%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO478^6 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.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 09:12:57 AM UTC 2026 % Result : Theorem 0.38s 0.60s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO478^6 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n017.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 : Wed Jun 3 00:15:16 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.38/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.60 % SZS status Theorem % 0.38/0.60 % SZS output start Proof % 0.38/0.60 ( % 0.38/0.60 (declare-sort $$unsorted 0) % 0.38/0.60 (declare-sort tptp.mu 0) % 0.38/0.60 (declare-const tptp.rel_s5 (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.f (-> tptp.mu $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.38/0.60 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.38/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.38/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.38/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.38/0.60 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.60 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.60 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.38/0.60 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.38/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.38/0.60 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.38/0.60 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.38/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.60 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.60 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.60 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.38/0.60 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.38/0.60 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.38/0.60 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.38/0.60 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.38/0.60 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.38/0.60 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.38/0.60 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s5 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.38/0.60 (define tptp.mdia_s5 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s5 (_ tptp.mnot _let_2))) _let_1))))) % 0.38/0.60 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.60 (define @t2 () (@var "X" tptp.mu)) % 0.38/0.60 (define @t3 () (_ tptp.f @t2)) % 0.38/0.60 (define @t4 () (_ @t3 @t1)) % 0.38/0.60 (define @t5 () (@list @t2 @t1)) % 0.38/0.60 (define @t6 () (lambda @t5 @t4)) % 0.38/0.60 (define @t7 () (lambda @t5 (_ (_ tptp.mbox_s5 @t3) @t1))) % 0.38/0.60 (define @t8 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mexists_ind @t7)) (_ tptp.mbox_s5 (_ tptp.mexists_ind @t6)))))) % 0.38/0.60 (define @t9 () (@var "Y" tptp.mu)) % 0.38/0.60 (define @t10 () (@var "W" $$unsorted)) % 0.38/0.60 (define @t11 () (lambda (@list @t2 @t9 @t10) (= @t2 @t9))) % 0.38/0.60 (define @t12 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.60 (define @t13 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.60 (define @t14 () (lambda (@list @t13 @t12 @t10) (= (_ @t13 @t10) (_ @t12 @t10)))) % 0.38/0.60 (define @t15 () (@var "Phi" (-> $$unsorted Bool))) % 0.38/0.60 (define @t16 () (_ @t15 @t10)) % 0.38/0.60 (define @t17 () (not @t16)) % 0.38/0.60 (define @t18 () (@list @t15 @t10)) % 0.38/0.60 (define @t19 () (lambda @t18 @t17)) % 0.38/0.60 (define @t20 () (@var "Psi" (-> $$unsorted Bool))) % 0.38/0.60 (define @t21 () (_ @t20 @t10)) % 0.38/0.60 (define @t22 () (lambda (@list @t15 @t20 @t10) (or @t16 @t21))) % 0.38/0.60 (define @t23 () (_ tptp.mnot @t20)) % 0.38/0.60 (define @t24 () (_ tptp.mnot @t15)) % 0.38/0.60 (define @t25 () (_ tptp.mor @t24)) % 0.38/0.60 (define @t26 () (@list @t15 @t20 @t1)) % 0.38/0.60 (define @t27 () (lambda @t26 (_ (_ tptp.mnot (_ @t25 @t23)) @t1))) % 0.38/0.60 (define @t28 () (lambda @t26 (_ (_ @t25 @t20) @t1))) % 0.38/0.60 (define @t29 () (lambda @t26 (_ (_ (_ tptp.mor @t23) @t15) @t1))) % 0.38/0.60 (define @t30 () (lambda @t26 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t15) @t20)) (_ (_ tptp.mimplies @t20) @t15)) @t1))) % 0.38/0.60 (define @t31 () (lambda @t26 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t15) @t20)) @t1))) % 0.38/0.60 (define @t32 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.38/0.60 (define @t33 () (_ @t32 @t2)) % 0.38/0.60 (define @t34 () (_ @t33 @t10)) % 0.38/0.60 (define @t35 () (@list @t2)) % 0.38/0.60 (define @t36 () (forall @t35 @t34)) % 0.38/0.60 (define @t37 () (@list @t32 @t10)) % 0.38/0.60 (define @t38 () (lambda @t37 @t36)) % 0.38/0.60 (define @t39 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.60 (define @t40 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.38/0.60 (define @t41 () (_ @t40 @t39)) % 0.38/0.60 (define @t42 () (lambda (@list @t40 @t10) (forall (@list @t39) (_ @t41 @t10)))) % 0.38/0.60 (define @t43 () (lambda @t5 (_ (_ tptp.mnot @t33) @t1))) % 0.38/0.60 (define @t44 () (@list @t32 @t1)) % 0.38/0.60 (define @t45 () (lambda @t44 (_ (_ tptp.mnot (_ tptp.mforall_ind @t43)) @t1))) % 0.38/0.60 (define @t46 () (lambda (@list @t40 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t39 @t1) (_ (_ tptp.mnot @t41) @t1)))) @t1))) % 0.38/0.60 (define @t47 () (@list @t10)) % 0.38/0.60 (define @t48 () (lambda @t47 true)) % 0.38/0.60 (define @t49 () (@var "V" $$unsorted)) % 0.38/0.60 (define @t50 () (_ @t15 @t49)) % 0.38/0.60 (define @t51 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.60 (define @t52 () (@list @t49)) % 0.38/0.60 (define @t53 () (lambda (@list @t51 @t15 @t10) (forall @t52 (or (not (_ (_ @t51 @t10) @t49)) @t50)))) % 0.38/0.60 (define @t54 () (lambda (@list @t51 @t15 @t1) (_ (_ tptp.mnot (_ (_ tptp.mbox @t51) @t24)) @t1))) % 0.38/0.60 (define @t55 () (@var "S" $$unsorted)) % 0.38/0.60 (define @t56 () (_ @t51 @t55)) % 0.38/0.60 (define @t57 () (@list @t55)) % 0.38/0.60 (define @t58 () (@list @t51)) % 0.38/0.60 (define @t59 () (lambda @t58 (forall @t57 (_ @t56 @t55)))) % 0.38/0.60 (define @t60 () (@var "T" $$unsorted)) % 0.38/0.60 (define @t61 () (_ @t51 @t60)) % 0.38/0.60 (define @t62 () (_ @t56 @t60)) % 0.38/0.60 (define @t63 () (lambda @t58 (forall (@list @t55 @t60) (=> @t62 (_ @t61 @t55))))) % 0.38/0.60 (define @t64 () (@list @t60)) % 0.38/0.60 (define @t65 () (lambda @t58 (forall @t57 (exists @t64 @t62)))) % 0.38/0.60 (define @t66 () (@var "U" $$unsorted)) % 0.38/0.60 (define @t67 () (_ @t56 @t66)) % 0.38/0.60 (define @t68 () (_ @t61 @t66)) % 0.38/0.60 (define @t69 () (@list @t55 @t60 @t66)) % 0.38/0.60 (define @t70 () (lambda @t58 (forall @t69 (=> (and @t62 @t68) @t67)))) % 0.38/0.60 (define @t71 () (and @t62 @t67)) % 0.38/0.60 (define @t72 () (lambda @t58 (forall @t69 (=> @t71 @t68)))) % 0.38/0.60 (define @t73 () (= @t60 @t66)) % 0.38/0.60 (define @t74 () (lambda @t58 (forall @t69 (=> @t71 @t73)))) % 0.38/0.60 (define @t75 () (@list @t66)) % 0.38/0.60 (define @t76 () (lambda @t58 (forall @t57 (exists @t64 (and @t62 (forall @t75 (=> @t67 @t73))))))) % 0.38/0.60 (define @t77 () (_ @t51 @t66)) % 0.38/0.60 (define @t78 () (_ @t77 @t60)) % 0.38/0.60 (define @t79 () (lambda @t58 (forall @t69 (=> @t62 (exists @t75 (and @t67 @t78)))))) % 0.38/0.60 (define @t80 () (lambda @t58 (forall @t69 (=> @t71 (or @t68 @t73 @t78))))) % 0.38/0.60 (define @t81 () (lambda @t58 (forall @t69 (=> @t71 (exists @t52 (and (_ @t61 @t49) (_ @t77 @t49))))))) % 0.38/0.60 (define @t82 () (forall @t47 @t16)) % 0.38/0.60 (define @t83 () (@list @t15)) % 0.38/0.60 (define @t84 () (lambda @t83 @t82)) % 0.38/0.60 (define @t85 () (lambda @t83 (forall @t47 @t17))) % 0.38/0.60 (define @t86 () (lambda @t83 (exists @t47 @t16))) % 0.38/0.60 (define @t87 () (lambda @t83 (exists @t47 @t17))) % 0.38/0.60 (define @t88 () (_ (_ tptp.rel_s5 @t10) @t49)) % 0.38/0.60 (define @t89 () (not @t88)) % 0.38/0.60 (define @t90 () (or @t89 @t50)) % 0.38/0.60 (define @t91 () (forall @t52 @t90)) % 0.38/0.60 (define @t92 () (lambda @t18 @t91)) % 0.38/0.60 (define @t93 () (lambda (@list @t15 @t1) (_ (_ tptp.mnot (_ tptp.mbox_s5 @t24)) @t1))) % 0.38/0.60 (define @t94 () (@var "BOUND_VARIABLE_8508" $$unsorted)) % 0.38/0.60 (define @t95 () (not (forall @t35 (not (tptp.f @t2 @t94))))) % 0.38/0.60 (define @t96 () (not (tptp.rel_s5 @t10 @t94))) % 0.38/0.60 (define @t97 () (@var "BOUND_VARIABLE_8502" tptp.mu)) % 0.38/0.60 (define @t98 () (tptp.rel_s5 @t10 @t49)) % 0.38/0.60 (define @t99 () (not @t98)) % 0.38/0.60 (define @t100 () (not (forall @t52 (or @t99 (tptp.f @t97 @t49))))) % 0.38/0.60 (define @t101 () (or @t100 @t96 @t95)) % 0.38/0.60 (define @t102 () (or @t96 @t95)) % 0.38/0.60 (define @t103 () (or @t100 @t102)) % 0.38/0.60 (define @t104 () (@list @t10 @t97 @t94)) % 0.38/0.60 (define @t105 () (forall @t104 @t103)) % 0.38/0.60 (define @t106 () (forall (@list @t97 @t94) @t103)) % 0.38/0.60 (define @t107 () (forall (@list @t94) @t102)) % 0.38/0.60 (define @t108 () (forall (@list @t97) @t100)) % 0.38/0.60 (define @t109 () (or @t108 @t107)) % 0.38/0.60 (define @t110 () (tptp.f @t2 @t49)) % 0.38/0.60 (define @t111 () (not (forall @t35 (not @t110)))) % 0.38/0.60 (define @t112 () (forall @t52 (or @t99 @t111))) % 0.38/0.60 (define @t113 () (forall @t52 (or @t99 @t110))) % 0.38/0.60 (define @t114 () (or (forall @t35 (not @t113)) @t112)) % 0.38/0.60 (define @t115 () (not (tptp.rel_s5 @t1 @t49))) % 0.38/0.60 (define @t116 () (forall @t52 (or @t115 @t111))) % 0.38/0.60 (define @t117 () (forall @t52 (or @t115 @t110))) % 0.38/0.60 (define @t118 () (forall @t35 (not @t117))) % 0.38/0.60 (define @t119 () (@list @t1)) % 0.38/0.60 (define @t120 () (lambda @t119 (or @t118 @t116))) % 0.38/0.60 (define @t121 () (_ @t120 @t10)) % 0.38/0.60 (define @t122 () (forall @t47 @t121)) % 0.38/0.60 (define @t123 () (_ @t15 @t10)) % 0.38/0.60 (define @t124 () (lambda @t83 (forall @t47 @t123))) % 0.38/0.60 (define @t125 () (lambda @t47 @t112)) % 0.38/0.60 (define @t126 () (_ @t125 @t1)) % 0.38/0.60 (define @t127 () (or @t118 @t126)) % 0.38/0.60 (define @t128 () (lambda @t119 @t127)) % 0.38/0.60 (define @t129 () (_ @t20 @t1)) % 0.38/0.60 (define @t130 () (@list @t20 @t1)) % 0.38/0.60 (define @t131 () (tptp.f @t2 @t1)) % 0.38/0.60 (define @t132 () (lambda @t119 (not (forall @t35 (not @t131))))) % 0.38/0.60 (define @t133 () (_ @t132 @t49)) % 0.38/0.60 (define @t134 () (or @t99 @t133)) % 0.38/0.60 (define @t135 () (forall @t52 @t134)) % 0.38/0.60 (define @t136 () (lambda @t47 @t135)) % 0.38/0.60 (define @t137 () (_ @t15 @t49)) % 0.38/0.60 (define @t138 () (lambda @t18 (forall @t52 (or @t99 @t137)))) % 0.38/0.60 (define @t139 () (not @t4)) % 0.38/0.60 (define @t140 () (_ @t6 @t2 @t1)) % 0.38/0.60 (define @t141 () (not @t140)) % 0.38/0.60 (define @t142 () (forall @t35 @t141)) % 0.38/0.60 (define @t143 () (not @t142)) % 0.38/0.60 (define @t144 () (lambda @t119 @t143)) % 0.38/0.60 (define @t145 () (not (forall @t35 (not (_ @t32 @t2 @t1))))) % 0.38/0.60 (define @t146 () (lambda @t44 @t145)) % 0.38/0.60 (define @t147 () (_ @t146 @t6)) % 0.38/0.60 (define @t148 () (not @t118)) % 0.38/0.60 (define @t149 () (lambda @t119 @t148)) % 0.38/0.60 (define @t150 () (_ @t149 @t1)) % 0.38/0.60 (define @t151 () (not @t150)) % 0.38/0.60 (define @t152 () (or @t151 @t129)) % 0.38/0.60 (define @t153 () (lambda @t130 @t152)) % 0.38/0.60 (define @t154 () (or (not (_ @t15 @t1)) @t129)) % 0.38/0.60 (define @t155 () (lambda @t26 @t154)) % 0.38/0.60 (define @t156 () (lambda @t5 @t117)) % 0.38/0.60 (define @t157 () (_ @t156 @t2 @t1)) % 0.38/0.60 (define @t158 () (not @t157)) % 0.38/0.60 (define @t159 () (forall @t35 @t158)) % 0.38/0.60 (define @t160 () (not @t159)) % 0.38/0.60 (define @t161 () (lambda @t119 @t160)) % 0.38/0.60 (define @t162 () (_ @t3 @t49)) % 0.38/0.60 (define @t163 () (or @t99 @t162)) % 0.38/0.60 (define @t164 () (_ @t3 @t49)) % 0.38/0.60 (define @t165 () (or @t99 @t164)) % 0.38/0.60 (define @t166 () (forall @t52 @t165)) % 0.38/0.60 (define @t167 () (lambda @t47 @t166)) % 0.38/0.60 (define @t168 () (_ @t138 @t3)) % 0.38/0.60 (define @t169 () (lambda @t5 (_ @t168 @t1))) % 0.38/0.60 (define @t170 () (_ @t32 @t2 @t10)) % 0.38/0.60 (define @t171 () (forall @t35 (not @t170))) % 0.38/0.60 (define @t172 () (lambda @t47 @t171)) % 0.38/0.60 (define @t173 () (_ @t172 @t10)) % 0.38/0.60 (define @t174 () (not @t173)) % 0.38/0.60 (define @t175 () (lambda @t47 @t174)) % 0.38/0.60 (define @t176 () (not @t34)) % 0.38/0.60 (define @t177 () (not (_ @t33 @t1))) % 0.38/0.60 (define @t178 () (lambda @t5 @t177)) % 0.38/0.60 (define @t179 () (_ @t178 @t2 @t10)) % 0.38/0.60 (define @t180 () (forall @t35 @t179)) % 0.38/0.60 (define @t181 () (lambda @t47 @t180)) % 0.38/0.60 (define @t182 () (lambda @t37 (forall @t35 @t170))) % 0.38/0.60 (define @t183 () (lambda @t47 @t176)) % 0.38/0.60 (define @t184 () (_ @t19 @t33)) % 0.38/0.60 (define @t185 () (or @t17 @t21)) % 0.38/0.60 (define @t186 () (lambda @t47 @t185)) % 0.38/0.60 (define @t187 () (@list @t20 @t10)) % 0.38/0.60 (define @t188 () (lambda @t47 @t17)) % 0.38/0.60 (define @t189 () (_ @t188 @t10)) % 0.38/0.60 (define @t190 () (or @t189 @t21)) % 0.38/0.60 (define @t191 () (lambda @t187 @t190)) % 0.38/0.60 (define @t192 () (forall @t104 @t101)) % 0.38/0.60 (define @t193 () (@quantifiers_skolemize @t192 2)) % 0.38/0.60 (define @t194 () (forall @t35 (not (tptp.f @t2 @t193)))) % 0.38/0.60 (define @t195 () (not @t194)) % 0.38/0.60 (define @t196 () (@quantifiers_skolemize @t192 0)) % 0.38/0.60 (define @t197 () (tptp.rel_s5 @t196 @t193)) % 0.38/0.60 (define @t198 () (not @t197)) % 0.38/0.60 (define @t199 () (@quantifiers_skolemize @t192 1)) % 0.38/0.60 (define @t200 () (forall @t52 (or (not (tptp.rel_s5 @t196 @t49)) (tptp.f @t199 @t49)))) % 0.38/0.60 (define @t201 () (not @t200)) % 0.38/0.60 (define @t202 () (or @t201 @t198 @t195)) % 0.38/0.60 (define @t203 () (@list true)) % 0.38/0.60 (define @t204 () (@list @t202)) % 0.38/0.60 (define @t205 () (tptp.f @t199 @t193)) % 0.38/0.60 (define @t206 () (or @t198 @t205)) % 0.38/0.60 (define @t207 () (@list false false)) % 0.38/0.60 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.38/0.60 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.38/0.60 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.38/0.60 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.38/0.60 (assume @p5 @t8) % 0.38/0.60 (assume @p6 true) % 0.38/0.60 (step @p7 (= tptp.meq_ind @t11) :rule refl :args (@t11)) % 0.38/0.60 (step @p8 (= tptp.meq_prop @t14) :rule refl :args (@t14)) % 0.38/0.60 (step @p9 (= tptp.mnot @t19) :rule refl :args (@t19)) % 0.38/0.60 (step @p10 (= tptp.mor @t22) :rule refl :args (@t22)) % 0.38/0.60 (step @p11 (= tptp.mand @t27) :rule refl :args (@t27)) % 0.38/0.60 (step @p12 (= tptp.mimplies @t28) :rule refl :args (@t28)) % 0.38/0.60 (step @p13 (= tptp.mimplied @t29) :rule refl :args (@t29)) % 0.38/0.60 (step @p14 (= tptp.mequiv @t30) :rule refl :args (@t30)) % 0.38/0.60 (step @p15 (= tptp.mxor @t31) :rule refl :args (@t31)) % 0.38/0.60 (step @p16 (= tptp.mforall_ind @t38) :rule refl :args (@t38)) % 0.38/0.60 (step @p17 (= tptp.mforall_prop @t42) :rule refl :args (@t42)) % 0.38/0.60 (step @p18 (= tptp.mexists_ind @t45) :rule refl :args (@t45)) % 0.38/0.60 (step @p19 (= tptp.mexists_prop @t46) :rule refl :args (@t46)) % 0.38/0.60 (step @p20 (= tptp.mtrue @t48) :rule refl :args (@t48)) % 0.38/0.60 (step @p21 (= tptp.mbox @t53) :rule refl :args (@t53)) % 0.38/0.60 (step @p22 (= tptp.mdia @t54) :rule refl :args (@t54)) % 0.38/0.60 (step @p23 (= tptp.mreflexive @t59) :rule refl :args (@t59)) % 0.38/0.60 (step @p24 (= tptp.msymmetric @t63) :rule refl :args (@t63)) % 0.38/0.60 (step @p25 (= tptp.mserial @t65) :rule refl :args (@t65)) % 0.38/0.60 (step @p26 (= tptp.mtransitive @t70) :rule refl :args (@t70)) % 0.38/0.60 (step @p27 (= tptp.meuclidean @t72) :rule refl :args (@t72)) % 0.38/0.60 (step @p28 (= tptp.mpartially_functional @t74) :rule refl :args (@t74)) % 0.38/0.60 (step @p29 (= tptp.mfunctional @t76) :rule refl :args (@t76)) % 0.38/0.60 (step @p30 (= tptp.mweakly_dense @t79) :rule refl :args (@t79)) % 0.38/0.60 (step @p31 (= tptp.mweakly_connected @t80) :rule refl :args (@t80)) % 0.38/0.60 (step @p32 (= tptp.mweakly_directed @t81) :rule refl :args (@t81)) % 0.38/0.60 (step @p33 (= tptp.mvalid @t84) :rule refl :args (@t84)) % 0.38/0.60 (step @p34 (= tptp.minvalid @t85) :rule refl :args (@t85)) % 0.38/0.60 (step @p35 (= tptp.msatisfiable @t86) :rule refl :args (@t86)) % 0.38/0.60 (step @p36 (= tptp.mcountersatisfiable @t87) :rule refl :args (@t87)) % 0.38/0.60 (step @p37 (= tptp.mbox_s5 @t92) :rule refl :args (@t92)) % 0.38/0.60 (step @p38 (= tptp.mdia_s5 @t93) :rule refl :args (@t93)) % 0.38/0.60 (step @p39 :rule aci_norm :args ((= @t103 @t101))) % 0.38/0.60 (step @p40 :rule cong :premises (@p39) :args (@t105)) % 0.38/0.60 (step @p41 :rule quant-merge-prenex :args ((= (forall @t47 @t106) @t105))) % 0.38/0.60 (step @p42 :rule alpha_equiv :args (@t107 (@list @t94) (@list @t49))) % 0.38/0.60 (step @p43 :rule alpha_equiv :args (@t108 (@list @t97) (@list @t2))) % 0.38/0.60 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t109)) % 0.38/0.60 (step @p45 :rule quant-miniscope-or :args ((= @t106 @t109))) % 0.38/0.60 (step @p46 :rule trans :premises (@p45 @p44)) % 0.38/0.60 (step @p47 :rule symm :premises (@p46)) % 0.38/0.60 (step @p48 :rule cong :premises (@p47) :args ((forall @t47 @t114))) % 0.38/0.60 (step @p49 :rule trans :premises (@p48 @p41)) % 0.38/0.60 (step @p50 :rule trans :premises (@p49 @p40)) % 0.38/0.60 (step @p51 :rule beta-reduce :args ((= @t121 @t114))) % 0.38/0.60 (step @p52 :rule cong :premises (@p51) :args (@t122)) % 0.38/0.60 (step @p53 :rule trans :premises (@p52 @p50)) % 0.38/0.60 (step @p54 :rule beta-reduce :args ((= (_ @t124 @t120) @t122))) % 0.38/0.60 (step @p55 :rule trans :premises (@p54 @p53)) % 0.38/0.60 (step @p56 :rule