%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET583^7 : 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 : n027.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:48:06 AM UTC 2026 % Result : Theorem 0.36s 0.66s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET583^7 : 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 % 0.16/0.35 % Computer : n027.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 16:03:36 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.36/0.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.66 % SZS status Theorem % 0.36/0.66 % SZS output start Proof % 0.36/0.66 ( % 0.36/0.66 (declare-sort tptp.mu 0) % 0.36/0.66 (declare-sort $$unsorted 0) % 0.36/0.66 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 0.36/0.66 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.36/0.66 (declare-const tptp.subset (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.36/0.66 (declare-const tptp.member (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.36/0.66 (declare-const tptp.qmltpeq (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.36/0.66 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.36/0.66 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.36/0.66 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.36/0.66 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.36/0.66 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.36/0.66 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.66 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.36/0.66 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.36/0.66 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.66 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.36/0.66 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.66 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.36/0.66 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.36/0.66 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.exists_in_world _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.66 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.36/0.66 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.36/0.66 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.66 (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)))))))) % 0.36/0.66 (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)))))))) % 0.36/0.66 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.36/0.66 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.36/0.66 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.36/0.66 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.36/0.66 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.36/0.66 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.36/0.66 (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))))))))))))) % 0.36/0.66 (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)))))) % 0.36/0.66 (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)))))) % 0.36/0.66 (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))))))) % 0.36/0.66 (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))))))) % 0.36/0.66 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.36/0.66 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.36/0.66 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.66 (define @t2 () (@var "X" tptp.mu)) % 0.36/0.66 (define @t3 () (_ tptp.exists_in_world @t2)) % 0.36/0.66 (define @t4 () (_ @t3 @t1)) % 0.36/0.66 (define @t5 () (@list @t2)) % 0.36/0.66 (define @t6 () (@list @t1)) % 0.36/0.66 (define @t7 () (@var "W" $$unsorted)) % 0.36/0.66 (define @t8 () (_ @t3 @t7)) % 0.36/0.66 (define @t9 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.66 (define @t10 () (_ tptp.qmltpeq @t2)) % 0.36/0.66 (define @t11 () (@list @t2 @t9)) % 0.36/0.66 (define @t12 () (@var "Y" tptp.mu)) % 0.36/0.66 (define @t13 () (_ tptp.qmltpeq @t12)) % 0.36/0.66 (define @t14 () (_ @t10 @t12)) % 0.36/0.66 (define @t15 () (@list @t12 @t9)) % 0.36/0.66 (define @t16 () (@var "Z" tptp.mu)) % 0.36/0.66 (define @t17 () (@var "C" tptp.mu)) % 0.36/0.66 (define @t18 () (@var "B" tptp.mu)) % 0.36/0.66 (define @t19 () (@var "A" tptp.mu)) % 0.36/0.66 (define @t20 () (_ tptp.mand (_ (_ tptp.qmltpeq @t19) @t18))) % 0.36/0.66 (define @t21 () (@list @t17 @t9)) % 0.36/0.66 (define @t22 () (@list @t18 @t9)) % 0.36/0.66 (define @t23 () (@list @t19 @t9)) % 0.36/0.66 (define @t24 () (_ tptp.member @t17)) % 0.36/0.66 (define @t25 () (_ tptp.subset @t18)) % 0.36/0.66 (define @t26 () (_ @t25 @t17)) % 0.36/0.66 (define @t27 () (_ tptp.subset @t17)) % 0.36/0.66 (define @t28 () (_ @t27 @t18)) % 0.36/0.66 (define @t29 () (_ (_ tptp.mand @t26) @t28)) % 0.36/0.66 (define @t30 () (_ tptp.qmltpeq @t18)) % 0.36/0.66 (define @t31 () (_ @t30 @t17)) % 0.36/0.66 (define @t32 () (lambda @t21 (_ (_ (_ tptp.mequiv @t31) @t29) @t9))) % 0.36/0.66 (define @t33 () (lambda @t22 (_ (_ tptp.mforall_ind @t32) @t9))) % 0.36/0.66 (define @t34 () (@var "D" tptp.mu)) % 0.36/0.66 (define @t35 () (_ tptp.member @t34)) % 0.36/0.66 (define @t36 () (lambda @t21 (_ (_ (_ tptp.mimplies @t29) @t31) @t9))) % 0.36/0.66 (define @t37 () (lambda @t22 (_ (_ tptp.mforall_ind @t36) @t9))) % 0.36/0.66 (define @t38 () (not (_ tptp.mvalid (_ tptp.mforall_ind @t37)))) % 0.36/0.66 (define @t39 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.66 (define @t40 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.66 (define @t41 () (lambda (@list @t40 @t39 @t7) (= (_ @t40 @t7) (_ @t39 @t7)))) % 0.36/0.66 (define @t42 () (@var "Phi" (-> $$unsorted Bool))) % 0.36/0.66 (define @t43 () (_ @t42 @t7)) % 0.36/0.66 (define @t44 () (not @t43)) % 0.36/0.66 (define @t45 () (@list @t42 @t7)) % 0.36/0.66 (define @t46 () (lambda @t45 @t44)) % 0.36/0.66 (define @t47 () (@var "Psi" (-> $$unsorted Bool))) % 0.36/0.66 (define @t48 () (_ @t47 @t7)) % 0.36/0.66 (define @t49 () (lambda (@list @t42 @t47 @t7) (or @t43 @t48))) % 0.36/0.66 (define @t50 () (_ @t42 @t1)) % 0.36/0.66 (define @t51 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.66 (define @t52 () (lambda (@list @t51 @t42 @t7) (forall @t6 (or (not (_ (_ @t51 @t7) @t1)) @t50)))) % 0.36/0.66 (define @t53 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.66 (define @t54 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.36/0.66 (define @t55 () (_ @t54 @t53)) % 0.36/0.66 (define @t56 () (lambda (@list @t54 @t7) (forall (@list @t53) (_ @t55 @t7)))) % 0.36/0.66 (define @t57 () (@list @t7)) % 0.36/0.66 (define @t58 () (lambda @t57 true)) % 0.36/0.66 (define @t59 () (_ tptp.mnot @t47)) % 0.36/0.66 (define @t60 () (_ tptp.mnot @t42)) % 0.36/0.66 (define @t61 () (_ tptp.mor @t60)) % 0.36/0.66 (define @t62 () (@list @t42 @t47 @t9)) % 0.36/0.66 (define @t63 () (lambda @t62 (_ (_ tptp.mnot (_ @t61 @t59)) @t9))) % 0.36/0.66 (define @t64 () (lambda @t62 (_ (_ @t61 @t47) @t9))) % 0.36/0.66 (define @t65 () (lambda @t62 (_ (_ (_ tptp.mor @t59) @t42) @t9))) % 0.36/0.66 (define @t66 () (lambda @t62 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t42) @t47)) (_ (_ tptp.mimplies @t47) @t42)) @t9))) % 0.36/0.66 (define @t67 () (lambda @t62 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t42) @t47)) @t9))) % 0.36/0.66 (define @t68 () (lambda (@list @t51 @t42 @t9) (_ (_ tptp.mnot (_ (_ tptp.mbox @t51) @t60)) @t9))) % 0.36/0.66 (define @t69 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.36/0.66 (define @t70 () (_ @t69 @t2)) % 0.36/0.66 (define @t71 () (_ @t70 @t7)) % 0.36/0.66 (define @t72 () (forall @t5 (=> @t8 @t71))) % 0.36/0.66 (define @t73 () (@list @t69 @t7)) % 0.36/0.66 (define @t74 () (lambda @t73 @t72)) % 0.36/0.66 (define @t75 () (lambda (@list @t69 @t9) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda @t11 (_ (_ tptp.mnot @t70) @t9)))) @t9))) % 0.36/0.66 (define @t76 () (lambda (@list @t54 @t9) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t53 @t9) (_ (_ tptp.mnot @t55) @t9)))) @t9))) % 0.36/0.66 (define @t77 () (@var "S" $$unsorted)) % 0.36/0.66 (define @t78 () (_ @t51 @t77)) % 0.36/0.66 (define @t79 () (@list @t77)) % 0.36/0.66 (define @t80 () (@list @t51)) % 0.36/0.66 (define @t81 () (lambda @t80 (forall @t79 (_ @t78 @t77)))) % 0.36/0.66 (define @t82 () (@var "T" $$unsorted)) % 0.36/0.66 (define @t83 () (_ @t51 @t82)) % 0.36/0.66 (define @t84 () (_ @t78 @t82)) % 0.36/0.66 (define @t85 () (lambda @t80 (forall (@list @t77 @t82) (=> @t84 (_ @t83 @t77))))) % 0.36/0.66 (define @t86 () (@list @t82)) % 0.36/0.66 (define @t87 () (lambda @t80 (forall @t79 (exists @t86 @t84)))) % 0.36/0.66 (define @t88 () (@var "U" $$unsorted)) % 0.36/0.66 (define @t89 () (_ @t78 @t88)) % 0.36/0.66 (define @t90 () (_ @t83 @t88)) % 0.36/0.66 (define @t91 () (@list @t77 @t82 @t88)) % 0.36/0.66 (define @t92 () (lambda @t80 (forall @t91 (=> (and @t84 @t90) @t89)))) % 0.36/0.66 (define @t93 () (and @t84 @t89)) % 0.36/0.66 (define @t94 () (lambda @t80 (forall @t91 (=> @t93 @t90)))) % 0.36/0.66 (define @t95 () (= @t82 @t88)) % 0.36/0.66 (define @t96 () (lambda @t80 (forall @t91 (=> @t93 @t95)))) % 0.36/0.66 (define @t97 () (@list @t88)) % 0.36/0.66 (define @t98 () (lambda @t80 (forall @t79 (exists @t86 (and @t84 (forall @t97 (=> @t89 @t95))))))) % 0.36/0.66 (define @t99 () (_ @t51 @t88)) % 0.36/0.66 (define @t100 () (_ @t99 @t82)) % 0.36/0.66 (define @t101 () (lambda @t80 (forall @t91 (=> @t84 (exists @t97 (and @t89 @t100)))))) % 0.36/0.66 (define @t102 () (lambda @t80 (forall @t91 (=> @t93 (or @t90 @t95 @t100))))) % 0.36/0.66 (define @t103 () (lambda @t80 (forall @t91 (=> @t93 (exists @t6 (and (_ @t83 @t1) (_ @t99 @t1))))))) % 0.36/0.66 (define @t104 () (forall @t57 @t43)) % 0.36/0.66 (define @t105 () (@list @t42)) % 0.36/0.66 (define @t106 () (lambda @t105 @t104)) % 0.36/0.66 (define @t107 () (lambda @t105 (exists @t57 @t43))) % 0.36/0.66 (define @t108 () (lambda @t105 (exists @t57 @t44))) % 0.36/0.66 (define @t109 () (lambda @t105 (forall @t57 @t44))) % 0.36/0.66 (define @t110 () (lambda @t45 (forall @t6 (or (not (_ (_ tptp.rel_s4 @t7) @t1)) @t50)))) % 0.36/0.66 (define @t111 () (lambda (@list @t42 @t9) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t60)) @t9))) % 0.36/0.66 (define @t112 () (@var "BOUND_VARIABLE_10098" tptp.mu)) % 0.36/0.66 (define @t113 () (not (tptp.subset @t112 @t2 @t7))) % 0.36/0.66 (define @t114 () (not (tptp.subset @t2 @t112 @t7))) % 0.36/0.66 (define @t115 () (tptp.qmltpeq @t2 @t112 @t7)) % 0.36/0.66 (define @t116 () (not (tptp.exists_in_world @t112 @t7))) % 0.36/0.66 (define @t117 () (tptp.exists_in_world @t2 @t7)) % 0.36/0.66 (define @t118 () (not @t117)) % 0.36/0.66 (define @t119 () (or @t118 @t116 @t115 @t114 @t113)) % 0.36/0.66 (define @t120 () (forall (@list @t7 @t2 @t112) @t119)) % 0.36/0.66 (define @t121 () (@list @t2 @t112)) % 0.36/0.66 (define @t122 () (forall @t121 @t119)) % 0.36/0.66 (define @t123 () (lambda @t57 @t122)) % 0.36/0.66 (define @t124 () (_ @t123 @t7)) % 0.36/0.66 (define @t125 () (forall @t57 @t124)) % 0.36/0.66 (define @t126 () (_ @t42 @t7)) % 0.36/0.66 (define @t127 () (lambda @t105 (forall @t57 @t126))) % 0.36/0.66 (define @t128 () (or @t116 @t115 @t114 @t113)) % 0.36/0.66 (define @t129 () (or @t118 @t128)) % 0.36/0.66 (define @t130 () (forall @t121 @t129)) % 0.36/0.66 (define @t131 () (@list @t112)) % 0.36/0.66 (define @t132 () (forall @t131 @t129)) % 0.36/0.66 (define @t133 () (forall @t131 @t128)) % 0.36/0.66 (define @t134 () (@var "BOUND_VARIABLE_10073" tptp.mu)) % 0.36/0.66 (define @t135 () (@list @t134)) % 0.36/0.66 (define @t136 () (or @t118 @t133)) % 0.36/0.66 (define @t137 () (@list @t134)) % 0.36/0.66 (define @t138 () (forall @t137 (or (not (tptp.exists_in_world @t134 @t7)) (tptp.qmltpeq @t2 @t134 @t7) (not (tptp.subset @t2 @t134 @t7)) (not (tptp.subset @t134 @t2 @t7))))) % 0.36/0.66 (define @t139 () (tptp.subset @t2 @t18 @t9)) % 0.36/0.66 (define @t140 () (not @t139)) % 0.36/0.66 (define @t141 () (tptp.subset @t18 @t2 @t9)) % 0.36/0.66 (define @t142 () (not @t141)) % 0.36/0.66 (define @t143 () (tptp.qmltpeq @t18 @t2 @t9)) % 0.36/0.66 (define @t144 () (not (tptp.exists_in_world @t2 @t9))) % 0.36/0.66 (define @t145 () (forall @t5 (or @t144 @t143 @t142 @t140))) % 0.36/0.66 (define @t146 () (@list @t2)) % 0.36/0.66 (define @t147 () (lambda @t22 @t145)) % 0.36/0.66 (define @t148 () (or @t118 (_ @t147 @t2 @t7))) % 0.36/0.66 (define @t149 () (forall @t5 @t148)) % 0.36/0.66 (define @t150 () (lambda @t57 @t149)) % 0.36/0.66 (define @t151 () (_ @t69 @t2 @t7)) % 0.36/0.66 (define @t152 () (lambda @t73 (forall @t5 (or @t118 @t151)))) % 0.36/0.66 (define @t153 () (tptp.subset @t2 @t18 @t7)) % 0.36/0.66 (define @t154 () (not @t153)) % 0.36/0.66 (define @t155 () (tptp.subset @t18 @t2 @t7)) % 0.36/0.66 (define @t156 () (not @t155)) % 0.36/0.66 (define @t157 () (tptp.qmltpeq @t18 @t2 @t7)) % 0.36/0.66 (define @t158 () (_ (_ (_ tptp.subset @t2) @t18) @t7)) % 0.36/0.66 (define @t159 () (not @t158)) % 0.36/0.66 (define @t160 () (_ (_ @t25 @t2) @t7)) % 0.36/0.66 (define @t161 () (not @t160)) % 0.36/0.66 (define @t162 () (_ (_ @t30 @t2) @t7)) % 0.36/0.66 (define @t163 () (or @t118 @t162 @t161 @t159)) % 0.36/0.66 (define @t164 () (or @t162 @t161 @t159)) % 0.36/0.66 (define @t165 () (not (_ @t28 @t9))) % 0.36/0.66 (define @t166 () (not (_ @t26 @t9))) % 0.36/0.66 (define @t167 () (_ @t31 @t9)) % 0.36/0.66 (define @t168 () (or @t167 @t166 @t165)) % 0.36/0.66 (define @t169 () (lambda @t21 @t168)) % 0.36/0.66 (define @t170 () (_ @t169 @t2 @t7)) % 0.36/0.66 (define @t171 () (or @t118 @t170)) % 0.36/0.66 (define @t172 () (forall @t5 @t171)) % 0.36/0.66 (define @t173 () (lambda @t57 @t172)) % 0.36/0.66 (define @t174 () (@list @t9)) % 0.36/0.66 (define @t175 () (lambda @t174 @t168)) % 0.36/0.66 (define @t176 () (_ @t47 @t9)) % 0.36/0.66 (define @t177 () (or @t176 @t166 @t165)) % 0.36/0.66 (define @t178 () (@list @t47 @t9)) % 0.36/0.66 (define @t179 () (or @t166 @t165)) % 0.36/0.66 (define @t180 () (not @t179)) % 0.36/0.66 (define @t181 () (lambda @t174 @t180)) % 0.36/0.66 (define @t182 () (_ @t181 @t9)) % 0.36/0.66 (define @t183 () (not @t182)) % 0.36/0.66 (define @t184 () (or @t183 @t176)) % 0.36/0.66 (define @t185 () (lambda @t178 @t184)) % 0.36/0.66 (define @t186 () (_ @t42 @t9)) % 0.36/0.66 (define @t187 () (not @t186)) % 0.36/0.66 (define @t188 () (or @t187 @t176)) % 0.36/0.66 (define @t189 () (lambda @t62 @t188)) % 0.36/0.66 (define @t190 () (not @t176)) % 0.36/0.66 (define @t191 () (lambda @t178 (not (or @t166 @t190)))) % 0.36/0.66 (define @t192 () (not (or @t187 @t190))) % 0.36/0.66 (define @t193 () (lambda @t62 @t192)) % 0.36/0.66 (define @t194 () (_ @t193 @t26)) % 0.36/0.66 (define @t195 () (_ @t194 @t28)) % 0.36/0.66 (define @t196 () (lambda @t21 (_ (_ (_ @t189 @t195) @t31) @t9))) % 0.36/0.66 (define @t197 () (lambda @t22 (_ (_ @t152 @t196) @t9))) % 0.36/0.66 (define @t198 () (not @t48)) % 0.36/0.66 (define @t199 () (or @t44 @t198)) % 0.36/0.66 (define @t200 () (lambda @t57 @t199)) % 0.36/0.66 (define @t201 () (_ @t200 @t7)) % 0.36/0.66 (define @t202 () (not @t201)) % 0.36/0.66 (define @t203 () (lambda @t57 @t202)) % 0.36/0.66 (define @t204 () (lambda @t57 @t198)) % 0.36/0.66 (define @t205 () (_ @t204 @t7)) % 0.36/0.66 (define @t206 () (or @t44 @t205)) % 0.36/0.66 (define @t207 () (lambda @t57 @t206)) % 0.36/0.66 (define @t208 () (or @t44 @t48)) % 0.36/0.66 (define @t209 () (@list @t47 @t7)) % 0.36/0.66 (define @t210 () (lambda @t209 @t208)) % 0.36/0.66 (define @t211 () (lambda @t57 @t44)) % 0.36/0.66 (define @t212 () (_ @t211 @t7)) % 0.36/0.66 (define @t213 () (or @t212 @t48)) % 0.36/0.66 (define @t214 () (lambda @t209 @t213)) % 0.36/0.66 (define @t215 () (lambda @t57 @t208)) % 0.36/0.66 (define @t216 () (not @t8)) % 0.36/0.66 (define @t217 () (or @t216 @t71)) % 0.36/0.66 (define @t218 () (@quantifiers_skolemize @t120 0)) % 0.36/0.66 (define @t219 () (@quantifiers_skolemize @t120 1)) % 0.36/0.66 (define @t220 () (tptp.exists_in_world @t219 @t218)) % 0.36/0.66 (define @t221 () (@quantifiers_skolemize @t120 2)) % 0.36/0.66 (define @t222 () (tptp.subset @t221 @t219 @t218)) % 0.36/0.66 (define @t223 () (not @t222)) % 0.36/0.66 (define @t224 () (tptp.subset @t219 @t221 @t218)) % 0.36/0.66 (define @t225 () (not @t224)) % 0.36/0.66 (define @t226 () (tptp.qmltpeq @t219 @t221 @t218)) % 0.36/0.66 (define @t227 () (tptp.exists_in_world @t221 @t218)) % 0.36/0.66 (define @t228 () (not @t227)) % 0.36/0.66 (define @t229 () (not @t220)) % 0.36/0.66 (define @t230 () (or @t229 @t228 @t226 @t225 @t223)) % 0.36/0.66 (define @t231 () (@list true)) % 0.36/0.66 (define @t232 () (@list @t230)) % 0.36/0.66 (define @t233 () (@var "BOUND_VARIABLE_9749" tptp.mu)) % 0.36/0.66 (define @t234 () (tptp.subset @t233 @t2 @t7)) % 0.36/0.66 (define @t235 () (tptp.subset @t2 @t233 @t7)) % 0.36/0.66 (define @t236 () (tptp.qmltpeq @t2 @t233 @t7)) % 0.36/0.66 (define @t237 () (and (or (not @t236) (and @t235 @t234)) (or @t236 (not @t235) (not @t234)))) % 0.36/0.66 (define @t238 () (not (tptp.exists_in_world @t233 @t7))) % 0.36/0.66 (define @t239 () (or @t118 @t238 @t237)) % 0.36/0.66 (define @t240 () (@list @t2 @t233)) % 0.36/0.66 (define @t241 () (forall @t240 @t239)) % 0.36/0.66 (define @t242 () (lambda @t57 @t241)) % 0.36/0.66 (define @t243 () (_ @t242 @t7)) % 0.36/0.66 (define @t244 () (forall @t57 @t243)) % 0.36/0.66 (define @t245 () (or @t238 @t237)) % 0.36/0.66 (define @t246 () (or @t118 @t245)) % 0.36/0.66 (define @t247 () (forall @t240 @t246)) % 0.36/0.66 (define @t248 () (@list @t233)) % 0.36/0.66 (define @t249 () (forall @t248 @t246)) % 0.36/0.66 (define @t250 () (forall @t248 @t245)) % 0.36/0.66 (define @t251 () (@var "BOUND_VARIABLE_9714" tptp.mu)) % 0.36/0.66 (define @t252 () (@list @t251)) % 0.36/0.66 (define @t253 () (or @t118 @t250)) % 0.36/0.66 (define @t254 () (tptp.subset @t251 @t2 @t7)) % 0.36/0.66 (define @t255 () (tptp.subset @t2 @t251 @t7)) % 0.36/0.66 (define @t256 () (tptp.qmltpeq @t2 @t251 @t7)) % 0.36/0.66 (define @t257 () (@list @t251)) % 0.36/0.66 (define @t258 () (forall @t257 (or (not (tptp.exists_in_world @t251 @t7)) (and (or (not @t256) (and @t255 @t254)) (or @t256 (not @t255) (not @t254)))))) % 0.36/0.66 (define @t259 () (tptp.subset @t251 @t18 @t9)) % 0.36/0.66 (define @t260 () (tptp.subset @t18 @t251 @t9)) % 0.36/0.66 (define @t261 () (tptp.qmltpeq @t18 @t251 @t9)) % 0.36/0.66 (define @t262 () (forall @t5 (or @t144 (and (or (not @t143) (and @t141 @t139)) (or @t143 @t142 @t140))))) % 0.36/0.66 (define @t263 () (lambda @t22 @t262)) % 0.36/0.66 (define @t264 () (or @t118 (_ @t263 @t2 @t7))) % 0.36/0.66 (define @t265 () (forall @t5 @t264)) % 0.36/0.66 (define @t266 () (lambda @t57 @t265)) % 0.36/0.66 (define @t267 () (and @t160 @t158)) % 0.36/0.66 (define @t268 () (not @t162)) % 0.36/0.66 (define @t269 () (or @t268 @t267)) % 0.36/0.66 (define @t270 () (and @t269 @t164)) % 0.36/0.66 (define @t271 () (or @t118 @t270)) % 0.36/0.66 (define @t272 () (or @t268 (not (or @t161 @t159)))) % 0.36/0.66 (define @t273 () (not @t164)) % 0.36/0.66 (define @t274 () (not @t272)) % 0.36/0.66 (define @t275 () (not (or @t274 @t273))) % 0.36/0.66 (define @t276 () (or @t118 @t275)) % 0.36/0.66 (define @t277 () (not @t167)) % 0.36/0.66 (define @t278 () (not (or (not (or @t277 @t180)) (not @t168)))) % 0.36/0.66 (define @t279 () (lambda @t21 @t278)) % 0.36/0.66 (define @t280 () (_ @t279 @t2 @t7)) % 0.36/0.66 (define @t281 () (or @t118 @t280)) % 0.36/0.66 (define @t282 () (forall @t5 @t281)) % 0.36/0.66 (define @t283 () (lambda @t57 @t282)) % 0.36/0.66 (define @t284 () (or @t183 @t167)) % 0.36/0.66 (define @t285 () (not @t284)) % 0.36/0.66 (define @t286 () (or @t277 @t182)) % 0.36/0.66 (define @t287 () (not @t286)) % 0.36/0.66 (define @t288 () (or @t287 @t285)) % 0.36/0.66 (define @t289 () (not @t288)) % 0.36/0.66 (define @t290 () (lambda @t174 @t289)) % 0.36/0.66 (define @t291 () (lambda @t178 (not (or (not (or @t277 @t176)) (not (or @t190 @t167)))))) % 0.36/0.66 (define @t292 () (or @t190 @t186)) % 0.36/0.66 (define @t293 () (not @t188)) % 0.36/0.66 (define @t294 () (not (or @t293 (not @t292)))) % 0.36/0.66 (define @t295 () (_ (lambda @t62 @t294) @t31)) % 0.36/0.66 (define @t296 () (lambda @t21 (_ (_ @t295 @t195) @t9))) % 0.36/0.66 (define @t297 () (lambda @t174 @t292)) % 0.36/0.66 (define @t298 () (_ @t297 @t9)) % 0.36/0.66 (define @t299 () (not @t298)) % 0.36/0.66 (define @t300 () (or @t293 @t299)) % 0.36/0.66 (define @t301 () (not @t300)) % 0.36/0.66 (define @t302 () (lambda @t174 @t301)) % 0.36/0.66 (define @t303 () (@var "BOUND_VARIABLE_7630" (-> $$unsorted Bool))) % 0.36/0.66 (define @t304 () (not (_ @t303 @t9))) % 0.36/0.66 (define @t305 () (@list @t303 @t9)) % 0.36/0.66 (define @t306 () (@var "BOUND_VARIABLE_7650" (-> $$unsorted Bool))) % 0.36/0.66 (define @t307 () (_ @t306 @t9)) % 0.36/0.66 (define @t308 () (lambda (@list @t306 @t9) (or @t190 @t307))) % 0.36/0.66 (define @t309 () (@list @t47)) % 0.36/0.66 (define @t310 () (lambda @t174 @t188)) % 0.36/0.66 (define @t311 () (_ @t310 @t9)) % 0.36/0.66 (define @t312 () (not @t311)) % 0.36/0.66 (define @t313 () (or @t312 @t304)) % 0.36/0.66 (define @t314 () (not @t313)) % 0.36/0.66 (define @t315 () (lambda @t305 @t314)) % 0.36/0.66 (define @t316 () (lambda @t178 @t188)) % 0.36/0.66 (define @t317 () (not @t226)) % 0.36/0.66 (define @t318 () (or @t226 @t225 @t223)) % 0.36/0.66 (define @t319 () (not @t318)) % 0.36/0.66 (define @t320 () (and (or @t317 (and @t224 @t222)) @t318)) % 0.36/0.66 (define @t321 () (not @t320)) % 0.36/0.66 (define @t322 () (or @t229 @t228 @t320)) % 0.36/0.66 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.36/0.66 (assume @p2 (forall @t6 (exists @t5 @t4))) % 0.36/0.66 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 0.36/0.66 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 0.36/0.66 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 0.36/0.66 (assume @p6 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t11 (_ (_ @t10 @t2) @t9))))) % 0.36/0.66 (assume @p7 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t11 (_ (_ tptp.mforall_ind (lambda @t15 (_ (_ (_ tptp.mimplies @t14) (_ @t13 @t2)) @t9))) @t9))))) % 0.36/0.66 (assume @p8 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t11 (_ (_ tptp.mforall_ind (lambda @t15 (_ (_ tptp.mforall_ind (lambda (@list @t16 @t9) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t14) (_ @t13 @t16))) (_ @t10 @t16)) @t9))) @t9))) @t9))))) % 0.36/0.66 (assume @p9 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t23 (_ (_ tptp.mforall_ind (lambda @t22 (_ (_ tptp.mforall_ind (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t20 (_ (_ tptp.member @t19) @t17))) (_ (_ tptp.member @t18) @t17)) @t9))) @t9))) @t9))))) % 0.36/0.66 (assume @p10 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t23 (_ (_ tptp.mforall_ind (lambda @t22 (_ (_ tptp.mforall_ind (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t20 (_ @t24 @t19))) (_ @t24 @t18)) @t9))) @t9))) @t9))))) % 0.36/0.66 (assume @p11 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t23 (_ (_ tptp.mforall_ind (lambda @t22 (_ (_ tptp.mforall_ind (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t20 (_ (_ tptp.subset @t19) @t17))) @t26) @t9))) @t9))) @t9))))) % 0.36/0.66 (assume @p12 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t23 (_ (_ tptp.mforall_ind (lambda @t22 (_ (_ tptp.mforall_ind (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t20 (_ @t27 @t19))) @t28) @t9))) @t9))) @t9))))) % 0.36/0.66 (assume @p13 (_ tptp.mvalid (_ tptp.mforall_ind @t33))) % 0.36/0.66 (assume @p14 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t22 (_ (_ tptp.mforall_ind (lambda @t21 (_ (_ (_ tptp.mequiv @t26) (_ tptp.mforall_ind (lambda (@list @t34 @t9) (_ (_ (_ tptp.mimplies (_ @t35 @t18)) (_ @t35 @t17)) @t9)))) @t9))) @t9))))) % 0.36/0.66 (assume @p15 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t22 (_ (_ @t25 @t18) @t9))))) % 0.36/0.66 (assume @p16 @t38) % 0.36/0.66 (assume @p17 true) % 0.36/0.66 (step @p18 (= tptp.meq_prop @t41) :rule refl :args (@t41)) % 0.36/0.66 (step @p19 (= tptp.mnot @t46) :rule refl :args (@t46)) % 0.36/0.66 (step @p20 (= tptp.mor @t49) :rule refl :args (@t49)) % 0.36/0.66 (step @p21 (= tptp.mbox @t52) :rule refl :args (@t52)) % 0.36/0.66 (step @p22 (= tptp.mforall_prop @t56) :rule refl :args (@t56)) % 0.36/0.66 (step @p23 (= tptp.mtrue @t58) :rule refl :args (@t58)) % 0.36/0.66 (step @p24 (= tptp.mand @t63) :rule refl :args (@t63)) % 0.36/0.66 (step @p25 (= tptp.mimplies @t64) :rule refl :args (@t64)) % 0.36/0.66 (step @p26 (= tptp.mimplied @t65) :rule refl :args (@t65)) % 0.36/0.66 (step @p27 (= tptp.mequiv @t66) :rule refl :args (@t66)) % 0.36/0.66 (step @p28 (= tptp.mxor @t67) :rule refl :args (@t67)) % 0.36/0.66 (step @p29 (= tptp.mdia @t68) :rule refl :args (@t68)) % 0.36/0.66 (step @p30 (= tptp.mforall_ind @t74) :rule refl :args (@t74)) % 0.36/0.66 (step @p31 (= tptp.mexists_ind @t75) :rule refl :args (@t75)) % 0.36/0.66 (step @p32 (= tptp.mexists_prop @t76) :rule refl :args (@t76)) % 0.36/0.66 (step @p33 (= tptp.mreflexive @t81) :rule refl :args (@t81)) % 0.36/0.66 (step @p34 (= tptp.msymmetric @t85) :rule refl :args (@t85)) % 0.36/0.66 (step @p35 (= tptp.mserial @t87) :rule refl :args (@t87)) % 0.36/0.66 (step @p36 (= tptp.mtransitive @t92) :rule refl :args (@t92)) % 0.36/0.66 (step @p37 (= tptp.meuclidean @t94) :rule refl :args (@t94)) % 0.36/0.66 (step @p38 (= tptp.mpartially_functional @t96) :rule refl :args (@t96)) % 0.36/0.66 (step @p39 (= tptp.mfunctional @t98) :rule refl :args (@t98)) % 0.36/0.66 (step @p40 (= tptp.mweakly_dense @t101) :rule refl :args (@t101)) % 0.36/0.66 (step @p41 (= tptp.mweakly_connected @t102) :rule refl :args (@t102)) % 0.36/0.66 (step @p42 (= tptp.mweakly_directed @t103) :rule refl :args (@t103)) % 0.36/0.66 (step @p43 (= tptp.mvalid @t106) :rule refl :args (@t106)) % 0.36/0.66 (step @p44 (= tptp.msatisfiable @t107) :rule refl :args (@t107)) % 0.36/0.66 (step @p45 (= tptp.mcountersatisfiable @t108) :rule refl :args (@t108)) % 0.36/0.66 (step @p46 (= tptp.minvalid @t109) :rule refl :args (@t109)) % 0.36/0.66 (step @p47 (= tptp.mbox_s4 @t110) :rule refl :args (@t110)) % 0.36/0.66 (step @p48 (= tptp.mdia_s4 @t111) :rule refl :args (@t111)) % 0.36/0.66 (step @p49 :rule quant-merge-prenex :args ((= (forall @t57 @t122) @t120))) % 0.36/0.66 (step @p50 :rule beta-reduce :args ((= @t124 @t122))) % 0.36/0.66 (step @p51 :rule cong :premises (@p50) :args (@t125)) % 0.36/0.66 (step @p52 :rule trans :premises (@p51 @p49)) % 0.36/0.66 (step @p53 :rule beta-reduce :args ((= (_ @t127 @t123) @t125))) % 0.36/0.66 (step @p54 :rule trans :premises (@p53 @p52)) % 0.36/0.66 (step @p55 :rule aci_norm :args ((= @t129 @t119))) % 0.36/0.66 (step @p56 :rule cong :premises (@p55) :args (@t130)) % 0.36/0.66 (step @p57 :rule quant-merge-prenex :args ((= (forall @t5 @t132) @t130))) % 0.36/0.66 (step @p58 :rule alpha_equiv :args (@t133 (@list @t112) @t135)) % 0.36/0.66 (step @p59 :rule refl :args (@t118)) % 0.36/0.66 (step @p60 :rule nary_cong :premises (@p59 @p58) :args (@t136)) % 0.36/0.66 (step @p61 :rule quant-miniscope-or :args ((= @t132 @t136))) % 0.36/0.66 (step @p62 :rule trans :premises (@p61 @p60)) % 0.36/0.66 (step @p63 :rule symm :premises (@p62)) % 0.36/0.66 (step @p64 :rule cong :premises (@p63) :args ((forall @t5 (or @t118 @t138)))) % 0.36/0.66 (step @p65 :rule trans :premises (@p64 @p57)) % 0.36/0.66 (step @p66 :rule trans :premises (@p65 @p56)) % 0.36/0.66 (step @p67 :rule beta-reduce :args ((= (_ (lambda @t22 (forall @t137 (or (not (tptp.exists_in_world @t134 @t9)) (tptp.qmltpeq @t18 @t134 @t9) (not (tptp.subset @t18 @t134 @t9)) (not (tptp.subset @t134 @t18 @t9))))) @t2 @t7) @t138))) % 0.36/0.66 (step @p68 :rule refl :args (@t7)) % 0.36/0.66 (step @p69 :rule refl :args (@t2)) % 0.36/0.66 (step @p70 :rule alpha_equiv :args (@t145 @t146 @t135)) % 0.36/0.66 (step @p71 :rule cong :premises (@p70) :args (@t147)) % 0.36/0.66 (step @p72 :rule ho_cong :premises (@p71 @p69 @p68)) % 0.36/0.66 (step @p73 :rule trans :premises (@p72 @p67)) % 0.36/0.66 (step @p74 :rule refl :args (@t118)) % 0.36/0.66 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t148)) % 0.36/0.66 (step @p76 :rule cong :premises (@p75) :args (@t149)) % 0.36/0.66 (step @p77 :rule trans :premises (@p76 @p66)) % 0.36/0.66 (step @p78 :rule cong :premises (@p77) :args (@t150)) % 0.36/0.66 (step @p79 :rule beta-reduce :args ((= (_ @t152 @t147) @t150))) % 0.36/0.66 (step @p80 :rule trans :premises (@p79 @p78)) % 0.36/0.66 (step @p81 :rule beta-reduce :args ((= (_ (lambda @t57 (forall @t5 (or @t118 @t157 @t156 @t154))) @t9) @t145))) % 0.36/0.66 (step @p82 :rule refl :args (@t9)) % 0.36/0.66 (step @p83 :rule refl :args (@t153)) % 0.36/0.66 (step @p84 :rule refl :args (@t158)) % 0.36/0.66 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t158 @t153))) % 0.36/0.66 (step @p86 :rule symm :premises (@p85)) % 0.36/0.66 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 0.36/0.66 (step @p88 :rule cong :premises (@p87) :args (@t159)) % 0.36/0.66 (step @p89 :rule refl :args (@t155)) % 0.36/0.66 (step @p90 :rule refl :args (@t160)) % 0.36/0.66 (step @p91 :rule cong :premises (@p90 @p89) :args ((= @t160 @t155))) % 0.36/0.66 (step @p92 :rule symm :premises (@p91)) % 0.36/0.66 (step @p93 :rule eq_resolve :premises (@p90 @p92)) % 0.36/0.66 (step @p94 :rule cong :premises (@p93) :args (@t161)) % 0.36/0.66 (step @p95 :rule refl :args (@t157)) % 0.36/0.66 (step @p96 :rule refl :args (@t162)) % 0.36/0.66 (step @p97 :rule cong :premises (@p96 @p95) :args ((= @t162 @t157))) % 0.36/0.66 (step @p98 :rule symm :premises (@p97)) % 0.36/0.66 (step @p99 :rule eq_resolve :premises (@p96 @p98)) % 0.36/0.66 (step @p100 :rule nary_cong :premises (@p59 @p99 @p94 @p88) :args (@t163)) % 0.36/0.66 (step @p101 :rule cong :premises (@p100) :args ((forall @t5 @t163))) % 0.36/0.66 (step @p102 :rule aci_norm :args ((= (or @t118 @t164) @t163))) % 0.36/0.66 (step @p103 :rule beta-reduce :args ((= @t170 @t164))) % 0.36/0.66 (step @p104 :rule nary_cong :premises (@p74 @p103) :args (@t171)) % 0.36/0.66 (step @p105 :rule trans :premises (@p104 @p102)) % 0.36/0.66 (step @p106 :rule cong :premises (@p105) :args (@t172)) % 0.36/0.66 (step @p107 :rule trans :premises (@p106 @p101)) % 0.36/0.66 (step @p108 :rule cong :premises (@p107) :args (@t173)) % 0.36/0.66 (step @p109 :rule beta-reduce :args ((= (_ @t152 @t169) @t173))) % 0.36/0.66 (step @p110 :rule trans :premises (@p109 @p108)) % 0.36/0.66 (step @p111 :rule beta-reduce :args ((= (_ @t175 @t9) @t168))) % 0.36/0.66 (step @p112 :rule beta-reduce :args ((= (_ (lambda @t178 @t177) @t31) @t175))) % 0.36/0.66 (step @p113 :rule refl :args (@t31)) % 0.36/0.66 (step @p114 :rule aci_norm :args ((= (or @t179 @t176) @t177))) % 0.36/0.66 (step @p115 :rule refl :args (@t176)) % 0.36/0.66 (step @p116 :rule bool-double-not-elim :args (@t179)) % 0.36/0.66 (step @p117 :rule beta-reduce :args ((= @t182 @t180))) % 0.36/0.66 (step @p118 :rule cong :premises (@p117) :args (@t183)) % 0.36/0.66 (step @p119 :rule trans :premises (@p118 @p116)) % 0.36/0.66 (step @p120 :rule nary_cong :premises (@p119 @p115) :args (@t184)) % 0.36/0.66 (step @p121 :rule trans :premises (@p120 @p114)) % 0.36/0.66 (step @p122 :rule cong :premises (@p121) :args (@t185)) % 0.36/0.66 (step @p123 :rule beta-reduce :args ((= (_ @t189 @t181) @t185))) % 0.36/0.66 (step @p124 :rule trans :premises (@p123 @p122)) % 0.36/0.66 (step @p125 :rule beta-reduce :args ((= (_ @t191 @t28) @t181))) % 0.36/0.66 (step @p126 :rule refl :args (@t28)) % 0.36/0.66 (step @p127 :rule beta-reduce :args ((= @t194 @t191))) % 0.36/0.66 (step @p128 :rule ho_cong :premises (@p127 @p126)) % 0.36/0.66 (step @p129 :rule trans :premises (@p128 @p125)) % 0.36/0.66 (step @p130 :rule refl :args (@t189)) % 0.36/0.66 (step @p131 :rule ho_cong :premises (@p130 @p129)) % 0.36/0.66 (step @p132 :rule trans :premises (@p131 @p124)) % 0.36/0.66 (step @p133 :rule ho_cong :premises (@p132 @p113)) % 0.36/0.66 (step @p134 :rule trans :premises (@p133 @p112)) % 0.36/0.66 (step @p135 :rule ho_cong :premises (@p134 @p82)) % 0.36/0.66 (step @p136 :rule trans :premises (@p135 @p111)) % 0.36/0.66 (step @p137 :rule cong :premises (@p136) :args (@t196)) % 0.36/0.66 (step @p138 :rule refl :args (@t152)) % 0.36/0.66 (step @p139 :rule ho_cong :premises (@p138 @p137)) % 0.36/0.66 (step @p140 :rule trans :premises (@p139 @p110)) % 0.36/0.66 (step @p141 :rule ho_cong :premises (@p140 @p82)) % 0.36/0.66 (step @p142 :rule trans :premises (@p141 @p81)) % 0.36/0.66 (step @p143 :rule cong :premises (@p142) :args (@t197)) % 0.36/0.66 (step @p144 :rule ho_cong :premises (@p138 @p143)) % 0.36/0.66 (step @p145 :rule trans :premises (@p144 @p80)) % 0.36/0.66 (step @p146 :rule refl :args (@t127)) % 0.36/0.66 (step @p147 :rule ho_cong :premises (@p146 @p145)) % 0.36/0.66 (step @p148 :rule trans :premises (@p147 @p54)) % 0.36/0.66 (step @p149 :rule cong :premises (@p148) :args ((not (_ @t127 (_ @t152 @t197))))) % 0.36/0.66 (step @p150 :rule refl :args (@t26)) % 0.36/0.66 (step @p151 :rule beta-reduce :args ((= (_ (lambda @t57 (not @t199)) @t9) @t192))) % 0.36/0.66 (step @p152 :rule beta-reduce :args ((= @t201 @t199))) % 0.36/0.66 (step @p153 :rule cong :premises (@p152) :args (@t202)) % 0.36/0.66 (step @p154 :rule cong :premises (@p153) :args (@t203)) % 0.36/0.66 (step @p155 :rule beta-reduce :args ((= (_ @t46 @t200) @t203))) % 0.36/0.66 (step @p156 :rule trans :premises (@p155 @p154)) % 0.36/0.66 (step @p157 :rule beta-reduce :args ((= @t205 @t198))) % 0.36/0.66 (step @p158 :rule refl :args (@t44)) % 0.36/0.66 (step @p159 :rule nary_cong :premises (@p158 @p157) :args (@t206)) % 0.36/0.66 (step @p160 :rule cong :premises (@p159) :args (@t207)) % 0.36/0.66 (step @p161 :rule beta-reduce :args ((= (_ @t210 @t204) @t207))) % 0.36/0.66 (step @p162 :rule trans :premises (@p161 @p160)) % 0.36/0.66 (step @p163 :rule beta-reduce :args ((= (_ @t46 @t47) @t204))) % 0.36/0.66 (step @p164 :rule refl :args (@t48)) % 0.36/0.66 (step @p165 :rule beta-reduce :args ((= @t212 @t44))) % 0.36/0.66 (step @p166 :rule nary_cong :premises (@p165 @p164) :args (@t213)) % 0.36/0.66 (step @p167 :rule cong :premises (@p166) :args (@t214)) % 0.36/0.66 (step @p168 :rule beta-reduce :args ((= (_ @t49 @t211) @t214))) % 0.36/0.66 (step @p169 :rule trans :premises (@p168 @p167)) % 0.36/0.66 (step @p170 :rule beta-reduce :args ((= (_ @t46 @t42) @t211))) % 0.36/0.66 (step @p171 :rule refl :args (@t49)) % 0.36/0.66 (step @p172 :rule ho_cong :premises (@p171 @p170)) % 0.36/0.66 (step @p173 :rule trans :premises (@p172 @p169)) % 0.36/0.66 (step @p174 :rule ho_cong :premises (@p173 @p163)) % 0.36/0.66 (step @p175 :rule trans :premises (@p174 @p162)) % 0.36/0.66 (step @p176 :rule refl :args (@t46)) % 0.36/0.66 (step @p177 :rule ho_cong :premises (@p176 @p175)) % 0.36/0.66 (step @p178 :rule trans :premises (@p177 @p156)) % 0.36/0.66 (step @p179 :rule ho_cong :premises (@p178 @p82)) % 0.36/0.66 (step @p180 :rule trans :premises (@p179 @p151)) % 0.36/0.66 (step @p181 :rule refl :args (@t47)) % 0.36/0.66 (step @p182 :rule ho_cong :premises (@p19 @p181)) % 0.36/0.66 (step @p183 :rule refl :args (@t42)) % 0.36/0.66 (step @p184 :rule ho_cong :premises (@p19 @p183)) % 0.36/0.66 (step @p185 :rule ho_cong :premises (@p20 @p184)) % 0.36/0.66 (step @p186 :rule ho_cong :premises (@p185 @p182)) % 0.36/0.66 (step @p187 :rule ho_cong :premises (@p19 @p186)) % 0.36/0.66 (step @p188 :rule ho_cong :premises (@p187 @p82)) % 0.36/0.66 (step @p189 :rule trans :premises (@p188 @p180)) % 0.36/0.66 (step @p190 :rule cong :premises (@p189) :args (@t63)) % 0.36/0.66 (step @p191 :rule trans :premises (@p24 @p190)) % 0.36/0.66 (step @p192 :rule ho_cong :premises (@p191 @p150)) % 0.36/0.66 (step @p193 :rule ho_cong :premises (@p192 @p126)) % 0.36/0.66 (step @p194 :rule beta-reduce :args ((= (_ @t215 @t9) @t188))) % 0.36/0.66 (step @p195 :rule beta-reduce :args ((= (_ @t210 @t47) @t215))) % 0.36/0.66 (step @p196 :rule ho_cong :premises (@p173 @p181)) % 0.36/0.66 (step @p197 :rule trans :premises (@p196 @p195)) % 0.36/0.66 (step @p198 :rule ho_cong :premises (@p197 @p82)) % 0.36/0.66 (step @p199 :rule trans :premises (@p198 @p194)) % 0.36/0.66 (step @p200 :rule ho_cong :premises (@p185 @p181)) % 0.36/0.66 (step @p201 :rule ho_cong :premises (@p200 @p82)) % 0.36/0.66 (step @p202 :rule trans :premises (@p201 @p199)) % 0.36/0.66 (step @p203 :rule cong :premises (@p202) :args (@t64)) % 0.36/0.66 (step @p204 :rule trans :premises (@p25 @p203)) % 0.36/0.66 (step @p205 :rule ho_cong :premises (@p204 @p193)) % 0.36/0.66 (step @p206 :rule ho_cong :premises (@p205 @p113)) % 0.36/0.66 (step @p207 :rule ho_cong :premises (@p206 @p82)) % 0.36/0.66 (step @p208 :rule cong :premises (@p207) :args (@t36)) % 0.36/0.66 (step @p209 :rule refl :args (@t151)) % 0.36/0.66 (step @p210 :rule refl :args (@t71)) % 0.36/0.66 (step @p211 :rule cong :premises (@p210 @p209) :args ((= @t71 @t151))) % 0.36/0.66 (step @p212 :rule symm :premises (@p211)) % 0.36/0.66 (step @p213 :rule eq_resolve :premises (@p210 @p212)) % 0.36/0.66 (step @p214 :rule refl :args (@t117)) % 0.36/0.66 (step @p215 :rule refl :args (@t8)) % 0.36/0.66 (step @p216 :rule cong :premises (@p215 @p214) :args ((= @t8 @t117))) % 0.36/0.66 (step @p217 :rule symm :premises (@p216)) % 0.36/0.66 (step @p218 :rule eq_resolve :premises (@p215 @p217)) % 0.36/0.66 (step @p219 :rule cong :premises (@p218) :args (@t216)) % 0.36/0.66 (step @p220 :rule nary_cong :premises (@p219 @p213) :args (@t217)) % 0.36/0.66 (step @p221 :rule cong :premises (@p220) :args ((forall @t5 @t217))) % 0.36/0.66 (step @p222 :rule bool-impl-elim :args (@t8 @t71)) % 0.36/0.66 (step @p223 :rule cong :premises (@p222) :args (@t72)) % 0.36/0.66 (step @p224 :rule trans :premises (@p223 @p221)) % 0.36/0.66 (step @p225 :rule cong :premises (@p224) :args (@t74)) % 0.36/0.66 (step @p226 :rule trans :premises (@p30 @p225)) % 0.36/0.66 (step @p227 :rule ho_cong :premises (@p226 @p208)) % 0.36/0.66 (step @p228 :rule ho_cong :premises (@p227 @p82)) % 0.36/0.66 (step @p229 :rule cong :premises (@p228) :args (@t37)) % 0.36/0.66 (step @p230 :rule ho_cong :premises (@p226 @p229)) % 0.36/0.66 (step @p231 :rule refl :args (@t126)) % 0.36/0.66 (step @p232 :rule refl :args (@t43)) % 0.36/0.66 (step @p233 :rule cong :premises (@p232 @p231) :args ((= @t43 @t126))) % 0.36/0.66 (step @p234 :rule symm :premises (@p233)) % 0.36/0.66 (step @p235 :rule eq_resolve :premises (@p232 @p234)) % 0.36/0.66 (step @p236 :rule cong :premises (@p235) :args (@t104)) % 0.36/0.66 (step @p237 :rule cong :premises (@p236) :args (@t106)) % 0.36/0.66 (step @p238 :rule trans :premises (@p43 @p237)) % 0.36/0.66 (step @p239 :rule ho_cong :premises (@p238 @p230)) % 0.36/0.66 (step @p240 :rule cong :premises (@p239) :args (@t38)) % 0.36/0.66 (step @p241 :rule trans :premises (@p240 @p149)) % 0.36/0.66 (step @p242 :rule eq_resolve :premises (@p16 @p241)) % 0.36/0.66 (step @p243 :rule skolemize :premises (@p242)) % 0.36/0.66 (step 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