 (step @p71 :rule symm :premises (@p70)) % 0.37/0.60 (step @p72 :rule cong :premises (@p71) :args ((forall @t5 (or @t126 @t147)))) % 0.37/0.60 (step @p73 :rule trans :premises (@p72 @p65)) % 0.37/0.60 (step @p74 :rule trans :premises (@p73 @p64)) % 0.37/0.60 (step @p75 :rule beta-reduce :args ((= (_ (lambda @t26 (forall @t146 (or (not (tptp.exists_in_world @t142 @t11)) (tptp.qmltpeq @t149 tptp.empty_set @t11) (tptp.qmltpeq @t149 @t148 @t11)))) @t2 @t7) @t147))) % 0.37/0.60 (step @p76 :rule refl :args (@t7)) % 0.37/0.60 (step @p77 :rule refl :args (@t2)) % 0.37/0.60 (step @p78 :rule alpha_equiv :args (@t154 @t155 @t143)) % 0.37/0.60 (step @p79 :rule cong :premises (@p78) :args (@t156)) % 0.37/0.60 (step @p80 :rule ho_cong :premises (@p79 @p77 @p76)) % 0.37/0.60 (step @p81 :rule trans :premises (@p80 @p75)) % 0.37/0.60 (step @p82 :rule refl :args (@t126)) % 0.37/0.60 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t157)) % 0.37/0.60 (step @p84 :rule cong :premises (@p83) :args (@t158)) % 0.37/0.60 (step @p85 :rule trans :premises (@p84 @p74)) % 0.37/0.60 (step @p86 :rule cong :premises (@p85) :args (@t159)) % 0.37/0.60 (step @p87 :rule beta-reduce :args ((= (_ @t161 @t156) @t159))) % 0.37/0.60 (step @p88 :rule trans :premises (@p87 @p86)) % 0.37/0.60 (step @p89 :rule beta-reduce :args ((= (_ (lambda @t64 (forall @t5 (or @t126 @t163 @t162))) @t11) @t154))) % 0.37/0.60 (step @p90 :rule refl :args (@t11)) % 0.37/0.60 (step @p91 :rule refl :args ((tptp.qmltpeq @t164 @t28 @t7))) % 0.37/0.60 (step @p92 :rule refl :args (@t148)) % 0.37/0.60 (step @p93 :rule refl :args ((tptp.set_difference @t28 @t2))) % 0.37/0.60 (step @p94 :rule cong :premises (@p92 @p77) :args (@t150)) % 0.37/0.60 (step @p95 :rule trans :premises (@p94 @p93)) % 0.37/0.60 (step @p96 :rule cong :premises (@p95 @p92 @p76) :args (@t162)) % 0.37/0.60 (step @p97 :rule trans :premises (@p96 @p91)) % 0.37/0.60 (step @p98 :rule refl :args (tptp.qmltpeq)) % 0.37/0.60 (step @p99 :rule ho_cong :premises (@p98 @p95)) % 0.37/0.60 (step @p100 :rule ho_cong :premises (@p99 @p92)) % 0.37/0.60 (step @p101 :rule ho_cong :premises (@p100 @p76)) % 0.37/0.60 (step @p102 :rule cong :premises (@p101 @p97) :args ((= (_ (_ @t165 @t148) @t7) @t162))) % 0.37/0.60 (step @p103 :rule symm :premises (@p102)) % 0.37/0.60 (step @p104 :rule refl :args (@t167)) % 0.37/0.60 (step @p105 :rule eq_resolve :premises (@p104 @p103)) % 0.37/0.60 (step @p106 :rule refl :args (@t28)) % 0.37/0.60 (step @p107 :rule cong :premises (@p106 @p92) :args ((= @t28 @t148))) % 0.37/0.60 (step @p108 :rule symm :premises (@p107)) % 0.37/0.60 (step @p109 :rule eq_resolve :premises (@p106 @p108)) % 0.37/0.60 (step @p110 :rule refl :args (tptp.set_difference)) % 0.37/0.60 (step @p111 :rule ho_cong :premises (@p110 @p92)) % 0.37/0.60 (step @p112 :rule ho_cong :premises (@p111 @p77)) % 0.37/0.60 (step @p113 :rule cong :premises (@p112 @p95) :args ((= (_ (_ tptp.set_difference @t148) @t2) @t150))) % 0.37/0.60 (step @p114 :rule symm :premises (@p113)) % 0.37/0.60 (step @p115 :rule refl :args (@t164)) % 0.37/0.60 (step @p116 :rule eq_resolve :premises (@p115 @p114)) % 0.37/0.60 (step @p117 :rule ho_cong :premises (@p110 @p109)) % 