beta-reduce :args ((= @t126 @t116))) % 0.38/0.60 (step @p57 :rule refl :args (@t118)) % 0.38/0.60 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t127)) % 0.38/0.60 (step @p59 :rule cong :premises (@p58) :args (@t128)) % 0.38/0.60 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t130 (or @t118 @t129)) @t125) @t128))) % 0.38/0.60 (step @p61 :rule trans :premises (@p60 @p59)) % 0.38/0.60 (step @p62 :rule beta-reduce :args ((= @t133 @t111))) % 0.38/0.60 (step @p63 :rule refl :args (@t99)) % 0.38/0.60 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t134)) % 0.38/0.60 (step @p65 :rule cong :premises (@p64) :args (@t135)) % 0.38/0.60 (step @p66 :rule cong :premises (@p65) :args (@t136)) % 0.38/0.60 (step @p67 :rule beta-reduce :args ((= (_ @t138 @t132) @t136))) % 0.38/0.60 (step @p68 :rule trans :premises (@p67 @p66)) % 0.38/0.60 (step @p69 :rule refl :args (@t131)) % 0.38/0.60 (step @p70 :rule refl :args (@t4)) % 0.38/0.60 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t4 @t131))) % 0.38/0.60 (step @p72 :rule symm :premises (@p71)) % 0.38/0.60 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.38/0.60 (step @p74 :rule cong :premises (@p73) :args (@t139)) % 0.38/0.60 (step @p75 :rule cong :premises (@p74) :args ((forall @t35 @t139))) % 0.38/0.60 (step @p76 :rule beta-reduce :args ((= @t140 @t4))) % 0.38/0.60 (step @p77 :rule cong :premises (@p76) :args (@t141)) % 0.38/0.60 (step @p78 :rule cong :premises (@p77) :args (@t142)) % 0.38/0.60 (step @p79 :rule trans :premises (@p78 @p75)) % 0.38/0.60 (step @p80 :rule cong :premises (@p79) :args (@t143)) % 0.38/0.60 (step @p81 :rule cong :premises (@p80) :args (@t144)) % 0.38/0.60 (step @p82 :rule beta-reduce :args ((= @t147 @t144))) % 0.38/0.60 (step @p83 :rule trans :premises (@p82 @p81)) % 0.38/0.60 (step @p84 :rule refl :args (@t138)) % 0.38/0.60 (step @p85 :rule ho_cong :premises (@p84 @p83)) % 0.38/0.60 (step @p86 :rule trans :premises (@p85 @p68)) % 0.38/0.60 (step @p87 :rule refl :args (@t129)) % 0.38/0.60 (step @p88 :rule bool-double-not-elim :args (@t118)) % 0.38/0.60 (step @p89 :rule beta-reduce :args ((= @t150 @t148))) % 0.38/0.60 (step @p90 :rule cong :premises (@p89) :args (@t151)) % 0.38/0.60 (step @p91 :rule trans :premises (@p90 @p88)) % 0.38/0.60 (step @p92 :rule nary_cong :premises (@p91 @p87) :args (@t152)) % 0.38/0.60 (step @p93 :rule cong :premises (@p92) :args (@t153)) % 0.38/0.60 (step @p94 :rule beta-reduce :args ((= (_ @t155 @t149) @t153))) % 0.38/0.60 (step @p95 :rule trans :premises (@p94 @p93)) % 0.38/0.60 (step @p96 :rule beta-reduce :args ((= @t157 @t117))) % 0.38/0.60 (step @p97 :rule cong :premises (@p96) :args (@t158)) % 0.38/0.60 (step @p98 :rule cong :premises (@p97) :args (@t159)) % 0.38/0.60 (step @p99 :rule cong :premises (@p98) :args (@t160)) % 0.38/0.60 (step @p100 :rule cong :premises (@p99) :args (@t161)) % 0.38/0.60 (step @p101 :rule beta-reduce :args ((= (_ @t146 @t156) @t161))) % 0.38/0.60 (step @p102 :rule