%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO566^7 : 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 : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:13:08 AM UTC 2026 % Result : Theorem 0.37s 0.61s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO566^7 : 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 % 0.17/0.34 % Computer : n018.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 00:21:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.37/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.61 % SZS status Theorem % 0.37/0.61 % SZS output start Proof % 0.37/0.61 ( % 0.37/0.61 (declare-sort $$unsorted 0) % 0.37/0.61 (declare-sort tptp.mu 0) % 0.37/0.61 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.f (-> tptp.mu $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.g (-> tptp.mu $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.37/0.61 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.61 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.61 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.61 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.37/0.61 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.61 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.37/0.61 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.37/0.61 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.61 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.61 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.37/0.61 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.37/0.61 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.37/0.61 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.exists_in_world _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.61 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.37/0.61 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.37/0.61 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.37/0.61 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.61 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.61 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.37/0.61 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.37/0.61 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.37/0.61 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.37/0.61 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.37/0.61 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.37/0.61 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.37/0.61 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.61 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.61 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.61 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.61 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.37/0.61 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.37/0.61 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.61 (define @t2 () (@var "X" tptp.mu)) % 0.37/0.61 (define @t3 () (_ tptp.exists_in_world @t2)) % 0.37/0.61 (define @t4 () (_ @t3 @t1)) % 0.37/0.61 (define @t5 () (@list @t2)) % 0.37/0.61 (define @t6 () (@list @t1)) % 0.37/0.61 (define @t7 () (@var "W" $$unsorted)) % 0.37/0.61 (define @t8 () (_ @t3 @t7)) % 0.37/0.61 (define @t9 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.61 (define @t10 () (_ tptp.g @t2)) % 0.37/0.61 (define @t11 () (_ @t10 @t9)) % 0.37/0.61 (define @t12 () (@list @t2 @t9)) % 0.37/0.61 (define @t13 () (lambda @t12 @t11)) % 0.37/0.61 (define @t14 () (_ tptp.f @t2)) % 0.37/0.61 (define @t15 () (_ @t14 @t9)) % 0.37/0.61 (define @t16 () (lambda @t12 @t15)) % 0.37/0.61 (define @t17 () (lambda @t12 (_ (_ (_ tptp.mimplies @t14) @t10) @t9))) % 0.37/0.61 (define @t18 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mbox_s4 (_ tptp.mforall_ind @t17))) (_ (_ tptp.mimplies (_ tptp.mforall_ind @t16)) (_ tptp.mforall_ind @t13)))))) % 0.37/0.61 (define @t19 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.61 (define @t20 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.61 (define @t21 () (lambda (@list @t20 @t19 @t7) (= (_ @t20 @t7) (_ @t19 @t7)))) % 0.37/0.61 (define @t22 () (@var "Phi" (-> $$unsorted Bool))) % 0.37/0.61 (define @t23 () (_ @t22 @t7)) % 0.37/0.61 (define @t24 () (not @t23)) % 0.37/0.61 (define @t25 () (@list @t22 @t7)) % 0.37/0.61 (define @t26 () (lambda @t25 @t24)) % 0.37/0.61 (define @t27 () (@var "Psi" (-> $$unsorted Bool))) % 0.37/0.61 (define @t28 () (_ @t27 @t7)) % 0.37/0.61 (define @t29 () (lambda (@list @t22 @t27 @t7) (or @t23 @t28))) % 0.37/0.61 (define @t30 () (_ @t22 @t1)) % 0.37/0.61 (define @t31 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.61 (define @t32 () (lambda (@list @t31 @t22 @t7) (forall @t6 (or (not (_ (_ @t31 @t7) @t1)) @t30)))) % 0.37/0.61 (define @t33 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.61 (define @t34 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.37/0.61 (define @t35 () (_ @t34 @t33)) % 0.37/0.61 (define @t36 () (lambda (@list @t34 @t7) (forall (@list @t33) (_ @t35 @t7)))) % 0.37/0.61 (define @t37 () (@list @t7)) % 0.37/0.61 (define @t38 () (lambda @t37 true)) % 0.37/0.61 (define @t39 () (_ tptp.mnot @t27)) % 0.37/0.61 (define @t40 () (_ tptp.mnot @t22)) % 0.37/0.61 (define @t41 () (_ tptp.mor @t40)) % 0.37/0.61 (define @t42 () (@list @t22 @t27 @t9)) % 0.37/0.61 (define @t43 () (lambda @t42 (_ (_ tptp.mnot (_ @t41 @t39)) @t9))) % 0.37/0.61 (define @t44 () (lambda @t42 (_ (_ @t41 @t27) @t9))) % 0.37/0.61 (define @t45 () (lambda @t42 (_ (_ (_ tptp.mor @t39) @t22) @t9))) % 0.37/0.61 (define @t46 () (lambda @t42 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t22) @t27)) (_ (_ tptp.mimplies @t27) @t22)) @t9))) % 0.37/0.61 (define @t47 () (lambda @t42 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t22) @t27)) @t9))) % 0.37/0.61 (define @t48 () (lambda (@list @t31 @t22 @t9) (_ (_ tptp.mnot (_ (_ tptp.mbox @t31) @t40)) @t9))) % 0.37/0.61 (define @t49 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.37/0.61 (define @t50 () (_ @t49 @t2)) % 0.37/0.61 (define @t51 () (_ @t50 @t7)) % 0.37/0.61 (define @t52 () (forall @t5 (=> @t8 @t51))) % 0.37/0.61 (define @t53 () (@list @t49 @t7)) % 0.37/0.61 (define @t54 () (lambda @t53 @t52)) % 0.37/0.61 (define @t55 () (lambda (@list @t49 @t9) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda @t12 (_ (_ tptp.mnot @t50) @t9)))) @t9))) % 0.37/0.61 (define @t56 () (lambda (@list @t34 @t9) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t33 @t9) (_ (_ tptp.mnot @t35) @t9)))) @t9))) % 0.37/0.61 (define @t57 () (@var "S" $$unsorted)) % 0.37/0.61 (define @t58 () (_ @t31 @t57)) % 0.37/0.61 (define @t59 () (_ @t58 @t57)) % 0.37/0.61 (define @t60 () (@list @t57)) % 0.37/0.61 (define @t61 () (forall @t60 @t59)) % 0.37/0.61 (define @t62 () (@list @t31)) % 0.37/0.61 (define @t63 () (lambda @t62 @t61)) % 0.37/0.61 (define @t64 () (@var "T" $$unsorted)) % 0.37/0.61 (define @t65 () (_ @t31 @t64)) % 0.37/0.61 (define @t66 () (_ @t58 @t64)) % 0.37/0.61 (define @t67 () (lambda @t62 (forall (@list @t57 @t64) (=> @t66 (_ @t65 @t57))))) % 0.37/0.61 (define @t68 () (@list @t64)) % 0.37/0.61 (define @t69 () (lambda @t62 (forall @t60 (exists @t68 @t66)))) % 0.37/0.61 (define @t70 () (@var "U" $$unsorted)) % 0.37/0.61 (define @t71 () (_ @t58 @t70)) % 0.37/0.61 (define @t72 () (_ @t65 @t70)) % 0.37/0.61 (define @t73 () (@list @t57 @t64 @t70)) % 0.37/0.61 (define @t74 () (lambda @t62 (forall @t73 (=> (and @t66 @t72) @t71)))) % 0.37/0.61 (define @t75 () (and @t66 @t71)) % 0.37/0.61 (define @t76 () (lambda @t62 (forall @t73 (=> @t75 @t72)))) % 0.37/0.61 (define @t77 () (= @t64 @t70)) % 0.37/0.61 (define @t78 () (lambda @t62 (forall @t73 (=> @t75 @t77)))) % 0.37/0.61 (define @t79 () (@list @t70)) % 0.37/0.61 (define @t80 () (lambda @t62 (forall @t60 (exists @t68 (and @t66 (forall @t79 (=> @t71 @t77))))))) % 0.37/0.61 (define @t81 () (_ @t31 @t70)) % 0.37/0.61 (define @t82 () (_ @t81 @t64)) % 0.37/0.61 (define @t83 () (lambda @t62 (forall @t73 (=> @t66 (exists @t79 (and @t71 @t82)))))) % 0.37/0.61 (define @t84 () (lambda @t62 (forall @t73 (=> @t75 (or @t72 @t77 @t82))))) % 0.37/0.61 (define @t85 () (lambda @t62 (forall @t73 (=> @t75 (exists @t6 (and (_ @t65 @t1) (_ @t81 @t1))))))) % 0.37/0.61 (define @t86 () (forall @t37 @t23)) % 0.37/0.61 (define @t87 () (@list @t22)) % 0.37/0.61 (define @t88 () (lambda @t87 @t86)) % 0.37/0.61 (define @t89 () (lambda @t87 (exists @t37 @t23))) % 0.37/0.61 (define @t90 () (lambda @t87 (exists @t37 @t24))) % 0.37/0.61 (define @t91 () (lambda @t87 (forall @t37 @t24))) % 0.37/0.61 (define @t92 () (_ (_ tptp.rel_s4 @t7) @t1)) % 0.37/0.61 (define @t93 () (not @t92)) % 0.37/0.61 (define @t94 () (or @t93 @t30)) % 0.37/0.61 (define @t95 () (forall @t6 @t94)) % 0.37/0.61 (define @t96 () (lambda @t25 @t95)) % 0.37/0.61 (define @t97 () (lambda (@list @t22 @t9) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t40)) @t9))) % 0.37/0.61 (define @t98 () (forall @t60 (tptp.rel_s4 @t57 @t57))) % 0.37/0.61 (define @t99 () (_ @t31 @t57 @t57)) % 0.37/0.61 (define @t100 () (@var "BOUND_VARIABLE_8588" tptp.mu)) % 