0.37/0.60 (step @p118 :rule ho_cong :premises (@p117 @p77)) % 0.37/0.60 (step @p119 :rule trans :premises (@p118 @p116)) % 0.37/0.60 (step @p120 :rule ho_cong :premises (@p98 @p119)) % 0.37/0.60 (step @p121 :rule ho_cong :premises (@p120 @p109)) % 0.37/0.60 (step @p122 :rule ho_cong :premises (@p121 @p76)) % 0.37/0.60 (step @p123 :rule trans :premises (@p122 @p105)) % 0.37/0.60 (step @p124 :rule refl :args ((tptp.qmltpeq @t164 tptp.empty_set @t7))) % 0.37/0.60 (step @p125 :rule refl :args (tptp.empty_set)) % 0.37/0.60 (step @p126 :rule cong :premises (@p95 @p125 @p76) :args (@t163)) % 0.37/0.60 (step @p127 :rule trans :premises (@p126 @p124)) % 0.37/0.60 (step @p128 :rule ho_cong :premises (@p99 @p125)) % 0.37/0.60 (step @p129 :rule ho_cong :premises (@p128 @p76)) % 0.37/0.60 (step @p130 :rule cong :premises (@p129 @p127) :args ((= (_ (_ @t165 tptp.empty_set) @t7) @t163))) % 0.37/0.60 (step @p131 :rule symm :premises (@p130)) % 0.37/0.60 (step @p132 :rule refl :args (@t168)) % 0.37/0.60 (step @p133 :rule eq_resolve :premises (@p132 @p131)) % 0.37/0.60 (step @p134 :rule ho_cong :premises (@p120 @p125)) % 0.37/0.60 (step @p135 :rule ho_cong :premises (@p134 @p76)) % 0.37/0.60 (step @p136 :rule trans :premises (@p135 @p133)) % 0.37/0.60 (step @p137 :rule nary_cong :premises (@p67 @p136 @p123) :args (@t169)) % 0.37/0.60 (step @p138 :rule cong :premises (@p137) :args ((forall @t5 @t169))) % 0.37/0.60 (step @p139 :rule aci_norm :args ((= (or @t126 @t170) @t169))) % 0.37/0.60 (step @p140 :rule beta-reduce :args ((= @t175 @t170))) % 0.37/0.60 (step @p141 :rule nary_cong :premises (@p82 @p140) :args (@t176)) % 0.37/0.60 (step @p142 :rule trans :premises (@p141 @p139)) % 0.37/0.60 (step @p143 :rule cong :premises (@p142) :args (@t177)) % 0.37/0.60 (step @p144 :rule trans :premises (@p143 @p138)) % 0.37/0.60 (step @p145 :rule cong :premises (@p144) :args (@t178)) % 0.37/0.60 (step @p146 :rule beta-reduce :args ((= (_ @t161 @t174) @t178))) % 0.37/0.60 (step @p147 :rule trans :premises (@p146 @p145)) % 0.37/0.60 (step @p148 :rule beta-reduce :args ((= (_ @t180 @t11) @t173))) % 0.37/0.60 (step @p149 :rule beta-reduce :args ((= (_ @t182 @t37) @t180))) % 0.37/0.60 (step @p150 :rule refl :args (@t37)) % 0.37/0.60 (step @p151 :rule beta-reduce :args ((= @t183 @t182))) % 0.37/0.60 (step @p152 :rule ho_cong :premises (@p151 @p150)) % 0.37/0.60 (step @p153 :rule trans :premises (@p152 @p149)) % 0.37/0.60 (step @p154 :rule ho_cong :premises (@p153 @p90)) % 0.37/0.60 (step @p155 :rule trans :premises (@p154 @p148)) % 0.37/0.60 (step @p156 :rule cong :premises (@p155) :args (@t184)) % 0.37/0.60 (step @p157 :rule refl :args (@t161)) % 0.37/0.60 (step @p158 :rule ho_cong :premises (@p157 @p156)) % 0.37/0.60 (step @p159 :rule trans :premises (@p158 @p147)) % 0.37/0.60 (step @p160 :rule ho_cong :premises (@p159 @p90)) % 0.37/0.60 (step @p161 :rule trans :premises (@p160 @p89)) % 0.37/0.60 (step @p162 :rule cong :premises (@p161) :args (@t185)) % 0.37/0.60 (step @p163 :rule ho_cong :premises (@p157 @p162)) % 0.37/0.60 (step @p164 :rule trans :premises (@p163 @p88)) % 0.37/0.60 (step @p165 :rule refl :args (@t135)) % 0.37/0.60 (step @p166 :rule ho_cong :premises (@p165 @p164)) % 0.37/0.60 (step @p167 :rule trans :premises (@p166 @p62)) % 0.37/0.60 (step @p168 :rule cong :premises (@p167) :args ((not (_ @t135 (_ @t161 @t185))))) % 0.37/0.60 (step @p169 :rule refl :args (@t40)) % 0.37/0.60 (step @p170 :rule ho_cong :premises (@p28 @p169)) % 0.37/0.60 (step @p171 :rule ho_cong :premises (@p170 @p150)) % 0.37/0.60 (step @p172 :rule ho_cong :premises (@p171 @p90)) % 0.37/0.60 (step @p173 :rule cong :premises (@p172) :args (@t43)) % 0.37/0.60 (step @p174 :rule refl :args (@t160)) % 0.37/0.60 (step @p175 :rule refl :args (@t78)) % 0.37/0.60 (step @p176 :rule cong :premises (@p175 @p174) :args ((= @t78 @t160))) % 0.37/0.60 (step @p177 :rule symm :premises (@p176)) % 0.37/0.60 (step @p178 :rule eq_resolve :premises (@p175 @p177)) % 0.37/0.60 (step @p179 :rule refl :args (@t125)) % 0.37/0.60 (step @p180 :rule refl :args (@t8)) % 0.37/0.60 (step @p181 :rule cong :premises (@p180 @p179) :args ((= @t8 @t125))) % 0.37/0.60 (step @p182 :rule symm :premises (@p181)) % 0.37/0.60 (step @p183 :rule eq_resolve :premises (@p180 @p182)) % 0.37/0.60 (step @p184 :rule cong :premises (@p183) :args (@t186)) % 0.37/0.60 (step @p185 :rule nary_cong :premises (@p184 @p178) :args (@t187)) % 0.37/0.60 (step @p186 :rule cong :premises (@p185) :args ((forall @t5 @t187))) % 0.37/0.60 (step @p187 :rule bool-impl-elim :args (@t8 @t78)) % 0.37/0.60 (step @p188 :rule cong :premises (@p187) :args (@t79)) % 0.37/0.60 (step @p189 :rule trans :premises (@p188 @p186)) % 0.37/0.60 (step @p190 :rule cong :premises (@p189) :args (@t81)) % 0.37/0.60 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:rule trans :premises (@p420 @p418)) % 0.37/0.61 (step @p422 :rule beta-reduce :args ((= (_ @t135 @t329) @t331))) % 0.37/0.61 (step @p423 :rule trans :premises (@p422 @p421)) % 0.37/0.61 (step @p424 :rule aci_norm :args ((= @t333 @t326))) % 0.37/0.61 (step @p425 :rule cong :premises (@p424) :args (@t334)) % 0.37/0.61 (step @p426 :rule quant-merge-prenex :args ((= (forall @t5 @t336) @t334))) % 0.37/0.61 (step @p427 :rule alpha_equiv :args (@t337 (@list @t321) @t339)) % 0.37/0.61 (step @p428 :rule nary_cong :premises (@p67 @p427) :args (@t340)) % 0.37/0.61 (step @p429 :rule quant-miniscope-or :args ((= @t336 @t340))) % 0.37/0.61 (step @p430 :rule trans :premises (@p429 @p428)) % 0.37/0.61 (step @p431 :rule symm :premises (@p430)) % 0.37/0.61 (step @p432 :rule cong :premises (@p431) :args ((forall @t5 (or @t126 @t344)))) % 0.37/0.61 (step @p433 :rule trans :premises (@p432 @p426)) % 0.37/0.61 (step @p434 :rule trans :premises (@p433 @p425)) % 0.37/0.61 (step @p435 :rule beta-reduce :args ((= (_ (lambda @t26 (forall @t343 (or (not (tptp.exists_in_world @t338 @t11)) (and (or (not @t345) (not @t346)) (or @t346 @t345))))) @t2 @t7) @t344))) % 0.37/0.61 (step @p436 :rule alpha_equiv :args (@t347 @t155 @t339)) % 0.37/0.61 (step @p437 :rule cong :premises (@p436) :args (@t348)) % 0.37/0.61 (step @p438 :rule ho_cong :premises (@p437 @p77 @p76)) % 0.37/0.61 (step @p439 :rule trans :premises (@p438 @p435)) % 0.37/0.61 (step @p440 :rule nary_cong :premises (@p82 @p439) :args (@t349)) % 0.37/0.61 (step @p441 :rule cong :premises (@p440) :args (@t350)) % 0.37/0.61 (step @p442 :rule trans :premises (@p441 @p434)) % 0.37/0.61 (step @p443 :rule cong :premises (@p442) :args (@t351)) % 0.37/0.61 (step @p444 :rule beta-reduce :args ((= (_ @t161 @t348) @t351))) % 0.37/0.61 (step @p445 :rule trans :premises (@p444 @p443)) % 0.37/0.61 (step @p446 :rule beta-reduce :args ((= (_ (lambda @t64 (forall @t5 (or @t126 (and (or (not @t162) @t237) (or @t236 @t162))))) @t11) @t347))) % 0.37/0.61 (step @p447 :rule nary_cong :premises (@p244 @p123) :args (@t352)) % 0.37/0.61 (step @p448 :rule cong :premises (@p123) :args (@t353)) % 0.37/0.61 (step @p449 :rule nary_cong :premises (@p448 @p245) :args (@t354)) % 0.37/0.61 (step @p450 :rule nary_cong :premises (@p449 @p447) :args (@t355)) % 0.37/0.61 (step @p451 :rule nary_cong :premises (@p67 @p450) :args (@t356)) % 0.37/0.61 (step @p452 :rule cong :premises (@p451) :args ((forall @t5 @t356))) % 0.37/0.61 (step @p453 :rule bool-double-not-elim :args (@t352)) % 0.37/0.61 (step @p454 :rule bool-double-not-elim :args (@t354)) % 0.37/0.61 (step @p455 :rule nary_cong :premises (@p454 @p453) :args ((and (not @t358) (not @t357)))) % 0.37/0.61 (step @p456 :rule bool-or-de-morgan :args (@t358 @t357 false)) % 0.37/0.61 (step @p457 :rule trans :premises (@p456 @p455)) % 0.37/0.61 (step @p458 :rule nary_cong :premises (@p67 @p457) :args (@t360)) % 0.37/0.61 (step @p459 :rule cong :premises (@p458) :args ((forall @t5 @t360))) % 0.37/0.61 (step @p460 :rule trans :premises (@p459 @p452)) % 0.37/0.61 (step @p461 :rule beta-reduce :args ((= @t364 @t359))) % 0.37/0.61 (step @p462 :rule nary_cong :premises (@p82 @p461) :args (@t365)) % 0.37/0.61 (step @p463 :rule cong :premises (@p462) :args (@t366)) % 0.37/0.61 (step @p464 :rule trans :premises (@p463 @p460)) % 0.37/0.61 (step @p465 :rule cong :premises (@p464) :args (@t367)) % 0.37/0.61 (step @p466 :rule beta-reduce :args ((= (_ @t161 @t363) @t367))) % 0.37/0.61 (step @p467 :rule trans :premises (@p466 @p465)) % 0.37/0.61 (step @p468 :rule beta-reduce :args ((= (_ (lambda @t258 @t362) @t11) @t362))) % 0.37/0.61 (step @p469 :rule refl :args (@t171)) % 0.37/0.61 (step @p470 :rule bool-double-not-elim :args (@t249)) % 0.37/0.61 (step @p471 :rule beta-reduce :args ((= @t369 @t250))) % 0.37/0.61 (step @p472 :rule cong :premises (@p471) :args (@t370)) % 0.37/0.61 (step @p473 :rule trans :premises (@p472 @p470)) % 0.37/0.61 (step @p474 :rule nary_cong :premises (@p473 @p469) :args (@t371)) % 0.37/0.61 (step @p475 :rule cong :premises (@p474) :args (@t372)) % 0.37/0.61 (step @p476 :rule refl :args (@t361)) % 0.37/0.61 (step @p477 :rule nary_cong :premises (@p476 @p471) :args (@t373)) % 0.37/0.61 (step @p478 :rule cong :premises (@p477) :args (@t374)) % 0.37/0.61 (step @p479 :rule nary_cong :premises (@p478 @p475) :args (@t375)) % 0.37/0.61 (step @p480 :rule cong :premises (@p479) :args (@t376)) % 0.37/0.61 (step @p481 :rule cong :premises (@p480) :args (@t377)) % 0.37/0.61 (step @p482 :rule beta-reduce :args ((= (_ @t378 @t368) @t377))) % 0.37/0.61 (step @p483 :rule trans :premises (@p482 @p481)) % 0.37/0.61 (step @p484 :rule beta-reduce :args ((= @t379 @t368))) % 0.37/0.61 (step @p485 :rule beta-reduce :args ((= @t380 @t378))) % 0.37/0.61 (step @p486 :rule ho_cong :premises (@p485 @p484)) % 0.37/0.61 (step @p487 :rule trans :premises (@p486 @p483)) % 0.37/0.61 (step @p488 :rule ho_cong :premises (@p487 @p90)) % 0.37/0.61 (step @p489 :rule trans :premises (@p488 @p468)) % 0.37/0.61 (step @p490 :rule cong :premises (@p489) :args (@t381)) % 0.37/0.61 (step @p491 :rule ho_cong :premises (@p157 @p490)) % 0.37/0.61 (step @p492 :rule trans :premises (@p491 @p467)) % 0.37/0.61 (step @p493 :rule ho_cong :premises (@p492 @p90)) % 0.37/0.61 (step @p494 :rule trans :premises (@p493 @p446)) % 0.37/0.61 (step @p495 :rule cong :premises (@p494) :args ((lambda @t26 (_ (_ @t161 @t381) @t11)))) % 0.37/0.61 (step @p496 :rule ho_cong :premises (@p157 @p495)) % 0.37/0.61 (step @p497 :rule trans :premises (@p496 @p445)) % 0.37/0.61 (step @p498 :rule ho_cong :premises (@p165 @p497)) % 0.37/0.61 (step @p499 :rule trans :premises (@p498 @p423)) % 0.37/0.61 (step @p500 :rule ho_cong :premises (@p27 @p269)) % 0.37/0.61 (step @p501 :rule ho_cong :premises (@p386 @p150)) % 0.37/0.61 (step @p502 :rule ho_cong :premises (@p501 @p500)) % 0.37/0.61 (step @p503 :rule ho_cong :premises (@p502 @p90)) % 0.37/0.61 (step @p504 :rule cong :premises (@p503) :args (@t38)) % 0.37/0.61 (step @p505 :rule ho_cong :premises (@p191 @p504)) % 0.37/0.61 (step @p506 :rule ho_cong :premises (@p505 @p90)) % 0.37/0.61 (step @p507 :rule cong :premises (@p506) :args (@t39)) % 0.37/0.61 (step @p508 :rule ho_cong :premises (@p191 @p507)) % 0.37/0.61 (step @p509 :rule ho_cong :premises (@p203 @p508)) % 0.37/0.61 (step @p510 :rule trans :premises (@p509 @p499)) % 0.37/0.61 (step @p511 :rule eq_resolve :premises (@p20 @p510)) % 0.37/0.61 (step @p512 :rule instantiate :premises (@p511) :args (@t313)) % 0.37/0.61 (step @p513 :rule cnf_or_pos :args (@t385)) % 0.37/0.61 (step @p514 :rule reordering :premises (@p513) :args ((or @t198 @t196 @t384 (not @t385)))) % 0.37/0.61 (step @p515 :rule chain_m_resolution :premises (@p514 @p411 @p405 @p512) :args (@t384 @t319 (@list @t197 @t195 @t385))) % 0.37/0.61 (step @p516 :rule cnf_and_pos :args (@t384 1)) % 0.37/0.61 (step @p517 :rule reordering :premises (@p516) :args ((or @t382 (not @t384)))) % 0.37/0.61 (step @p518 :rule chain_m_resolution :premises (@p517 @p515) :args (@t382 @t320 (@list @t384))) % 0.37/0.61 (step @p519 :rule cnf_or_neg :args (@t199 3)) % 0.37/0.61 (step @p520 :rule chain_m_resolution :premises (@p519 @p208) :args (@t383 @t201 @t202)) % 0.37/0.61 (step @p521 :rule cnf_or_pos :args (@t382)) % 0.37/0.61 (step @p522 :rule reordering :premises (@p521) :args ((or @t193 @t314 (not @t382)))) % 0.37/0.61 (step @p523 :rule chain_m_resolution :premises (@p522 @p520 @p518) :args (@t314 (@list true false) (@list @t193 @t382))) % 0.37/0.61 (step @p524 :rule cnf_or_pos :args (@t316)) % 0.37/0.61 (step @p525 :rule reordering :premises (@p524) :args ((or @t194 @t315 (not @t316)))) % 0.37/0.61 (step @p526 false :rule chain_m_resolution :premises (@p525 @p523 @p417 @p210) :args (false (@list false false true) (@list @t314 @t316 @t194))) % 0.37/0.61 ) % 0.37/0.61 % SZS output end Proof % 0.37/0.61 % cvc5 exiting %------------------------------------------------------------------------------