%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET062^7 : TPTP v9.2.1. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : 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 08:47:12 AM UTC 2026 % Result : Theorem 1.52s 1.73s % Output : Proof 1.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET062^7 : TPTP v9.2.1. Released v5.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/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 14:49:18 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.51 %----Proving TH0 % 1.52/1.73 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.52/1.73 % SZS status Theorem % 1.52/1.73 % SZS output start Proof % 1.52/1.73 ( % 1.52/1.73 (declare-sort tptp.mu 0) % 1.52/1.73 (declare-sort $$unsorted 0) % 1.52/1.73 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 1.52/1.73 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 1.52/1.73 (declare-const tptp.member (-> tptp.mu tptp.mu $$unsorted Bool)) % 1.52/1.73 (declare-const tptp.equal_set (-> tptp.mu tptp.mu $$unsorted Bool)) % 1.52/1.73 (declare-const tptp.qmltpeq (-> tptp.mu tptp.mu $$unsorted Bool)) % 1.52/1.73 (declare-const tptp.power_set (-> tptp.mu tptp.mu)) % 1.52/1.73 (declare-const tptp.sum (-> tptp.mu tptp.mu)) % 1.52/1.73 (declare-const tptp.subset (-> tptp.mu tptp.mu $$unsorted Bool)) % 1.52/1.73 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 1.52/1.73 (declare-const tptp.product (-> tptp.mu tptp.mu)) % 1.52/1.73 (declare-const tptp.union (-> tptp.mu tptp.mu tptp.mu)) % 1.52/1.73 (declare-const tptp.singleton (-> tptp.mu tptp.mu)) % 1.52/1.73 (declare-const tptp.intersection (-> tptp.mu tptp.mu tptp.mu)) % 1.52/1.73 (declare-const tptp.difference (-> tptp.mu tptp.mu tptp.mu)) % 1.52/1.73 (declare-const tptp.unordered_pair (-> tptp.mu tptp.mu tptp.mu)) % 1.52/1.73 (declare-const tptp.empty_set tptp.mu) % 1.52/1.73 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 1.52/1.73 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 1.52/1.73 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 1.52/1.73 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 1.52/1.73 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 1.52/1.73 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 1.52/1.73 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 1.52/1.73 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 1.52/1.73 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 1.52/1.73 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 1.52/1.73 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 1.52/1.73 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 1.52/1.73 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.exists_in_world _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 1.52/1.73 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 1.52/1.73 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 1.52/1.73 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 1.52/1.73 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 1.52/1.73 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 1.52/1.73 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 1.52/1.73 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 1.52/1.73 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 1.52/1.73 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 1.52/1.73 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 1.52/1.73 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 1.52/1.73 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 1.52/1.73 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 1.52/1.73 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 1.52/1.73 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 1.52/1.73 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 1.52/1.73 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 1.52/1.73 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 1.52/1.73 (define @t1 () (@var "V" $$unsorted)) % 1.52/1.73 (define @t2 () (@var "X" tptp.mu)) % 1.52/1.73 (define @t3 () (_ tptp.exists_in_world @t2)) % 1.52/1.73 (define @t4 () (_ @t3 @t1)) % 1.52/1.73 (define @t5 () (@list @t2)) % 1.52/1.73 (define @t6 () (@list @t1)) % 1.52/1.73 (define @t7 () (@var "W" $$unsorted)) % 1.52/1.73 (define @t8 () (_ @t3 @t7)) % 1.52/1.73 (define @t9 () (@var "V1" tptp.mu)) % 1.52/1.73 (define @t10 () (@list @t1 @t9)) % 1.52/1.73 (define @t11 () (@var "V2" tptp.mu)) % 1.52/1.73 (define @t12 () (@list @t1 @t11 @t9)) % 1.52/1.73 (define @t13 () (_ (_ tptp.exists_in_world tptp.empty_set) @t1)) % 1.52/1.73 (define @t14 () (forall @t6 @t13)) % 1.52/1.73 (define @t15 () (@var "__flatten_var_0" $$unsorted)) % 1.52/1.73 (define @t16 () (_ tptp.qmltpeq @t2)) % 1.52/1.73 (define @t17 () (@list @t2 @t15)) % 1.52/1.73 (define @t18 () (@var "Y" tptp.mu)) % 1.52/1.73 (define @t19 () (_ tptp.qmltpeq @t18)) % 1.52/1.73 (define @t20 () (_ @t16 @t18)) % 1.52/1.73 (define @t21 () (@list @t18 @t15)) % 1.52/1.73 (define @t22 () (@var "Z" tptp.mu)) % 1.52/1.73 (define @t23 () (@var "C" tptp.mu)) % 1.52/1.73 (define @t24 () (@var "B" tptp.mu)) % 1.52/1.73 (define @t25 () (@var "A" tptp.mu)) % 1.52/1.73 (define @t26 () (_ (_ tptp.qmltpeq @t25) @t24)) % 1.52/1.73 (define @t27 () (_ tptp.mimplies @t26)) % 1.52/1.73 (define @t28 () (@list @t23 @t15)) % 1.52/1.73 (define @t29 () (@list @t24 @t15)) % 1.52/1.73 (define @t30 () (@list @t25 @t15)) % 1.52/1.73 (define @t31 () (_ tptp.difference @t23)) % 1.52/1.73 (define @t32 () (_ tptp.intersection @t25)) % 1.52/1.73 (define @t33 () (_ tptp.intersection @t23)) % 1.52/1.73 (define @t34 () (_ tptp.power_set @t25)) % 1.52/1.73 (define @t35 () (_ tptp.product @t25)) % 1.52/1.73 (define @t36 () (_ tptp.singleton @t25)) % 1.52/1.73 (define @t37 () (_ tptp.sum @t25)) % 1.52/1.73 (define @t38 () (_ tptp.union @t25)) % 1.52/1.73 (define @t39 () (_ tptp.union @t23)) % 1.52/1.73 (define @t40 () (_ tptp.unordered_pair @t25)) % 1.52/1.73 (define @t41 () (_ tptp.unordered_pair @t23)) % 1.52/1.73 (define @t42 () (_ tptp.equal_set @t25)) % 1.52/1.73 (define @t43 () (_ tptp.mand @t26)) % 1.52/1.73 (define @t44 () (_ tptp.equal_set @t23)) % 1.52/1.73 (define @t45 () (_ tptp.member @t24)) % 1.52/1.73 (define @t46 () (_ tptp.member @t23)) % 1.52/1.73 (define @t47 () (_ tptp.subset @t24)) % 1.52/1.73 (define @t48 () (_ tptp.subset @t25)) % 1.52/1.73 (define @t49 () (_ tptp.subset @t23)) % 1.52/1.73 (define @t50 () (_ tptp.member @t2)) % 1.52/1.73 (define @t51 () (_ @t50 @t24)) % 1.52/1.73 (define @t52 () (_ @t50 @t25)) % 1.52/1.73 (define @t53 () (lambda @t17 (_ (_ (_ tptp.mimplies @t52) @t51) @t15))) % 1.52/1.73 (define @t54 () (_ @t48 @t24)) % 1.52/1.73 (define @t55 () (lambda @t29 (_ (_ (_ tptp.mequiv @t54) (_ tptp.mforall_ind @t53)) @t15))) % 1.52/1.73 (define @t56 () (lambda @t30 (_ (_ tptp.mforall_ind @t55) @t15))) % 1.52/1.73 (define @t57 () (_ @t50 tptp.empty_set)) % 1.52/1.73 (define @t58 () (lambda @t17 (_ (_ tptp.mnot @t57) @t15))) % 1.52/1.73 (define @t59 () (@var "E" tptp.mu)) % 1.52/1.73 (define @t60 () (_ @t16 @t25)) % 1.52/1.73 (define @t61 () (_ @t50 @t18)) % 1.52/1.73 (define @t62 () (_ (_ tptp.member @t18) @t25)) % 1.52/1.73 (define @t63 () (_ tptp.subset tptp.empty_set)) % 1.52/1.73 (define @t64 () (lambda @t30 (_ (_ @t63 @t25) @t15))) % 1.52/1.73 (define @t65 () (not (_ tptp.mvalid (_ tptp.mforall_ind @t64)))) % 1.52/1.73 (define @t66 () (@var "Y" (-> $$unsorted Bool))) % 1.52/1.73 (define @t67 () (@var "X" (-> $$unsorted Bool))) % 1.52/1.73 (define @t68 () (lambda (@list @t67 @t66 @t7) (= (_ @t67 @t7) (_ @t66 @t7)))) % 1.52/1.73 (define @t69 () (@var "Phi" (-> $$unsorted Bool))) % 1.52/1.73 (define @t70 () (_ @t69 @t7)) % 1.52/1.73 (define @t71 () (not @t70)) % 1.52/1.73 (define @t72 () (@list @t69 @t7)) % 1.52/1.73 (define @t73 () (lambda @t72 @t71)) % 1.52/1.73 (define @t74 () (@var "Psi" (-> $$unsorted Bool))) % 1.52/1.73 (define @t75 () (_ @t74 @t7)) % 1.52/1.73 (define @t76 () (lambda (@list @t69 @t74 @t7) (or @t70 @t75))) % 1.52/1.73 (define @t77 () (_ @t69 @t1)) % 1.52/1.73 (define @t78 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 1.52/1.73 (define @t79 () (lambda (@list @t78 @t69 @t7) (forall @t6 (or (not (_ (_ @t78 @t7) @t1)) @t77)))) % 1.52/1.73 (define @t80 () (@var "P" (-> $$unsorted Bool))) % 1.52/1.73 (define @t81 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 1.52/1.73 (define @t82 () (_ @t81 @t80)) % 1.52/1.73 (define @t83 () (lambda (@list @t81 @t7) (forall (@list @t80) (_ @t82 @t7)))) % 1.52/1.73 (define @t84 () (@list @t7)) % 1.52/1.73 (define @t85 () (lambda @t84 true)) % 1.52/1.73 (define @t86 () (_ tptp.mnot @t74)) % 1.52/1.73 (define @t87 () (_ tptp.mnot @t69)) % 1.52/1.73 (define @t88 () (_ tptp.mor @t87)) % 1.52/1.73 (define @t89 () (@list @t69 @t74 @t15)) % 1.52/1.73 (define @t90 () (lambda @t89 (_ (_ tptp.mnot (_ @t88 @t86)) @t15))) % 1.52/1.73 (define @t91 () (lambda @t89 (_ (_ @t88 @t74) @t15))) % 1.52/1.73 (define @t92 () (lambda @t89 (_ (_ (_ tptp.mor @t86) @t69) @t15))) % 1.52/1.73 (define @t93 () (lambda @t89 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t69) @t74)) (_ (_ tptp.mimplies @t74) @t69)) @t15))) % 1.52/1.73 (define @t94 () (lambda @t89 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t69) @t74)) @t15))) % 1.52/1.73 (define @t95 () (lambda (@list @t78 @t69 @t15) (_ (_ tptp.mnot (_ (_ tptp.mbox @t78) @t87)) @t15))) % 1.52/1.73 (define @t96 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 1.52/1.73 (define @t97 () (_ @t96 @t2)) % 1.52/1.73 (define @t98 () (_ @t97 @t7)) % 1.52/1.73 (define @t99 () (forall @t5 (=> @t8 @t98))) % 1.52/1.73 (define @t100 () (@list @t96 @t7)) % 1.52/1.73 (define @t101 () (lambda @t100 @t99)) % 1.52/1.73 (define @t102 () (lambda (@list @t96 @t15) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mnot @t97) @t15)))) @t15))) % 1.52/1.73 (define @t103 () (lambda (@list @t81 @t15) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t80 @t15) (_ (_ tptp.mnot @t82) @t15)))) @t15))) % 1.52/1.73 (define @t104 () (@var "S" $$unsorted)) % 1.52/1.73 (define @t105 () (_ @t78 @t104)) % 1.52/1.73 (define @t106 () (@list @t104)) % 1.52/1.73 (define @t107 () (@list @t78)) % 1.52/1.73 (define @t108 () (lambda @t107 (forall @t106 (_ @t105 @t104)))) % 1.52/1.73 (define @t109 () (@var "T" $$unsorted)) % 1.52/1.73 (define @t110 () (_ @t78 @t109)) % 1.52/1.73 (define @t111 () (_ @t105 @t109)) % 1.52/1.73 (define @t112 () (lambda @t107 (forall (@list @t104 @t109) (=> @t111 (_ @t110 @t104))))) % 1.52/1.73 (define @t113 () (@list @t109)) % 1.52/1.73 (define @t114 () (lambda @t107 (forall @t106 (exists @t113 @t111)))) % 1.52/1.73 (define @t115 () (@var "U" $$unsorted)) % 1.52/1.73 (define @t116 () (_ @t105 @t115)) % 1.52/1.73 (define @t117 () (_ @t110 @t115)) % 1.52/1.73 (define @t118 () (@list @t104 @t109 @t115)) % 1.52/1.73 (define @t119 () (lambda @t107 (forall @t118 (=> (and @t111 @t117) @t116)))) % 1.52/1.73 (define @t120 () (and @t111 @t116)) % 1.52/1.73 (define @t121 () (lambda @t107 (forall @t118 (=> @t120 @t117)))) % 1.52/1.73 (define @t122 () (= @t109 @t115)) % 1.52/1.73 (define @t123 () (lambda @t107 (forall @t118 (=> @t120 @t122)))) % 1.52/1.73 (define @t124 () (@list @t115)) % 1.52/1.73 (define @t125 () (lambda @t107 (forall @t106 (exists @t113 (and @t111 (forall @t124 (=> @t116 @t122))))))) % 1.52/1.73 (define @t126 () (_ @t78 @t115)) % 1.52/1.73 (define @t127 () (_ @t126 @t109)) % 1.52/1.73 (define @t128 () (lambda @t107 (forall @t118 (=> @t111 (exists @t124 (and @t116 @t127)))))) % 1.52/1.73 (define @t129 () (lambda @t107 (forall @t118 (=> @t120 (or @t117 @t122 @t127))))) % 1.52/1.73 (define @t130 () (lambda @t107 (forall @t118 (=> @t120 (exists @t6 (and (_ @t110 @t1) (_ @t126 @t1))))))) % 1.52/1.73 (define @t131 () (forall @t84 @t70)) % 1.52/1.73 (define @t132 () (@list @t69)) % 1.52/1.73 (define @t133 () (lambda @t132 @t131)) % 1.52/1.73 (define @t134 () (lambda @t132 (exists @t84 @t70))) % 1.52/1.73 (define @t135 () (lambda @t132 (exists @t84 @t71))) % 1.52/1.73 (define @t136 () (lambda @t132 (forall @t84 @t71))) % 1.52/1.73 (define @t137 () (lambda @t72 (forall @t6 (or (not (_ (_ tptp.rel_s4 @t7) @t1)) @t77)))) % 1.52/1.73 (define @t138 () (lambda (@list @t69 @t15) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t87)) @t15))) % 1.52/1.73 (define @t139 () (tptp.member @t2 tptp.empty_set @t7)) % 1.52/1.73 (define @t140 () (tptp.exists_in_world @t2 @t7)) % 1.52/1.73 (define @t141 () (not @t140)) % 1.52/1.73 (define @t142 () (or @t141 (not @t139))) % 1.52/1.73 (define @t143 () (@list @t7 @t2)) % 1.52/1.73 (define @t144 () (forall @t143 @t142)) % 1.52/1.73 (define @t145 () (forall @t5 @t142)) % 1.52/1.73 (define @t146 () (lambda @t84 @t145)) % 1.52/1.73 (define @t147 () (_ @t146 @t7)) % 1.52/1.73 (define @t148 () (forall @t84 @t147)) % 1.52/1.73 (define @t149 () (_ @t69 @t7)) % 1.52/1.73 (define @t150 () (lambda @t132 (forall @t84 @t149))) % 1.52/1.73 (define @t151 () (_ @t57 @t7)) % 1.52/1.73 (define @t152 () (not @t151)) % 1.52/1.73 (define @t153 () (or @t141 @t152)) % 1.52/1.73 (define @t154 () (not (_ @t57 @t15))) % 1.52/1.73 (define @t155 () (lambda @t17 @t154)) % 1.52/1.73 (define @t156 () (_ @t155 @t2 @t7)) % 1.52/1.73 (define @t157 () (or @t141 @t156)) % 1.52/1.73 (define @t158 () (forall @t5 @t157)) % 1.52/1.73 (define @t159 () (lambda @t84 @t158)) % 1.52/1.73 (define @t160 () (_ @t96 @t2 @t7)) % 1.52/1.73 (define @t161 () (lambda @t100 (forall @t5 (or @t141 @t160)))) % 1.52/1.73 (define @t162 () (lambda @t84 @t152)) % 1.52/1.73 (define @t163 () (_ @t73 @t57)) % 1.52/1.73 (define @t164 () (not @t8)) % 1.52/1.73 (define @t165 () (or @t164 @t98)) % 1.52/1.73 (define @t166 () (@var "BOUND_VARIABLE_12210" tptp.mu)) % 1.52/1.73 (define @t167 () (tptp.subset @t2 @t166 @t7)) % 1.52/1.73 (define @t168 () (@var "BOUND_VARIABLE_12090" tptp.mu)) % 1.52/1.73 (define @t169 () (tptp.member @t168 @t2 @t7)) % 1.52/1.73 (define @t170 () (not @t169)) % 1.52/1.73 (define @t171 () (not (tptp.exists_in_world @t168 @t7))) % 1.52/1.73 (define @t172 () (@list @t168)) % 1.52/1.73 (define @t173 () (@var "BOUND_VARIABLE_12212" tptp.mu)) % 1.52/1.73 (define @t174 () (and (or (not @t167) (not (tptp.exists_in_world @t173 @t7)) (not (tptp.member @t173 @t2 @t7)) (tptp.member @t173 @t166 @t7)) (or (not (forall @t172 (or @t171 @t170 (tptp.member @t168 @t166 @t7)))) @t167))) % 1.52/1.73 (define @t175 () (not (tptp.exists_in_world @t166 @t7))) % 1.52/1.73 (define @t176 () (or @t141 @t175 @t174)) % 1.52/1.73 (define @t177 () (@list @t2 @t166 @t173)) % 1.52/1.73 (define @t178 () (forall @t177 @t176)) % 1.52/1.73 (define @t179 () (lambda @t84 @t178)) % 1.52/1.73 (define @t180 () (_ @t179 @t7)) % 1.52/1.73 (define @t181 () (forall @t84 @t180)) % 1.52/1.73 (define @t182 () (or @t175 @t174)) % 1.52/1.73 (define @t183 () (or @t141 @t182)) % 1.52/1.73 (define @t184 () (forall @t177 @t183)) % 1.52/1.73 (define @t185 () (@list @t166 @t173)) % 1.52/1.73 (define @t186 () (forall @t185 @t183)) % 1.52/1.73 (define @t187 () (forall @t185 @t182)) % 1.52/1.73 (define @t188 () (@var "BOUND_VARIABLE_12133" tptp.mu)) % 1.52/1.73 (define @t189 () (@var "BOUND_VARIABLE_12173" tptp.mu)) % 1.52/1.73 (define @t190 () (or @t141 @t187)) % 1.52/1.73 (define @t191 () (tptp.subset @t2 @t189 @t7)) % 1.52/1.73 (define @t192 () (tptp.member @t188 @t2 @t7)) % 1.52/1.73 (define @t193 () (not (tptp.exists_in_world @t188 @t7))) % 1.52/1.73 (define @t194 () (@list @t189 @t188)) % 1.52/1.73 (define @t195 () (forall @t194 (or (not (tptp.exists_in_world @t189 @t7)) (and (or (not @t191) @t193 (not @t192) (tptp.member @t188 @t189 @t7)) (or (not (forall @t172 (or @t171 @t170 (tptp.member @t168 @t189 @t7)))) @t191))))) % 1.52/1.73 (define @t196 () (tptp.subset @t25 @t189 @t15)) % 1.52/1.73 (define @t197 () (not (tptp.member @t168 @t25 @t15))) % 1.52/1.73 (define @t198 () (not (tptp.exists_in_world @t168 @t15))) % 1.52/1.73 (define @t199 () (not (tptp.member @t188 @t25 @t15))) % 1.52/1.73 (define @t200 () (not (tptp.exists_in_world @t188 @t15))) % 1.52/1.73 (define @t201 () (tptp.subset @t25 @t2 @t15)) % 1.52/1.73 (define @t202 () (not (tptp.exists_in_world @t2 @t15))) % 1.52/1.73 (define @t203 () (@list @t2 @t188)) % 1.52/1.73 (define @t204 () (forall @t203 (or @t202 (and (or (not @t201) @t200 @t199 (tptp.member @t188 @t2 @t15)) (or (not (forall @t172 (or @t198 @t197 (tptp.member @t168 @t2 @t15)))) @t201))))) % 1.52/1.73 (define @t205 () (@list @t2)) % 1.52/1.73 (define @t206 () (lambda @t30 @t204)) % 1.52/1.73 (define @t207 () (or @t141 (_ @t206 @t2 @t7))) % 1.52/1.73 (define @t208 () (forall @t5 @t207)) % 1.52/1.73 (define @t209 () (lambda @t84 @t208)) % 1.52/1.73 (define @t210 () (tptp.subset @t25 @t2 @t7)) % 1.52/1.73 (define @t211 () (forall @t172 (or @t171 (not (tptp.member @t168 @t25 @t7)) @t169))) % 1.52/1.73 (define @t212 () (not @t211)) % 1.52/1.73 (define @t213 () (or @t212 @t210)) % 1.52/1.73 (define @t214 () (not (tptp.member @t188 @t25 @t7))) % 1.52/1.73 (define @t215 () (not @t210)) % 1.52/1.73 (define @t216 () (or @t215 @t193 @t214 @t192)) % 1.52/1.73 (define @t217 () (or @t193 @t214 @t192)) % 1.52/1.73 (define @t218 () (or @t215 @t217)) % 1.52/1.73 (define @t219 () (and @t218 @t213)) % 1.52/1.73 (define @t220 () (or @t141 @t219)) % 1.52/1.73 (define @t221 () (forall @t203 @t220)) % 1.52/1.73 (define @t222 () (@list @t188)) % 1.52/1.73 (define @t223 () (forall @t222 @t220)) % 1.52/1.73 (define @t224 () (forall @t222 @t213)) % 1.52/1.73 (define @t225 () (forall @t222 @t217)) % 1.52/1.73 (define @t226 () (@list @t168)) % 1.52/1.73 (define @t227 () (or @t215 @t225)) % 1.52/1.73 (define @t228 () (forall @t222 @t218)) % 1.52/1.73 (define @t229 () (and @t228 @t224)) % 1.52/1.73 (define @t230 () (forall @t222 @t219)) % 1.52/1.73 (define @t231 () (or @t141 @t230)) % 1.52/1.73 (define @t232 () (_ (_ @t48 @t2) @t7)) % 1.52/1.73 (define @t233 () (or @t212 @t232)) % 1.52/1.73 (define @t234 () (not @t232)) % 1.52/1.73 (define @t235 () (or @t234 @t211)) % 1.52/1.73 (define @t236 () (and @t235 @t233)) % 1.52/1.73 (define @t237 () (or @t141 @t236)) % 1.52/1.73 (define @t238 () (not @t233)) % 1.52/1.73 (define @t239 () (not @t235)) % 1.52/1.73 (define @t240 () (not (or @t239 @t238))) % 1.52/1.73 (define @t241 () (or @t141 @t240)) % 1.52/1.73 (define @t242 () (_ @t54 @t15)) % 1.52/1.73 (define @t243 () (forall @t172 (or @t198 @t197 (tptp.member @t168 @t24 @t15)))) % 1.52/1.73 (define @t244 () (not @t242)) % 1.52/1.73 (define @t245 () (forall @t5 (or @t202 (not (tptp.member @t2 @t25 @t15)) (tptp.member @t2 @t24 @t15)))) % 1.52/1.73 (define @t246 () (not @t245)) % 1.52/1.73 (define @t247 () (or @t246 @t242)) % 1.52/1.73 (define @t248 () (not @t247)) % 1.52/1.73 (define @t249 () (or @t244 @t245)) % 1.52/1.73 (define @t250 () (not @t249)) % 1.52/1.73 (define @t251 () (or @t250 @t248)) % 1.52/1.73 (define @t252 () (not @t251)) % 1.52/1.73 (define @t253 () (lambda @t29 @t252)) % 1.52/1.73 (define @t254 () (or @t141 (_ @t253 @t2 @t7))) % 1.52/1.73 (define @t255 () (forall @t5 @t254)) % 1.52/1.73 (define @t256 () (lambda @t84 @t255)) % 1.52/1.73 (define @t257 () (@list @t15)) % 1.52/1.73 (define @t258 () (tptp.member @t2 @t24 @t7)) % 1.52/1.73 (define @t259 () (tptp.member @t2 @t25 @t7)) % 1.52/1.73 (define @t260 () (lambda @t84 (forall @t5 (or @t141 (not @t259) @t258)))) % 1.52/1.73 (define @t261 () (_ @t260 @t15)) % 1.52/1.73 (define @t262 () (not @t261)) % 1.52/1.73 (define @t263 () (or @t262 @t242)) % 1.52/1.73 (define @t264 () (not @t263)) % 1.52/1.73 (define @t265 () (or @t244 @t261)) % 1.52/1.73 (define @t266 () (not @t265)) % 1.52/1.73 (define @t267 () (or @t266 @t264)) % 1.52/1.73 (define @t268 () (not @t267)) % 1.52/1.73 (define @t269 () (lambda @t257 @t268)) % 1.52/1.73 (define @t270 () (_ @t74 @t15)) % 1.52/1.73 (define @t271 () (not @t270)) % 1.52/1.73 (define @t272 () (@list @t74 @t15)) % 1.52/1.73 (define @t273 () (lambda @t272 (not (or (not (or @t244 @t270)) (not (or @t271 @t242)))))) % 1.52/1.73 (define @t274 () (_ @t51 @t7)) % 1.52/1.73 (define @t275 () (_ @t52 @t7)) % 1.52/1.73 (define @t276 () (not @t275)) % 1.52/1.73 (define @t277 () (or @t141 @t276 @t274)) % 1.52/1.73 (define @t278 () (or @t276 @t274)) % 1.52/1.73 (define @t279 () (not (_ @t52 @t15))) % 1.52/1.73 (define @t280 () (or @t279 (_ @t51 @t15))) % 1.52/1.73 (define @t281 () (lambda @t17 @t280)) % 1.52/1.73 (define @t282 () (_ @t281 @t2 @t7)) % 1.52/1.73 (define @t283 () (or @t141 @t282)) % 1.52/1.73 (define @t284 () (forall @t5 @t283)) % 1.52/1.73 (define @t285 () (lambda @t84 @t284)) % 1.52/1.73 (define @t286 () (lambda @t257 @t280)) % 1.52/1.73 (define @t287 () (lambda @t272 (or @t279 @t270))) % 1.52/1.73 (define @t288 () (_ @t69 @t15)) % 1.52/1.73 (define @t289 () (not @t288)) % 1.52/1.73 (define @t290 () (or @t289 @t270)) % 1.52/1.73 (define @t291 () (lambda @t89 @t290)) % 1.52/1.73 (define @t292 () (_ @t291 @t52)) % 1.52/1.73 (define @t293 () (lambda @t17 (_ (_ @t292 @t51) @t15))) % 1.52/1.73 (define @t294 () (or @t271 @t288)) % 1.52/1.73 (define @t295 () (not @t290)) % 1.52/1.73 (define @t296 () (not (or @t295 (not @t294)))) % 1.52/1.73 (define @t297 () (_ (lambda @t89 @t296) @t54)) % 1.52/1.73 (define @t298 () (lambda @t29 (_ (_ @t297 (_ @t161 @t293)) @t15))) % 1.52/1.73 (define @t299 () (or @t71 @t75)) % 1.52/1.73 (define @t300 () (lambda @t84 @t299)) % 1.52/1.73 (define @t301 () (@list @t74 @t7)) % 1.52/1.73 (define @t302 () (lambda @t301 @t299)) % 1.52/1.73 (define @t303 () (lambda @t84 @t71)) % 1.52/1.73 (define @t304 () (_ @t303 @t7)) % 1.52/1.73 (define @t305 () (or @t304 @t75)) % 1.52/1.73 (define @t306 () (lambda @t301 @t305)) % 1.52/1.73 (define @t307 () (lambda @t257 @t294)) % 1.52/1.73 (define @t308 () (_ @t307 @t15)) % 1.52/1.73 (define @t309 () (not @t308)) % 1.52/1.73 (define @t310 () (or @t295 @t309)) % 1.52/1.73 (define @t311 () (not @t310)) % 1.52/1.73 (define @t312 () (lambda @t257 @t311)) % 1.52/1.73 (define @t313 () (@var "BOUND_VARIABLE_7630" (-> $$unsorted Bool))) % 1.52/1.73 (define @t314 () (not (_ @t313 @t15))) % 1.52/1.73 (define @t315 () (@list @t313 @t15)) % 1.52/1.73 (define @t316 () (@var "BOUND_VARIABLE_7650" (-> $$unsorted Bool))) % 1.52/1.73 (define @t317 () (_ @t316 @t15)) % 1.52/1.73 (define @t318 () (lambda (@list @t316 @t15) (or @t271 @t317))) % 1.52/1.73 (define @t319 () (@list @t74)) % 1.52/1.73 (define @t320 () (lambda @t257 @t290)) % 1.52/1.73 (define @t321 () (_ @t320 @t15)) % 1.52/1.73 (define @t322 () (not @t321)) % 1.52/1.73 (define @t323 () (or @t322 @t314)) % 1.52/1.73 (define @t324 () (not @t323)) % 1.52/1.73 (define @t325 () (lambda @t315 @t324)) % 1.52/1.73 (define @t326 () (not (or @t289 @t271))) % 1.52/1.73 (define @t327 () (lambda @t89 @t326)) % 1.52/1.73 (define @t328 () (lambda @t272 @t290)) % 1.52/1.73 (define @t329 () (not @t75)) % 1.52/1.73 (define @t330 () (or @t71 @t329)) % 1.52/1.73 (define @t331 () (lambda @t84 @t330)) % 1.52/1.73 (define @t332 () (_ @t331 @t7)) % 1.52/1.73 (define @t333 () (not @t332)) % 1.52/1.73 (define @t334 () (lambda @t84 @t333)) % 1.52/1.73 (define @t335 () (lambda @t84 @t329)) % 1.52/1.73 (define @t336 () (_ @t335 @t7)) % 1.52/1.73 (define @t337 () (or @t71 @t336)) % 1.52/1.73 (define @t338 () (lambda @t84 @t337)) % 1.52/1.73 (define @t339 () (tptp.subset tptp.empty_set @t2 @t7)) % 1.52/1.73 (define @t340 () (or @t141 @t339)) % 1.52/1.73 (define @t341 () (forall @t143 @t340)) % 1.52/1.73 (define @t342 () (@quantifiers_skolemize @t341 1)) % 1.52/1.73 (define @t343 () (@quantifiers_skolemize @t341 0)) % 1.52/1.73 (define @t344 () (tptp.exists_in_world tptp.empty_set @t1)) % 1.52/1.73 (define @t345 () (forall @t5 @t340)) % 1.52/1.73 (define @t346 () (lambda @t84 @t345)) % 1.52/1.73 (define @t347 () (_ @t346 @t7)) % 1.52/1.73 (define @t348 () (forall @t84 @t347)) % 1.52/1.73 (define @t349 () (_ (_ @t63 @t2) @t7)) % 1.52/1.73 (define @t350 () (or @t141 @t349)) % 1.52/1.73 (define @t351 () (_ @t64 @t2 @t7)) % 1.52/1.73 (define @t352 () (or @t141 @t351)) % 1.52/1.73 (define @t353 () (forall @t5 @t352)) % 1.52/1.73 (define @t354 () (lambda @t84 @t353)) % 1.52/1.73 (define @t355 () (_ @t161 @t64)) % 1.52/1.73 (define @t356 () (tptp.exists_in_world @t342 @t343)) % 1.52/1.73 (define @t357 () (tptp.subset tptp.empty_set @t342 @t343)) % 1.52/1.73 (define @t358 () (not @t356)) % 1.52/1.73 (define @t359 () (or @t358 @t357)) % 1.52/1.73 (define @t360 () (@list true)) % 1.52/1.73 (define @t361 () (@list @t359)) % 1.52/1.73 (define @t362 () (forall @t172 (or (not (tptp.exists_in_world @t168 @t343)) (not (tptp.member @t168 tptp.empty_set @t343)) (tptp.member @t168 @t342 @t343)))) % 1.52/1.73 (define @t363 () (not @t362)) % 1.52/1.73 (define @t364 () (or @t363 @t357)) % 1.52/1.73 (define @t365 () (not @t357)) % 1.52/1.73 (define @t366 () (and (or @t365 @t358 (not (tptp.member @t342 tptp.empty_set @t343)) (tptp.member @t342 @t342 @t343)) @t364)) % 1.52/1.73 (define @t367 () (tptp.exists_in_world tptp.empty_set @t343)) % 1.52/1.73 (define @t368 () (not @t367)) % 1.52/1.73 (define @t369 () (or @t368 @t358 @t366)) % 1.52/1.73 (define @t370 () (@list true false)) % 1.52/1.73 (define @t371 () (@quantifiers_skolemize @t362 0)) % 1.52/1.73 (define @t372 () (tptp.member @t371 tptp.empty_set @t343)) % 1.52/1.73 (define @t373 () (not @t372)) % 1.52/1.73 (define @t374 () (tptp.exists_in_world @t371 @t343)) % 1.52/1.73 (define @t375 () (not @t374)) % 1.52/1.73 (define @t376 () (or @t375 @t373 (tptp.member @t371 @t342 @t343))) % 1.52/1.73 (define @t377 () (@list @t376)) % 1.52/1.73 (define @t378 () (or @t375 @t373)) % 1.52/1.73 (define @t379 () (not @t378)) % 1.52/1.73 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 1.52/1.73 (assume @p2 (forall @t6 (exists @t5 @t4))) % 1.52/1.73 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 1.52/1.73 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 1.52/1.73 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 1.52/1.73 (assume @p6 (forall @t10 (_ (_ tptp.exists_in_world (_ tptp.power_set @t9)) @t1))) % 1.52/1.73 (assume @p7 (forall @t12 (_ (_ tptp.exists_in_world (_ (_ tptp.intersection @t11) @t9)) @t1))) % 1.52/1.73 (assume @p8 (forall @t12 (_ (_ tptp.exists_in_world (_ (_ tptp.union @t11) @t9)) @t1))) % 1.52/1.73 (assume @p9 (forall @t12 (_ (_ tptp.exists_in_world (_ (_ tptp.difference @t11) @t9)) @t1))) % 1.52/1.73 (assume @p10 (forall @t10 (_ (_ tptp.exists_in_world (_ tptp.singleton @t9)) @t1))) % 1.52/1.73 (assume @p11 (forall @t12 (_ (_ tptp.exists_in_world (_ (_ tptp.unordered_pair @t11) @t9)) @t1))) % 1.52/1.73 (assume @p12 (forall @t10 (_ (_ tptp.exists_in_world (_ tptp.sum @t9)) @t1))) % 1.52/1.73 (assume @p13 (forall @t10 (_ (_ tptp.exists_in_world (_ tptp.product @t9)) @t1))) % 1.52/1.73 (assume @p14 @t14) % 1.52/1.73 (assume @p15 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ @t16 @t2) @t15))))) % 1.52/1.73 (assume @p16 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t21 (_ (_ (_ tptp.mimplies @t20) (_ @t19 @t2)) @t15))) @t15))))) % 1.52/1.73 (assume @p17 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t21 (_ (_ tptp.mforall_ind (lambda (@list @t22 @t15) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t20) (_ @t19 @t22))) (_ @t16 @t22)) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p18 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ @t27 (_ (_ tptp.qmltpeq (_ (_ tptp.difference @t25) @t23)) (_ (_ tptp.difference @t24) @t23))) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p19 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ @t27 (_ (_ tptp.qmltpeq (_ @t31 @t25)) (_ @t31 @t24))) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p20 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ @t27 (_ (_ tptp.qmltpeq (_ @t32 @t23)) (_ (_ tptp.intersection @t24) @t23))) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p21 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ @t27 (_ (_ tptp.qmltpeq (_ @t33 @t25)) (_ @t33 @t24))) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p22 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ @t27 (_ (_ tptp.qmltpeq @t34) (_ tptp.power_set @t24))) @t15))) @t15))))) % 1.52/1.73 (assume @p23 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ @t27 (_ (_ tptp.qmltpeq @t35) (_ tptp.product @t24))) @t15))) @t15))))) % 1.52/1.73 (assume @p24 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ @t27 (_ (_ tptp.qmltpeq @t36) (_ tptp.singleton @t24))) @t15))) @t15))))) % 1.52/1.73 (assume @p25 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ @t27 (_ (_ tptp.qmltpeq @t37) (_ tptp.sum @t24))) @t15))) @t15))))) % 1.52/1.73 (assume @p26 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ @t27 (_ (_ tptp.qmltpeq (_ @t38 @t23)) (_ (_ tptp.union @t24) @t23))) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p27 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ @t27 (_ (_ tptp.qmltpeq (_ @t39 @t25)) (_ @t39 @t24))) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p28 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ @t27 (_ (_ tptp.qmltpeq (_ @t40 @t23)) (_ (_ tptp.unordered_pair @t24) @t23))) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p29 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ @t27 (_ (_ tptp.qmltpeq (_ @t41 @t25)) (_ @t41 @t24))) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p30 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ (_ tptp.mimplies (_ @t43 (_ @t42 @t23))) (_ (_ tptp.equal_set @t24) @t23)) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p31 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ (_ tptp.mimplies (_ @t43 (_ @t44 @t25))) (_ @t44 @t24)) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p32 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ (_ tptp.mimplies (_ @t43 (_ (_ tptp.member @t25) @t23))) (_ @t45 @t23)) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p33 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ (_ tptp.mimplies (_ @t43 (_ @t46 @t25))) (_ @t46 @t24)) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p34 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ (_ tptp.mimplies (_ @t43 (_ @t48 @t23))) (_ @t47 @t23)) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p35 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t28 (_ (_ (_ tptp.mimplies (_ @t43 (_ @t49 @t25))) (_ @t49 @t24)) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p36 (_ tptp.mvalid (_ tptp.mforall_ind @t56))) % 1.52/1.73 (assume @p37 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ (_ tptp.mequiv (_ @t42 @t24)) (_ (_ tptp.mand @t54) (_ @t47 @t25))) @t15))) @t15))))) % 1.52/1.73 (assume @p38 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ (_ tptp.mequiv (_ @t50 @t34)) (_ (_ tptp.subset @t2) @t25)) @t15))) @t15))))) % 1.52/1.73 (assume @p39 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ (_ tptp.mequiv (_ @t50 (_ @t32 @t24))) (_ (_ tptp.mand @t52) @t51)) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p40 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ (_ tptp.mequiv (_ @t50 (_ @t38 @t24))) (_ (_ tptp.mor @t52) @t51)) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p41 (_ tptp.mvalid (_ tptp.mforall_ind @t58))) % 1.52/1.73 (assume @p42 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t29 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda (@list @t59 @t15) (_ (_ (_ tptp.mequiv (_ @t45 (_ (_ tptp.difference @t59) @t25))) (_ (_ tptp.mand (_ @t45 @t59)) (_ tptp.mnot (_ @t45 @t25)))) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p43 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ (_ tptp.mequiv (_ @t50 @t36)) @t60) @t15))) @t15))))) % 1.52/1.73 (assume @p44 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ tptp.mforall_ind (lambda @t29 (_ (_ (_ tptp.mequiv (_ @t50 (_ @t40 @t24))) (_ (_ tptp.mor @t60) (_ @t16 @t24))) @t15))) @t15))) @t15))))) % 1.52/1.73 (assume @p45 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ (_ tptp.mequiv (_ @t50 @t37)) (_ tptp.mexists_ind (lambda @t21 (_ (_ (_ tptp.mand @t62) @t61) @t15)))) @t15))) @t15))))) % 1.52/1.73 (assume @p46 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda @t30 (_ (_ (_ tptp.mequiv (_ @t50 @t35)) (_ tptp.mforall_ind (lambda @t21 (_ (_ (_ tptp.mimplies @t62) @t61) @t15)))) @t15))) @t15))))) % 1.52/1.73 (assume @p47 @t65) % 1.52/1.73 (assume @p48 true) % 1.52/1.73 (step @p49 (= tptp.meq_prop @t68) :rule refl :args (@t68)) % 1.52/1.73 (step @p50 (= tptp.mnot @t73) :rule refl :args (@t73)) % 1.52/1.73 (step @p51 (= tptp.mor @t76) :rule refl :args (@t76)) % 1.52/1.73 (step @p52 (= tptp.mbox @t79) :rule refl :args (@t79)) % 1.52/1.73 (step @p53 (= tptp.mforall_prop @t83) :rule refl :args (@t83)) % 1.52/1.73 (step @p54 (= tptp.mtrue @t85) :rule refl :args (@t85)) % 1.52/1.73 (step @p55 (= tptp.mand @t90) :rule refl :args (@t90)) % 1.52/1.73 (step @p56 (= tptp.mimplies @t91) :rule refl :args (@t91)) % 1.52/1.73 (step @p57 (= tptp.mimplied @t92) :rule refl :args (@t92)) % 1.52/1.73 (step @p58 (= tptp.mequiv @t93) :rule refl :args (@t93)) % 1.52/1.73 (step @p59 (= tptp.mxor @t94) :rule refl :args (@t94)) % 1.52/1.73 (step @p60 (= tptp.mdia @t95) :rule refl :args (@t95)) % 1.52/1.73 (step @p61 (= tptp.mforall_ind @t101) :rule refl :args (@t101)) % 1.52/1.73 (step @p62 (= tptp.mexists_ind @t102) :rule refl :args (@t102)) % 1.52/1.73 (step @p63 (= tptp.mexists_prop @t103) :rule refl :args (@t103)) % 1.52/1.73 (step @p64 (= tptp.mreflexive @t108) :rule refl :args (@t108)) % 1.52/1.73 (step @p65 (= tptp.msymmetric @t112) :rule refl :args (@t112)) % 1.52/1.73 (step @p66 (= tptp.mserial @t114) :rule refl :args (@t114)) % 1.52/1.73 (step @p67 (= tptp.mtransitive @t119) :rule refl :args (@t119)) % 1.52/1.73 (step @p68 (= tptp.meuclidean @t121) :rule refl :args (@t121)) % 1.52/1.73 (step @p69 (= tptp.mpartially_functional @t123) :rule refl :args (@t123)) % 1.52/1.73 (step @p70 (= tptp.mfunctional @t125) :rule refl :args (@t125)) % 1.52/1.73 (step @p71 (= tptp.mweakly_dense @t128) :rule refl :args (@t128)) % 1.52/1.73 (step @p72 (= tptp.mweakly_connected @t129) :rule refl :args (@t129)) % 1.52/1.73 (step @p73 (= tptp.mweakly_directed @t130) :rule refl :args (@t130)) % 1.52/1.73 (step @p74 (= tptp.mvalid @t133) :rule refl :args (@t133)) % 1.52/1.73 (step @p75 (= tptp.msatisfiable @t134) :rule refl :args (@t134)) % 1.52/1.73 (step @p76 (= tptp.mcountersatisfiable @t135) :rule refl :args (@t135)) % 1.52/1.73 (step @p77 (= tptp.minvalid @t136) :rule refl :args (@t136)) % 1.52/1.73 (step @p78 (= tptp.mbox_s4 @t137) :rule refl :args (@t137)) % 1.52/1.73 (step @p79 (= tptp.mdia_s4 @t138) :rule refl :args (@t138)) % 1.52/1.73 (step @p80 :rule quant-merge-prenex :args ((= (forall @t84 @t145) @t144))) % 1.52/1.73 (step @p81 :rule beta-reduce :args ((= @t147 @t145))) % 1.52/1.73 (step @p82 :rule cong :premises (@p81) :args (@t148)) % 1.52/1.73 (step @p83 :rule trans :premises (@p82 @p80)) % 1.52/1.73 (step @p84 :rule beta-reduce :args ((= (_ @t150 @t146) @t148))) % 1.52/1.73 (step @p85 :rule trans :premises (@p84 @p83)) % 1.52/1.73 (step @p86 :rule refl :args (@t139)) % 1.52/1.73 (step @p87 :rule refl :args (@t151)) % 1.52/1.73 (step @p88 :rule cong :premises (@p87 @p86) :args ((= @t151 @t139))) % 1.52/1.73 (step @p89 :rule symm :premises (@p88)) % 1.52/1.73 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 1.52/1.73 (step @p91 :rule cong :premises (@p90) :args (@t152)) % 1.52/1.73 (step @p92 :rule refl :args (@t141)) % 1.52/1.73 (step @p93 :rule nary_cong :premises (@p92 @p91) :args (@t153)) % 1.52/1.73 (step @p94 :rule cong :premises (@p93) :args ((forall @t5 @t153))) % 1.52/1.73 (step @p95 :rule beta-reduce :args ((= @t156 @t152))) % 1.52/1.73 (step @p96 :rule refl :args (@t141)) % 1.52/1.73 (step @p97 :rule nary_cong :premises (@p96 @p95) :args (@t157)) % 1.52/1.73 (step @p98 :rule cong :premises (@p97) :args (@t158)) % 1.52/1.73 (step @p99 :rule trans :premises (@p98 @p94)) % 1.52/1.73 (step @p100 :rule cong :premises (@p99) :args (@t159)) % 1.52/1.73 (step @p101 :rule beta-reduce :args ((= (_ @t161 @t155) @t159))) % 1.52/1.73 (step @p102 :rule trans :premises (@p101 @p100)) % 1.52/1.73 (step @p103 :rule