0.37/0.61 (define @t101 () (tptp.g @t100 @t7)) % 0.37/0.61 (define @t102 () (not (tptp.exists_in_world @t100 @t7))) % 0.37/0.61 (define @t103 () (tptp.f @t2 @t7)) % 0.37/0.61 (define @t104 () (tptp.exists_in_world @t2 @t7)) % 0.37/0.61 (define @t105 () (not @t104)) % 0.37/0.61 (define @t106 () (forall @t5 (or @t105 @t103))) % 0.37/0.61 (define @t107 () (not @t106)) % 0.37/0.61 (define @t108 () (@var "BOUND_VARIABLE_8508" tptp.mu)) % 0.37/0.61 (define @t109 () (tptp.g @t108 @t1)) % 0.37/0.61 (define @t110 () (not (tptp.f @t108 @t1))) % 0.37/0.61 (define @t111 () (not (tptp.exists_in_world @t108 @t1))) % 0.37/0.61 (define @t112 () (tptp.rel_s4 @t7 @t1)) % 0.37/0.61 (define @t113 () (not @t112)) % 0.37/0.61 (define @t114 () (or @t113 @t111 @t110 @t109)) % 0.37/0.61 (define @t115 () (@list @t1 @t108)) % 0.37/0.61 (define @t116 () (forall @t115 @t114)) % 0.37/0.61 (define @t117 () (not @t116)) % 0.37/0.61 (define @t118 () (or @t117 @t107 @t102 @t101)) % 0.37/0.61 (define @t119 () (or @t102 @t101)) % 0.37/0.61 (define @t120 () (or @t117 @t107 @t119)) % 0.37/0.61 (define @t121 () (@list @t7 @t100)) % 0.37/0.61 (define @t122 () (forall @t121 @t120)) % 0.37/0.61 (define @t123 () (@list @t100)) % 0.37/0.61 (define @t124 () (forall @t123 @t120)) % 0.37/0.61 (define @t125 () (forall @t123 @t119)) % 0.37/0.61 (define @t126 () (@list @t2)) % 0.37/0.61 (define @t127 () (or @t117 @t107 @t125)) % 0.37/0.61 (define @t128 () (tptp.g @t2 @t7)) % 0.37/0.61 (define @t129 () (forall @t5 (or @t105 @t128))) % 0.37/0.61 (define @t130 () (or @t117 @t107 @t129)) % 0.37/0.61 (define @t131 () (not (tptp.exists_in_world @t2 @t9))) % 0.37/0.61 (define @t132 () (forall @t5 (or @t131 (tptp.g @t2 @t9)))) % 0.37/0.61 (define @t133 () (forall @t5 (or @t131 (tptp.f @t2 @t9)))) % 0.37/0.61 (define @t134 () (not @t133)) % 0.37/0.61 (define @t135 () (forall @t115 (or (not (tptp.rel_s4 @t9 @t1)) @t111 @t110 @t109))) % 0.37/0.61 (define @t136 () (not @t135)) % 0.37/0.61 (define @t137 () (or @t136 @t134 @t132)) % 0.37/0.61 (define @t138 () (@list @t9)) % 0.37/0.61 (define @t139 () (lambda @t138 @t137)) % 0.37/0.61 (define @t140 () (_ @t139 @t7)) % 0.37/0.61 (define @t141 () (forall @t37 @t140)) % 0.37/0.61 (define @t142 () (_ @t22 @t7)) % 0.37/0.61 (define @t143 () (lambda @t87 (forall @t37 @t142))) % 0.37/0.61 (define @t144 () (or @t134 @t132)) % 0.37/0.61 (define @t145 () (lambda @t138 @t144)) % 0.37/0.61 (define @t146 () (_ @t145 @t9)) % 0.37/0.61 (define @t147 () (or @t136 @t146)) % 0.37/0.61 (define @t148 () (lambda @t138 @t147)) % 0.37/0.61 (define @t149 () (_ @t27 @t9)) % 0.37/0.61 (define @t150 () (@list @t27 @t9)) % 0.37/0.61 (define @t151 () (lambda @t37 @t129)) % 0.37/0.61 (define @t152 () (_ @t151 @t9)) % 0.37/0.61 (define @t153 () (or @t134 @t152)) % 0.37/0.61 (define @t154 () (lambda @t138 @t153)) % 0.37/0.61 (define @t155 () (_ @t10 @t7)) % 0.37/0.61 (define @t156 () (or @t105 @t155)) % 0.37/0.61 (define @t157 () (_ @t13 @t2 @t7)) % 0.37/0.61 (define @t158 () (or @t105 @t157)) % 0.37/0.61 (define @t159 () (forall @t5 @t158)) % 0.37/0.61 (define @t160 () (lambda @t37 @t159)) % 0.37/0.61 (define @t161 () (_ @t49 @t2 @t7)) % 0.37/0.61 (define @t162 () (lambda @t53 (forall @t5 (or @t105 @t161)))) % 0.37/0.61 (define @t163 () (_ @t162 @t13)) % 0.37/0.61 (define @t164 () (lambda @t37 @t106)) % 0.37/0.61 (define @t165 () (_ @t164 @t9)) % 0.37/0.61 (define @t166 () (not @t165)) % 0.37/0.61 (define @t167 () (or @t166 @t149)) % 0.37/0.61 (define @t168 () (lambda @t150 @t167)) % 0.37/0.61 (define @t169 () (or (not (_ @t22 @t9)) @t149)) % 0.37/0.61 (define @t170 () (lambda @t42 @t169)) % 0.37/0.61 (define @t171 () (_ @t14 @t7)) % 0.37/0.61 (define @t172 () (or @t105 @t171)) % 0.37/0.61 (define @t173 () (_ @t16 @t2 @t7)) % 0.37/0.61 (define @t174 () (or @t105 @t173)) % 0.37/0.61 (define @t175 () (forall @t5 @t174)) % 0.37/0.61 (define @t176 () (lambda @t37 @t175)) % 0.37/0.61 (define @t177 () (_ @t162 @t16)) % 0.37/0.61 (define @t178 () (lambda @t37 @t116)) % 0.37/0.61 (define @t179 () (_ @t178 @t9)) % 0.37/0.61 (define @t180 () (not @t179)) % 0.37/0.61 (define @t181 () (or @t180 @t149)) % 0.37/0.61 (define @t182 () (lambda @t150 @t181)) % 0.37/0.61 (define @t183 () (or @t111 @t110 @t109)) % 0.37/0.61 (define @t184 () (or @t113 @t183)) % 0.37/0.61 (define @t185 () (forall @t115 @t184)) % 0.37/0.61 (define @t186 () (@list @t108)) % 0.37/0.61 (define @t187 () (forall @t186 @t184)) % 0.37/0.61 (define @t188 () (forall @t186 @t183)) % 0.37/0.61 (define @t189 () (or @t113 @t188)) % 