beta-reduce :args ((= (_ @t162 @t15) @t154))) % 1.52/1.73 (step @p104 :rule refl :args (@t15)) % 1.52/1.73 (step @p105 :rule beta-reduce :args ((= @t163 @t162))) % 1.52/1.73 (step @p106 :rule ho_cong :premises (@p105 @p104)) % 1.52/1.73 (step @p107 :rule trans :premises (@p106 @p103)) % 1.52/1.73 (step @p108 :rule cong :premises (@p107) :args ((lambda @t17 (_ @t163 @t15)))) % 1.52/1.73 (step @p109 :rule refl :args (@t161)) % 1.52/1.73 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 1.52/1.73 (step @p111 :rule trans :premises (@p110 @p102)) % 1.52/1.73 (step @p112 :rule refl :args (@t150)) % 1.52/1.73 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 1.52/1.73 (step @p114 :rule trans :premises (@p113 @p85)) % 1.52/1.73 (step @p115 :rule refl :args (@t57)) % 1.52/1.73 (step @p116 :rule ho_cong :premises (@p50 @p115)) % 1.52/1.73 (step @p117 :rule ho_cong :premises (@p116 @p104)) % 1.52/1.73 (step @p118 :rule cong :premises (@p117) :args (@t58)) % 1.52/1.73 (step @p119 :rule refl :args (@t160)) % 1.52/1.73 (step @p120 :rule refl :args (@t98)) % 1.52/1.73 (step @p121 :rule cong :premises (@p120 @p119) :args ((= @t98 @t160))) % 1.52/1.73 (step @p122 :rule symm :premises (@p121)) % 1.52/1.73 (step @p123 :rule eq_resolve :premises (@p120 @p122)) % 1.52/1.73 (step @p124 :rule refl :args (@t140)) % 1.52/1.73 (step @p125 :rule refl :args (@t8)) % 1.52/1.73 (step @p126 :rule cong :premises (@p125 @p124) :args ((= @t8 @t140))) % 1.52/1.73 (step @p127 :rule symm :premises (@p126)) % 1.52/1.73 (step @p128 :rule eq_resolve :premises (@p125 @p127)) % 1.52/1.73 (step @p129 :rule cong :premises (@p128) :args (@t164)) % 1.52/1.73 (step @p130 :rule nary_cong :premises (@p129 @p123) :args (@t165)) % 1.52/1.73 (step @p131 :rule cong :premises (@p130) :args ((forall @t5 @t165))) % 1.52/1.73 (step @p132 :rule bool-impl-elim :args (@t8 @t98)) % 1.52/1.73 (step @p133 :rule cong :premises (@p132) :args (@t99)) % 1.52/1.73 (step @p134 :rule trans :premises (@p133 @p131)) % 1.52/1.73 (step @p135 :rule cong :premises (@p134) :args (@t101)) % 1.52/1.73 (step @p136 :rule trans :premises (@p61 @p135)) % 1.52/1.73 (step @p137 :rule ho_cong :premises (@p136 @p118)) % 1.52/1.73 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@t328))) % 1.52/1.73 (step @p369 :rule ho_cong :premises (@p368 @p309)) % 1.52/1.73 (step @p370 :rule trans :premises (@p369 @p367)) % 1.52/1.73 (step @p371 :rule refl :args (@t327)) % 1.52/1.73 (step @p372 :rule ho_cong :premises (@p371 @p370)) % 1.52/1.73 (step @p373 :rule trans :premises (@p372 @p366)) % 1.52/1.73 (step @p374 :rule ho_cong :premises (@p373 @p354)) % 1.52/1.73 (step @p375 :rule trans :premises (@p374 @p346)) % 1.52/1.73 (step @p376 :rule ho_cong :premises (@p375 @p104)) % 1.52/1.73 (step @p377 :rule trans :premises (@p376 @p338)) % 1.52/1.73 (step @p378 :rule ho_cong :premises (@p331 @p309)) % 1.52/1.73 (step @p379 :rule ho_cong :premises (@p378 @p324)) % 1.52/1.73 (step @p380 :rule ho_cong :premises (@p331 @p324)) % 1.52/1.73 (step @p381 :rule ho_cong :premises (@p380 @p309)) % 1.52/1.73 (step @p382 :rule beta-reduce :args ((= (_ (lambda @t84 (not @t330)) @t15) @t326))) % 1.52/1.73 (step @p383 :rule beta-reduce :args ((= @t332 @t330))) % 1.52/1.73 (step @p384 :rule cong :premises (@p383) :args (@t333)) % 1.52/1.73 (step @p385 :rule cong :premises (@p384) :args (@t334)) % 1.52/1.73 (step @p386 :rule beta-reduce :args ((= (_ @t73 @t331) @t334))) % 1.52/1.73 (step @p387 :rule trans :premises (@p386 @p385)) % 1.52/1.73 (step @p388 :rule beta-reduce :args ((= @t336 @t329))) % 1.52/1.73 (step @p389 :rule refl :args (@t71)) % 1.52/1.73 (step @p390 :rule nary_cong :premises (@p389 @p388) :args (@t337)) % 1.52/1.73 (step @p391 :rule cong :premises (@p390) :args (@t338)) % 1.52/1.73 (step @p392 :rule beta-reduce :args ((= (_ @t302 @t335) @t338))) % 1.52/1.73 (step @p393 :rule trans :premises (@p392 @p391)) % 1.52/1.73 (step @p394 :rule beta-reduce :args ((= (_ @t73 @t74) @t335))) % 1.52/1.73 (step @p395 :rule ho_cong :premises (@p319 @p394)) % 1.52/1.73 (step @p396 :rule trans :premises (@p395 @p393)) % 1.52/1.73 (step @p397 :rule refl :args (@t73)) % 1.52/1.73 (step @p398 :rule ho_cong :premises (@p397 @p396)) % 1.52/1.73 (step @p399 :rule trans :premises (@p398 @p387)) % 1.52/1.73 (step @p400 :rule ho_cong :premises (@p399 @p104)) % 1.52/1.73 (step @p401 :rule trans :premises (@p400 @p382)) % 1.52/1.73 (step @p402 :rule ho_cong :premises (@p50 @p309)) % 1.52/1.73 (step @p403 :rule ho_cong :premises (@p326 @p402)) % 1.52/1.73 (step @p404 :rule ho_cong :premises (@p50 @p403)) % 1.52/1.73 (step @p405 :rule ho_cong :premises (@p404 @p104)) % 1.52/1.73 (step @p406 :rule trans :premises (@p405 @p401)) % 1.52/1.73 (step @p407 :rule cong :premises (@p406) :args (@t90)) % 1.52/1.73 (step @p408 :rule trans :premises (@p55 @p407)) % 1.52/1.73 (step @p409 :rule ho_cong :premises (@p408 @p381)) % 1.52/1.73 (step @p410 :rule ho_cong :premises (@p409 @p379)) % 1.52/1.73 (step @p411 :rule ho_cong :premises (@p410 @p104)) % 1.52/1.73 (step @p412 :rule trans :premises (@p411 @p377)) % 1.52/1.73 (step @p413 :rule cong :premises (@p412) :args (@t93)) % 1.52/1.73 (step @p414 :rule trans :premises (@p58 @p413)) % 1.52/1.73 (step @p415 :rule ho_cong :premises (@p414 @p337)) % 1.52/1.73 (step @p416 :rule ho_cong :premises (@p415 @p336)) % 1.52/1.73 (step @p417 :rule ho_cong :premises (@p416 @p104)) % 1.52/1.73 (step @p418 :rule cong :premises (@p417) :args (@t55)) % 1.52/1.73 (step @p419 :rule ho_cong :premises (@p136 @p418)) % 1.52/1.73 (step @p420 :rule ho_cong :premises (@p419 @p104)) % 1.52/1.73 (step @p421 :rule cong :premises (@p420) :args (@t56)) % 1.52/1.73 (step @p422 :rule ho_cong :premises (@p136 @p421)) % 1.52/1.73 (step @p423 :rule ho_cong :premises (@p145 @p422)) % 1.52/1.73 (step @p424 :rule trans :premises (@p423 @p305)) % 1.52/1.73 (step @p425 :rule eq_resolve :premises (@p36 @p424)) % 1.52/1.73 (step @p426 :rule instantiate :premises (@p425) :args ((@list @t343 tptp.empty_set @t342 @t342))) % 1.52/1.73 (step @p427 :rule refl :args (@t344)) % 1.52/1.73 (step @p428 :rule refl :args (@t13)) % 1.52/1.73 (step @p429 :rule cong :premises (@p428 @p427) :args ((= @t13 @t344))) % 1.52/1.73 (step @p430 :rule symm :premises (@p429)) % 1.52/1.73 (step @p431 :rule eq_resolve :premises (@p428 @p430)) % 1.52/1.73 (step @p432 :rule cong :premises (@p431) :args (@t14)) % 1.52/1.73 (step @p433 :rule eq_resolve :premises (@p14 @p432)) % 1.52/1.73 (step @p434 :rule instantiate :premises (@p433) :args ((@list @t343))) % 1.52/1.73 (step @p435 :rule quant-merge-prenex :args ((= (forall @t84 @t345) @t341))) % 1.52/1.73 (step @p436 :rule beta-reduce :args ((= @t347 @t345))) % 1.52/1.73 (step @p437 :rule cong :premises (@p436) :args (@t348)) % 1.52/1.73 (step @p438 :rule trans :premises (@p437 @p435)) % 1.52/1.73 (step @p439 :rule beta-reduce :args ((= (_ @t150 @t346) @t348))) % 1.52/1.73 (step @p440 :rule trans :premises (@p439 @p438)) % 1.52/1.73 (step @p441 :rule refl :args (@t339)) % 1.52/1.73 (step @p442 :rule refl :args (@t349)) % 1.52/1.73 (step @p443 :rule cong :premises (@p442 @p441) :args ((= @t349 @t339))) % 1.52/1.73 (step @p444 :rule symm :premises (@p443)) % 1.52/1.73 (step @p445 :rule eq_resolve :premises (@p442 @p444)) % 1.52/1.73 (step @p446 :rule nary_cong :premises (@p92 @p445) :args (@t350)) % 1.52/1.73 (step @p447 :rule cong :premises (@p446) :args ((forall @t5 @t350))) % 1.52/1.73 (step @p448 :rule beta-reduce :args ((= @t351 @t349))) % 1.52/1.73 (step @p449 :rule nary_cong :premises (@p96 @p448) :args (@t352)) % 1.52/1.73 (step @p450 :rule cong :premises (@p449) :args (@t353)) % 1.52/1.73 (step @p451 :rule trans :premises (@p450 @p447)) % 1.52/1.73 (step @p452 :rule cong :premises (@p451) :args (@t354)) % 1.52/1.73 (step @p453 :rule beta-reduce :args ((= @t355 @t354))) % 1.52/1.73 (step @p454 :rule trans :premises (@p453 @p452)) % 1.52/1.73 (step @p455 :rule ho_cong :premises (@p112 @p454)) % 1.52/1.73 (step @p456 :rule trans :premises (@p455 @p440)) % 1.52/1.73 (step @p457 :rule cong :premises (@p456) :args ((not (_ @t150 @t355)))) % 1.52/1.73 (step @p458 :rule refl :args (@t64)) % 1.52/1.73 (step @p459 :rule ho_cong :premises (@p136 @p458)) % 1.52/1.73 (step @p460 :rule ho_cong :premises (@p145 @p459)) % 1.52/1.73 (step @p461 :rule cong :premises (@p460) :args (@t65)) % 1.52/1.73 (step @p462 :rule trans :premises (@p461 @p457)) % 1.52/1.73 (step @p463 :rule eq_resolve :premises (@p47 @p462)) % 1.52/1.73 (step @p464 :rule skolemize :premises (@p463)) % 1.52/1.73 (step @p465 :rule bool-double-not-elim :args (@t356)) % 1.52/1.73 (step @p466 :rule refl :args (@t359)) % 1.52/1.73 (step @p467 :rule nary_cong :premises (@p466 @p465) :args ((or @t359 (not @t358)))) % 1.52/1.73 (step @p468 :rule cnf_or_neg :args (@t359 0)) % 1.52/1.73 (step @p469 :rule eq_resolve :premises (@p468 @p467)) % 1.52/1.73 (step @p470 :rule reordering :premises (@p469) :args ((or @t356 @t359))) % 1.52/1.73 (step @p471 :rule chain_m_resolution :premises (@p470 @p464) :args (@t356 @t360 @t361)) % 1.52/1.73 (step @p472 :rule cnf_or_pos :args (@t369)) % 1.52/1.73 (step @p473 :rule reordering :premises (@p472) :args ((or @t358 @t368 @t366 (not @t369)))) % 1.52/1.73 (step @p474 :rule chain_m_resolution :premises (@p473 @p471 @p434 @p426) :args (@t366 (@list false false false) (@list @t356 @t367 @t369))) % 1.52/1.73 (step @p475 :rule cnf_and_pos :args (@t366 1)) % 1.52/1.73 (step @p476 :rule reordering :premises (@p475) :args ((or @t364 (not @t366)))) % 1.52/1.73 (step @p477 :rule chain_m_resolution :premises (@p476 @p474) :args (@t364 (@list false) (@list @t366))) % 1.52/1.73 (step @p478 :rule cnf_or_neg :args (@t359 1)) % 1.52/1.73 (step @p479 :rule chain_m_resolution :premises (@p478 @p464) :args (@t365 @t360 @t361)) % 1.52/1.73 (step @p480 :rule cnf_or_pos :args (@t364)) % 1.52/1.73 (step @p481 :rule reordering :premises (@p480) :args ((or @t357 @t363 (not @t364)))) % 1.52/1.73 (step @p482 :rule chain_m_resolution :premises (@p481 @p479 @p477) :args (@t363 @t370 (@list @t357 @t364))) % 1.52/1.73 (step @p483 :rule skolemize :premises (@p482)) % 1.52/1.73 (step @p484 :rule bool-double-not-elim :args (@t372)) % 1.52/1.73 (step @p485 :rule refl :args (@t376)) % 1.52/1.73 (step @p486 :rule nary_cong :premises (@p485 @p484) :args ((or @t376 (not @t373)))) % 1.52/1.73 (step @p487 :rule cnf_or_neg :args (@t376 1)) % 1.52/1.73 (step @p488 :rule eq_resolve :premises (@p487 @p486)) % 1.52/1.73 (step @p489 :rule reordering :premises (@p488) :args ((or @t372 @t376))) % 1.52/1.73 (step @p490 :rule chain_m_resolution :premises (@p489 @p483) :args (@t372 @t360 @t377)) % 1.52/1.73 (step @p491 :rule bool-double-not-elim :args (@t374)) % 1.52/1.73 (step @p492 :rule nary_cong :premises (@p485 @p491) :args ((or @t376 (not @t375)))) % 1.52/1.73 (step @p493 :rule cnf_or_neg :args (@t376 0)) % 1.52/1.73 (step @p494 :rule eq_resolve :premises (@p493 @p492)) % 1.52/1.73 (step @p495 :rule reordering :premises (@p494) :args ((or @t374 @t376))) % 1.52/1.73 (step @p496 :rule chain_m_resolution :premises (@p495 @p483) :args (@t374 @t360 @t377)) % 1.52/1.73 (step @p497 :rule cnf_or_pos :args (@t378)) % 1.52/1.73 (step @p498 :rule reordering :premises (@p497) :args ((or @t375 @t373 @t379))) % 1.52/1.73 (step @p499 :rule chain_m_resolution :premises (@p498 @p496 @p490) :args (@t379 (@list false false) (@list @t374 @t372))) % 1.52/1.73 (assume-push @p506 @t144) % 1.52/1.73 (step @p501 :rule instantiate :premises (@p148) :args ((@list @t343 @t371))) % 1.52/1.73 (step-pop @p507 :rule scope :premises (@p501)) % 1.52/1.73 (step @p502 :rule process_scope :premises (@p507) :args (@t378)) % 1.52/1.73 (step @p504 :rule implies_elim :premises (@p502)) % 1.52/1.73 (step @p505 false :rule chain_m_resolution :premises (@p504 @p499 @p148) :args (false @t370 (@list @t378 @t144))) % 1.52/1.73 ) % 1.52/1.73 % SZS output end Proof % 1.52/1.73 % cvc5 exiting %------------------------------------------------------------------------------