0.37/0.61 (define @t190 () (forall @t5 (or (not (tptp.exists_in_world @t2 @t1)) (not (tptp.f @t2 @t1)) (tptp.g @t2 @t1)))) % 0.37/0.61 (define @t191 () (lambda @t37 (forall @t5 (or @t105 (not @t103) @t128)))) % 0.37/0.61 (define @t192 () (_ @t191 @t1)) % 0.37/0.61 (define @t193 () (or @t113 @t192)) % 0.37/0.61 (define @t194 () (forall @t6 @t193)) % 0.37/0.61 (define @t195 () (lambda @t37 @t194)) % 0.37/0.61 (define @t196 () (_ @t22 @t1)) % 0.37/0.61 (define @t197 () (lambda @t25 (forall @t6 (or @t113 @t196)))) % 0.37/0.61 (define @t198 () (not @t171)) % 0.37/0.61 (define @t199 () (or @t105 @t198 @t155)) % 0.37/0.61 (define @t200 () (or @t198 @t155)) % 0.37/0.61 (define @t201 () (not @t15)) % 0.37/0.61 (define @t202 () (or @t201 @t11)) % 0.37/0.61 (define @t203 () (lambda @t12 @t202)) % 0.37/0.61 (define @t204 () (_ @t203 @t2 @t7)) % 0.37/0.61 (define @t205 () (or @t105 @t204)) % 0.37/0.61 (define @t206 () (forall @t5 @t205)) % 0.37/0.61 (define @t207 () (lambda @t37 @t206)) % 0.37/0.61 (define @t208 () (lambda @t138 @t202)) % 0.37/0.61 (define @t209 () (lambda @t150 (or @t201 @t149))) % 0.37/0.61 (define @t210 () (_ @t170 @t14)) % 0.37/0.61 (define @t211 () (lambda @t12 (_ (_ @t210 @t10) @t9))) % 0.37/0.61 (define @t212 () (not @t8)) % 0.37/0.61 (define @t213 () (or @t212 @t51)) % 0.37/0.61 (define @t214 () (or @t24 @t28)) % 0.37/0.61 (define @t215 () (lambda @t37 @t214)) % 0.37/0.61 (define @t216 () (@list @t27 @t7)) % 0.37/0.61 (define @t217 () (lambda @t37 @t24)) % 0.37/0.61 (define @t218 () (_ @t217 @t7)) % 0.37/0.61 (define @t219 () (or @t218 @t28)) % 0.37/0.61 (define @t220 () (lambda @t216 @t219)) % 0.37/0.61 (define @t221 () (forall @t121 @t118)) % 0.37/0.61 (define @t222 () (@quantifiers_skolemize @t221 0)) % 0.37/0.61 (define @t223 () (forall @t115 (or (not (tptp.rel_s4 @t222 @t1)) @t111 @t110 @t109))) % 0.37/0.61 (define @t224 () (@quantifiers_skolemize @t221 1)) % 0.37/0.61 (define @t225 () (tptp.g @t224 @t222)) % 0.37/0.61 (define @t226 () (tptp.exists_in_world @t224 @t222)) % 0.37/0.61 (define @t227 () (not @t226)) % 0.37/0.61 (define @t228 () (forall @t5 (or (not (tptp.exists_in_world @t2 @t222)) (tptp.f @t2 @t222)))) % 0.37/0.61 (define @t229 () (not @t228)) % 0.37/0.61 (define @t230 () (not @t223)) % 0.37/0.61 (define @t231 () (or @t230 @t229 @t227 @t225)) % 0.37/0.61 (define @t232 () (@list true)) % 0.37/0.61 (define @t233 () (@list @t231)) % 0.37/0.61 (define @t234 () (tptp.f @t224 @t222)) % 0.37/0.61 (define @t235 () (or @t227 @t234)) % 0.37/0.61 (define @t236 () (not @t234)) % 0.37/0.61 (define @t237 () (tptp.rel_s4 @t222 @t222)) % 0.37/0.61 (define @t238 () (not @t237)) % 0.37/0.61 (define @t239 () (or @t238 @t227 @t236 @t225)) % 0.37/0.61 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.37/0.61 (assume @p2 (forall @t6 (exists @t5 @t4))) % 0.37/0.61 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 0.37/0.61 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 0.37/0.61 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 0.37/0.61 (assume @p6 @t18) % 0.37/0.61 (assume @p7 true) % 0.37/0.61 (step @p8 (= tptp.meq_prop @t21) :rule refl :args (@t21)) % 0.37/0.61 (step @p9 (= tptp.mnot @t26) :rule refl :args (@t26)) % 0.37/0.61 (step @p10 (= tptp.mor @t29) :rule refl :args (@t29)) % 0.37/0.61 (step @p11 (= tptp.mbox @t32) :rule refl :args (@t32)) % 0.37/0.61 (step @p12 (= tptp.mforall_prop @t36) :rule refl :args (@t36)) % 0.37/0.61 (step @p13 (= tptp.mtrue @t38) :rule refl :args (@t38)) % 0.37/0.61 (step @p14 (= tptp.mand @t43) :rule refl :args (@t43)) % 0.37/0.61 (step @p15 (= tptp.mimplies @t44) :rule refl :args (@t44)) % 0.37/0.61 (step @p16 (= tptp.mimplied @t45) :rule refl :args (@t45)) % 0.37/0.61 (step @p17 (= tptp.mequiv @t46) :rule refl :args (@t46)) % 0.37/0.61 (step @p18 (= tptp.mxor @t47) :rule refl :args (@t47)) % 0.37/0.61 (step @p19 (= tptp.mdia @t48) :rule refl :args (@t48)) % 0.37/0.61 (step @p20 (= tptp.mforall_ind @t54) :rule refl :args (@t54)) % 0.37/0.61 (step @p21 (= tptp.mexists_ind @t55) :rule refl :args (@t55)) % 0.37/0.61 (step @p22 (= tptp.mexists_prop @t56) :rule refl :args (@t56)) % 0.37/0.61 (step @p23 (= tptp.mreflexive @t63) :rule refl :args (@t63)) % 0.37/0.61 (step @p24 (= tptp.msymmetric @t67) :rule refl :args (@t67)) % 0.37/0.61 (step @p25 (= tptp.mserial @t69) :rule refl :args (@t69)) % 0.37/0.61 (step @p26 (= tptp.mtransitive @t74) :rule refl :args (@t74)) % 0.37/0.61 (step @p27 (= tptp.meuclidean @t76) :rule refl :args (@t76)) % 0.37/0.61 (step @p28 (= tptp.mpartially_functional @t78) :rule refl :args (@t78)) % 0.37/0.61 (step @p29 (= tptp.mfunctional @t80) :rule refl :args (@t80)) % 0.37/0.61 (step @p30 (= tptp.mweakly_dense @t83) :rule refl :args (@t83)) % 0.37/0.61 (step @p31 (= tptp.mweakly_connected @t84) :rule refl :args (@t84)) % 0.37/0.61 (step @p32 (= tptp.mweakly_directed @t85) :rule refl :args (@t85)) % 0.37/0.61 (step @p33 (= tptp.mvalid @t88) :rule refl :args (@t88)) % 0.37/0.61 (step @p34 (= tptp.msatisfiable @t89) :rule refl :args (@t89)) % 0.37/0.61 (step @p35 (= tptp.mcountersatisfiable @t90) :rule refl :args (@t90)) % 0.37/0.61 (step @p36 (= tptp.minvalid @t91) :rule refl :args (@t91)) % 0.37/0.61 (step @p37 (= tptp.mbox_s4 @t96) :rule refl :args (@t96)) % 0.37/0.61 (step @p38 (= tptp.mdia_s4 @t97) :rule refl :args (@t97)) % 0.37/0.61 (step @p39 :rule beta-reduce :args ((= (_ (lambda @t62 (forall @t60 @t99)) tptp.rel_s4) @t98))) % 0.37/0.61 (step @p40 :rule refl :args (tptp.rel_s4)) % 0.37/0.61 (step @p41 :rule refl :args (@t99)) % 0.37/0.61 (step @p42 :rule refl :args (@t59)) % 0.37/0.61 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t59 @t99))) % 0.37/0.61 (step @p44 :rule symm :premises (@p43)) % 0.37/0.61 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.37/0.61 (step @p46 :rule cong :premises (@p45) :args (@t61)) % 0.37/0.61 (step @p47 :rule cong :premises (@p46) :args (@t63)) % 0.37/0.61 (step @p48 :rule trans :premises (@p23 @p47)) % 0.37/0.61 (step @p49 :rule ho_cong :premises (@p48 @p40)) % 0.37/0.61 (step @p50 :rule trans :premises (@p49 @p39)) % 0.37/0.61 (step @p51 :rule eq_resolve :premises (@p3 @p50)) % 0.37/0.61 (step @p52 :rule aci_norm :args ((= @t120 @t118))) % 0.37/0.61 (step @p53 :rule cong :premises (@p52) :args (@t122)) % 0.37/0.61 (step @p54 :rule quant-merge-prenex :args ((= (forall @t37 @t124) @t122))) % 0.37/0.61 (step @p55 :rule alpha_equiv :args (@t125 (@list @t100) @t126)) % 0.37/0.61 (step @p56 :rule refl :args (@t107)) % 0.37/0.61 (step @p57 :rule refl :args (@t117)) % 0.37/0.61 (step @p58 :rule nary_cong :premises (@p57 @p56 @p55) :args (@t127)) % 0.37/0.61 (step @p59 :rule quant-miniscope-or :args ((= @t124 @t127))) % 0.37/0.61 (step @p60 :rule trans :premises (@p59 @p58)) % 0.37/0.61 (step @p61 :rule symm :premises (@p60)) % 0.37/0.61 (step @p62 :rule cong :premises (@p61) :args ((forall @t37 @t130))) % 0.37/0.61 (step @p63 :rule trans :premises (@p62 @p54)) % 0.37/0.61 (step @p64 :rule trans :premises (@p63 @p53)) % 0.37/0.61 (step @p65 :rule beta-reduce :args ((= @t140 @t130))) % 0.37/0.61 (step @p66 :rule cong :premises (@p65) :args (@t141)) % 0.37/0.61 (step @p67 :rule trans :premises (@p66 @p64)) % 0.37/0.61 (step @p68 :rule beta-reduce :args ((= (_ @t143 @t139) @t141))) % 0.37/0.61 (step @p69 :rule trans :premises (@p68 @p67)) % 0.37/0.61 (step @p70 :rule aci_norm :args ((= (or @t136 @t144) @t137))) % 0.37/0.61 (step @p71 :rule beta-reduce :args ((= @t146 @t144))) % 0.37/0.61 (step @p72 :rule refl :args (@t136)) % 0.37/0.61 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t147)) % 0.37/0.61 (step @p74 :rule trans :premises (@p73 @p70)) % 0.37/0.61 (step @p75 :rule cong :premises (@p74) :args (@t148)) % 0.37/0.61 (step @p76 :rule beta-reduce :args ((= (_ (lambda @t150 (or @t136 @t149)) @t145) @t148))) % 0.37/0.61 (step @p77 :rule trans :premises (@p76 @p75)) % 0.37/0.61 (step @p78 :rule beta-reduce :args ((= @t152 @t132))) % 0.37/0.61 (step @p79 :rule refl :args (@t134)) % 0.37/0.61 (step @p80 :rule nary_cong :premises (@p79 @p78) :args (@t153)) % 0.37/0.61 (step @p81 :rule cong :premises (@p80) :args (@t154)) % 0.37/0.61 (step @p82 :rule beta-reduce :args ((= (_ (lambda @t150 (or @t134 @t149)) @t151) @t154))) % 0.37/0.61 (step @p83 :rule trans :premises (@p82 @p81)) % 0.37/0.61 (step @p84 :rule refl :args (@t128)) % 0.37/0.61 (step @p85 :rule refl :args (@t155)) % 0.37/0.61 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t155 @t128))) % 0.37/0.61 (step @p87 :rule symm :premises (@p86)) % 0.37/0.61 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.37/0.61 (step @p89 :rule refl :args (@t105)) % 0.37/0.61 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t156)) % 0.37/0.61 (step @p91 :rule cong :premises (@p90) :args ((forall @t5 @t156))) % 0.37/0.61 (step @p92 :rule beta-reduce :args ((= @t157 @t155))) % 0.37/0.61 (step @p93 :rule refl :args (@t105)) % 0.37/0.61 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t158)) % 0.37/0.61 (step @p95 :rule cong :premises (@p94) :args (@t159)) % 0.37/0.61 (step @p96 :rule trans :premises (@p95 @p91)) % 0.37/0.61 (step @p97 :rule cong :premises (@p96) :args (@t160)) % 0.37/0.61 (step @p98 :rule beta-reduce :args ((= @t163 @t160))) % 0.37/0.61 (step @p99 :rule trans :premises (@p98 @p97)) % 0.37/0.61 (step @p100 :rule refl :args (@t149)) % 0.37/0.61 (step @p101 :rule beta-reduce :args ((= @t165 @t133))) % 0.37/0.61 (step @p102 :rule cong :premises (@p101) :args (@t166)) % 0.37/0.61 (step @p103 :rule nary_cong :premises (@p102 @p100) :args (@t167)) % 0.37/0.61 (step @p104 :rule cong :premises (@p103) :args (@t168)) % 0.37/0.61 (step @p105 :rule beta-reduce :args ((= (_ @t170 @t164) @t168))) % 0.37/0.61 (step @p106 :rule trans :premises (@p105 @p104)) % 0.37/0.61 (step @p107 :rule refl :args (@t103)) % 0.37/0.61 (step @p108 :rule refl :args (@t171)) % 0.37/0.61 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t171 @t103))) % 0.37/0.61 (step @p110 :rule symm :premises (@p109)) % 0.37/0.61 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 0.37/0.61 (step @p112 :rule nary_cong :premises (@p89 @p111) :args (@t172)) % 0.37/0.61 (step @p113 :rule cong :premises (@p112) :args ((forall @t5 @t172))) % 0.37/0.61 (step @p114 :rule beta-reduce :args ((= @t173 @t171))) % 0.37/0.61 (step @p115 :rule nary_cong :premises (@p93 @p114) :args (@t174)) % 0.37/0.61 (step @p116 :rule cong :premises (@p115) :args (@t175)) % 0.37/0.61 (step @p117 :rule trans :premises (@p116 @p113)) % 0.37/0.61 (step @p118 :rule cong :premises (@p117) :args (@t176)) % 0.37/0.61 (step @p119 :rule beta-reduce :args ((= @t177 @t176))) % 0.37/0.61 (step @p120 :rule trans :premises (@p119 @p118)) % 0.37/0.61 (step @p121 :rule refl :args (@t170)) % 0.37/0.61 (step @p122 :rule ho_cong :premises (@p121 @p120)) % 0.37/0.61 (step @p123 :rule trans :premises (@p122 @p106)) % 0.37/0.61 (step @p124 :rule ho_cong :premises (@p123 @p99)) % 0.37/0.61 (step @p125 :rule trans :premises (@p124 @p83)) % 0.37/0.61 (step @p126 :rule beta-reduce :args ((= @t179 @t135))) % 0.37/0.61 (step @p127 :rule cong :premises (@p126) :args (@t180)) % 0.37/0.61 (step @p128 :rule nary_cong :premises (@p127 @p100) :args (@t181)) % 0.37/0.61 (step @p129 :rule cong :premises (@p128) :args (@t182)) % 0.37/0.61 (step @p130 :rule beta-reduce :args ((= (_ @t170 @t178) @t182))) % 0.37/0.61 (step @p131 :rule trans :premises (@p130 @p129)) % 0.37/0.61 (step @p132 :rule aci_norm :args ((= @t184 @t114))) % 0.37/0.61 (step @p133 :rule cong :premises (@p132) :args (@t185)) % 0.37/0.61 (step @p134 :rule quant-merge-prenex :args ((= (forall @t6 @t187) @t185))) % 0.37/0.61 (step @p135 :rule alpha_equiv :args (@t188 (@list @t108) @t126)) % 0.37/0.61 (step @p136 :rule refl :args (@t113)) % 0.37/0.61 (step @p137 :rule nary_cong :premises (@p136 @p135) :args (@t189)) % 0.37/0.61 (step @p138 :rule quant-miniscope-or :args ((= @t187 @t189))) % 0.37/0.61 (step @p139 :rule trans :premises (@p138 @p137)) % 0.37/0.61 (step @p140 :rule symm :premises (@p139)) % 0.37/0.61 (step @p141 :rule cong :premises (@p140) :args ((forall @t6 (or @t113 @t190)))) % 0.37/0.61 (step @p142 :rule trans :premises (@p141 @p134)) % 0.37/0.61 (step @p143 :rule trans :premises (@p142 @p133)) % 0.37/0.61 (step @p144 :rule beta-reduce :args ((= @t192 @t190))) % 0.37/0.61 (step @p145 :rule refl :args (@t113)) % 0.37/0.61 (step @p146 :rule nary_cong :premises (@p145 @p144) :args (@t193)) % 0.37/0.61 (step @p147 :rule cong :premises (@p146) :args (@t194)) % 0.37/0.61 (step @p148 :rule trans :premises (@p147 @p143)) % 0.37/0.61 (step @p149 :rule cong :premises (@p148) :args (@t195)) % 0.37/0.61 (step @p150 :rule beta-reduce :args ((= (_ @t197 @t191) @t195))) % 0.37/0.61 (step @p151 :rule trans :premises (@p150 @p149)) % 0.37/0.61 (step @p152 :rule cong :premises (@p111) :args (@t198)) % 0.37/0.61 (step @p153 :rule nary_cong :premises (@p89 @p152 @p88) :args (@t199)) % 0.37/0.61 (step @p154 :rule cong :premises (@p153) :args ((forall @t5 @t199))) % 0.37/0.61 (step @p155 :rule aci_norm :args ((= (or @t105 @t200) @t199))) % 0.37/0.61 (step @p156 :rule beta-reduce :args ((= @t204 @t200))) % 0.37/0.61 (step @p157 :rule nary_cong :premises (@p93 @p156) :args (@t205)) % 0.37/0.61 (step @p158 :rule trans :premises (@p157 @p155)) % 0.37/0.61 (step @p159 :rule cong :premises (@p158) :args (@t206)) % 0.37/0.61 (step @p160 :rule trans :premises (@p159 @p154)) % 0.37/0.61 (step @p161 :rule cong :premises (@p160) :args (@t207)) % 0.37/0.61 (step @p162 :rule beta-reduce :args ((= (_ @t162 @t203) @t207))) % 0.37/0.61 (step @p163 :rule trans :premises (@p162 @p161)) % 0.37/0.61 (step @p164 :rule beta-reduce :args ((= (_ @t208 @t9) @t202))) % 0.37/0.61 (step @p165 :rule refl :args (@t9)) % 0.37/0.61 (step @p166 :rule beta-reduce :args ((= (_ @t209 @t10) @t208))) % 0.37/0.61 (step @p167 :rule refl :args (@t10)) % 0.37/0.61 (step @p168 :rule beta-reduce :args ((= @t210 @t209))) % 0.37/0.61 (step @p169 :rule ho_cong :premises (@p168 @p167)) % 0.37/0.61 (step @p170 :rule trans :premises (@p169 @p166)) % 0.37/0.61 (step @p171 :rule ho_cong :premises (@p170 @p165)) % 0.37/0.61 (step @p172 :rule trans :premises (@p171 @p164)) % 0.37/0.61 (step @p173 :rule cong :premises (@p172) :args (@t211)) % 0.37/0.61 (step @p174 :rule refl :args (@t162)) % 0.37/0.61 (step @p175 :rule ho_cong :premises (@p174 @p173)) % 0.37/0.61 (step @p176 :rule trans :premises (@p175 @p163)) % 0.37/0.61 (step @p177 :rule refl :args (@t197)) % 0.37/0.61 (step @p178 :rule ho_cong :premises (@p177 @p176)) % 0.37/0.61 (step @p179 :rule trans :premises (@p178 @p151)) % 0.37/0.61 (step @p180 :rule ho_cong :premises (@p121 @p179)) % 0.37/0.61 (step @p181 :rule trans :premises (@p180 @p131)) % 0.37/0.61 (step @p182 :rule ho_cong :premises (@p181 @p125)) % 0.37/0.61 (step @p183 :rule trans 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0.37/0.61 (step @p199 :rule cong :premises (@p198) :args (@t212)) % 0.37/0.61 (step @p200 :rule nary_cong :premises (@p199 @p193) :args (@t213)) % 0.37/0.61 (step @p201 :rule cong :premises (@p200) :args ((forall @t5 @t213))) % 0.37/0.61 (step @p202 :rule bool-impl-elim :args (@t8 @t51)) % 0.37/0.61 (step @p203 :rule cong :premises (@p202) :args (@t52)) % 0.37/0.61 (step @p204 :rule trans :premises (@p203 @p201)) % 0.37/0.61 (step @p205 :rule cong :premises (@p204) :args (@t54)) % 0.37/0.61 (step @p206 :rule trans :premises (@p20 @p205)) % 0.37/0.61 (step @p207 :rule ho_cong :premises (@p206 @p188)) % 0.37/0.61 (step @p208 :rule refl :args (@t16)) % 0.37/0.61 (step @p209 :rule ho_cong :premises (@p206 @p208)) % 0.37/0.61 (step @p210 :rule beta-reduce :args ((= (_ @t215 @t9) @t169))) % 0.37/0.61 (step @p211 :rule beta-reduce :args ((= (_ (lambda @t216 @t214) @t27) @t215))) % 0.37/0.61 (step @p212 :rule refl :args (@t27)) % 0.37/0.61 (step @p213 :rule refl :args (@t28)) % 0.37/0.61 (step @p214 :rule beta-reduce :args ((= @t218 @t24))) % 0.37/0.61 (step @p215 :rule nary_cong :premises (@p214 @p213) :args (@t219)) % 0.37/0.61 (step @p216 :rule cong :premises (@p215) :args (@t220)) % 0.37/0.61 (step @p217 :rule beta-reduce :args ((= (_ @t29 @t217) @t220))) % 0.37/0.61 (step @p218 :rule trans :premises (@p217 @p216)) % 0.37/0.61 (step @p219 :rule beta-reduce :args ((= (_ @t26 @t22) @t217))) % 0.37/0.61 (step @p220 :rule refl :args (@t29)) % 0.37/0.61 (step @p221 :rule ho_cong :premises (@p220 @p219)) % 0.37/0.61 (step @p222 :rule trans :premises (@p221 @p218)) % 0.37/0.61 (step @p223 :rule ho_cong :premises (@p222 @p212)) % 0.37/0.61 (step @p224 :rule trans :premises (@p223 @p211)) % 0.37/0.61 (step @p225 :rule ho_cong :premises (@p224 @p165)) % 0.37/0.61 (step @p226 :rule trans :premises (@p225 @p210)) % 0.37/0.61 (step @p227 :rule refl :args (@t22)) % 0.37/0.61 (step @p228 :rule ho_cong :premises (@p9 @p227)) % 0.37/0.61 (step @p229 :rule ho_cong :premises (@p10 @p228)) % 0.37/0.61 (step @p230 :rule ho_cong :premises (@p229 @p212)) % 0.37/0.61 (step @p231 :rule ho_cong :premises (@p230 @p165)) % 0.37/0.61 (step @p232 :rule trans :premises (@p231 @p226)) % 0.37/0.61 (step @p233 :rule cong :premises (@p232) :args (@t44)) % 0.37/0.61 (step @p234 :rule trans :premises (@p15 @p233)) % 0.37/0.61 (step @p235 :rule ho_cong :premises (@p234 @p209)) % 0.37/0.61 (step @p236 :rule ho_cong :premises (@p235 @p207)) % 0.37/0.61 (step @p237 :rule refl :args (@t14)) % 0.37/0.61 (step @p238 :rule ho_cong :premises (@p234 @p237)) % 0.37/0.61 (step @p239 :rule ho_cong :premises (@p238 @p167)) % 0.37/0.61 (step @p240 :rule ho_cong :premises (@p239 @p165)) % 0.37/0.61 (step @p241 :rule cong :premises (@p240) :args (@t17)) % 0.37/0.61 (step @p242 :rule ho_cong :premises (@p206 @p241)) % 0.37/0.61 (step @p243 :rule refl :args (@t196)) % 0.37/0.61 (step @p244 :rule refl :args (@t30)) % 0.37/0.61 (step @p245 :rule cong :premises (@p244 @p243) :args ((= @t30 @t196))) % 0.37/0.61 (step @p246 :rule symm :premises (@p245)) % 0.37/0.61 (step @p247 :rule eq_resolve :premises (@p244 @p246)) % 0.37/0.61 (step @p248 :rule refl :args (@t112)) % 0.37/0.61 (step @p249 :rule refl :args (@t92)) % 0.37/0.61 (step @p250 :rule cong :premises (@p249 @p248) :args ((= @t92 @t112))) % 0.37/0.61 (step @p251 :rule symm :premises (@p250)) % 0.37/0.61 (step @p252 :rule eq_resolve :premises (@p249 @p251)) % 0.37/0.61 (step @p253 :rule cong :premises (@p252) :args (@t93)) % 0.37/0.61 (step @p254 :rule nary_cong :premises (@p253 @p247) :args (@t94)) % 0.37/0.61 (step @p255 :rule cong :premises (@p254) :args (@t95)) % 0.37/0.61 (step @p256 :rule cong :premises (@p255) :args (@t96)) % 0.37/0.61 (step @p257 :rule trans :premises (@p37 @p256)) % 0.37/0.61 (step @p258 :rule ho_cong :premises (@p257 @p242)) % 0.37/0.61 (step @p259 :rule ho_cong :premises (@p234 @p258)) % 0.37/0.61 (step @p260 :rule ho_cong :premises (@p259 @p236)) % 0.37/0.61 (step @p261 :rule refl :args (@t142)) % 0.37/0.61 (step @p262 :rule refl :args (@t23)) % 0.37/0.61 (step @p263 :rule cong :premises (@p262 @p261) :args ((= @t23 @t142))) % 0.37/0.61 (step @p264 :rule symm :premises (@p263)) % 0.37/0.61 (step @p265 :rule eq_resolve :premises (@p262 @p264)) % 0.37/0.61 (step @p266 :rule cong :premises (@p265) :args (@t86)) % 0.37/0.61 (step @p267 :rule cong :premises (@p266) :args (@t88)) % 0.37/0.61 (step @p268 :rule trans :premises (@p33 @p267)) % 0.37/0.61 (step @p269 :rule ho_cong :premises (@p268 @p260)) % 0.37/0.61 (step @p270 :rule cong :premises (@p269) :args (@t18)) % 0.37/0.61 (step @p271 :rule trans :premises (@p270 @p187)) % 0.37/0.61 (step @p272 :rule eq_resolve :premises (@p6 @p271)) % 0.37/0.61 (step @p273 :rule skolemize :premises (@p272)) % 0.37/0.61 (step @p274 :rule bool-double-not-elim :args (@t223)) % 0.37/0.61 (step @p275 :rule refl :args (@t231)) % 0.37/0.61 (step @p276 :rule nary_cong :premises (@p275 @p274) :args ((or @t231 (not @t230)))) % 0.37/0.61 (step @p277 :rule cnf_or_neg :args (@t231 0)) % 0.37/0.61 (step @p278 :rule eq_resolve :premises (@p277 @p276)) % 0.37/0.61 (step @p279 :rule reordering :premises (@p278) :args ((or @t223 @t231))) % 0.37/0.61 (step @p280 :rule chain_m_resolution :premises (@p279 @p273) :args (@t223 @t232 @t233)) % 0.37/0.61 (step @p281 :rule instantiate :premises (@p280) :args ((@list @t222 @t224))) % 0.37/0.61 (step @p282 :rule bool-double-not-elim :args (@t228)) % 0.37/0.61 (step @p283 :rule nary_cong :premises (@p275 @p282) :args ((or @t231 (not @t229)))) % 0.37/0.61 (step @p284 :rule cnf_or_neg :args (@t231 1)) % 0.37/0.61 (step @p285 :rule eq_resolve :premises (@p284 @p283)) % 0.37/0.61 (step @p286 :rule reordering :premises (@p285) :args ((or @t228 @t231))) % 0.37/0.61 (step @p287 :rule chain_m_resolution :premises (@p286 @p273) :args (@t228 @t232 @t233)) % 0.37/0.61 (step @p288 :rule instantiate :premises (@p287) :args ((@list @t224))) % 0.37/0.61 (step @p289 :rule bool-double-not-elim :args (@t226)) % 0.37/0.61 (step @p290 :rule nary_cong :premises (@p275 @p289) :args ((or @t231 (not @t227)))) % 0.37/0.61 (step @p291 :rule cnf_or_neg :args (@t231 2)) % 0.37/0.61 (step @p292 :rule eq_resolve :premises (@p291 @p290)) % 0.37/0.61 (step @p293 :rule reordering :premises (@p292) :args ((or @t226 @t231))) % 0.37/0.61 (step @p294 :rule chain_m_resolution :premises (@p293 @p273) :args (@t226 @t232 @t233)) % 0.37/0.61 (step @p295 :rule cnf_or_pos :args (@t235)) % 0.37/0.61 (step @p296 :rule reordering :premises (@p295) :args ((or @t227 @t234 (not @t235)))) % 0.37/0.61 (step @p297 :rule chain_m_resolution :premises (@p296 @p294 @p288) :args (@t234 (@list false false) (@list @t226 @t235))) % 0.37/0.61 (step @p298 :rule cnf_or_neg :args (@t231 3)) % 0.37/0.61 (step @p299 :rule chain_m_resolution :premises (@p298 @p273) :args ((not @t225) @t232 @t233)) % 0.37/0.61 (step @p300 :rule cnf_or_pos :args (@t239)) % 0.37/0.61 (step @p301 :rule reordering :premises (@p300) :args ((or @t227 @t225 @t238 @t236 (not @t239)))) % 0.37/0.61 (step @p302 :rule chain_m_resolution :premises (@p301 @p294 @p299 @p297 @p281) :args (@t238 (@list false true false false) (@list @t226 @t225 @t234 @t239))) % 0.37/0.61 (assume-push @p309 @t98) % 0.37/0.61 (step @p304 :rule instantiate :premises (@p51) :args ((@list @t222))) % 0.37/0.61 (step-pop @p310 :rule scope :premises (@p304)) % 0.37/0.61 (step @p305 :rule process_scope :premises (@p310) :args (@t237)) % 0.37/0.61 (step @p307 :rule implies_elim :premises (@p305)) % 0.37/0.61 (step @p308 false :rule chain_m_resolution :premises (@p307 @p302 @p51) :args (false (@list true false) (@list @t237 @t98))) % 0.37/0.61 ) % 0.37/0.61 % SZS output end Proof % 0.37/0.61 % cvc5 exiting %------------------------------------------------------------------------------