trans :premises (@p101 @p100)) % 0.38/0.60 (step @p103 :rule beta-reduce :args ((= (_ (lambda @t47 @t113) @t1) @t117))) % 0.38/0.60 (step @p104 :rule refl :args (@t1)) % 0.38/0.60 (step @p105 :rule refl :args (@t110)) % 0.38/0.60 (step @p106 :rule refl :args (@t162)) % 0.38/0.60 (step @p107 :rule cong :premises (@p106 @p105) :args ((= @t162 @t110))) % 0.38/0.60 (step @p108 :rule symm :premises (@p107)) % 0.38/0.60 (step @p109 :rule eq_resolve :premises (@p106 @p108)) % 0.38/0.60 (step @p110 :rule refl :args (@t99)) % 0.38/0.60 (step @p111 :rule nary_cong :premises (@p110 @p109) :args (@t163)) % 0.38/0.60 (step @p112 :rule cong :premises (@p111) :args ((forall @t52 @t163))) % 0.38/0.60 (step @p113 :rule refl :args (@t164)) % 0.38/0.60 (step @p114 :rule nary_cong :premises (@p63 @p113) :args (@t165)) % 0.38/0.60 (step @p115 :rule cong :premises (@p114) :args (@t166)) % 0.38/0.60 (step @p116 :rule trans :premises (@p115 @p112)) % 0.38/0.60 (step @p117 :rule cong :premises (@p116) :args (@t167)) % 0.38/0.60 (step @p118 :rule beta-reduce :args ((= @t168 @t167))) % 0.38/0.60 (step @p119 :rule trans :premises (@p118 @p117)) % 0.38/0.60 (step @p120 :rule ho_cong :premises (@p119 @p104)) % 0.38/0.60 (step @p121 :rule trans :premises (@p120 @p103)) % 0.38/0.60 (step @p122 :rule cong :premises (@p121) :args (@t169)) % 0.38/0.60 (step @p123 :rule refl :args (@t146)) % 0.38/0.60 (step @p124 :rule ho_cong :premises (@p123 @p122)) % 0.38/0.60 (step @p125 :rule trans :premises (@p124 @p102)) % 0.38/0.60 (step @p126 :rule refl :args (@t155)) % 0.38/0.60 (step @p127 :rule ho_cong :premises (@p126 @p125)) % 0.38/0.60 (step @p128 :rule trans :premises (@p127 @p95)) % 0.38/0.60 (step @p129 :rule ho_cong :premises (@p128 @p86)) % 0.38/0.60 (step @p130 :rule trans :premises (@p129 @p61)) % 0.38/0.60 (step @p131 :rule refl :args (@t124)) % 0.38/0.60 (step @p132 :rule ho_cong :premises (@p131 @p130)) % 0.38/0.60 (step @p133 :rule trans :premises (@p132 @p55)) % 0.38/0.60 (step @p134 :rule cong :premises (@p133) :args ((not (_ @t124 (_ (_ @t155 (_ @t146 @t169)) (_ @t138 @t147)))))) % 0.38/0.60 (step @p135 :rule refl :args (@t6)) % 0.38/0.60 (step @p136 :rule beta-reduce :args ((= (_ (lambda @t47 (not @t171)) @t1) @t145))) % 0.38/0.60 (step @p137 :rule beta-reduce :args ((= @t173 @t171))) % 0.38/0.60 (step @p138 :rule cong :premises (@p137) :args (@t174)) % 0.38/0.60 (step @p139 :rule cong :premises (@p138) :args (@t175)) % 0.38/0.60 (step @p140 :rule beta-reduce :args ((= (_ @t19 @t172) @t175))) % 0.38/0.60 (step @p141 :rule trans :premises (@p140 @p139)) % 0.38/0.60 (step @p142 :rule refl :args (@t170)) % 0.38/0.60 (step @p143 :rule refl :args (@t34)) % 0.38/0.60 (step @p144 :rule cong :premises (@p143 @p142) :args ((= @t34 @t170))) % 0.38/0.60 (step @p145 :rule symm :premises (@p144)) % 0.38/0.60 (step @p146 :rule eq_resolve :premises (@p143 @p145)) % 0.38/0.60 (step @p147 :rule cong :premises (@p146) :args (@t176)) % 0.38/0.60 (step @p148 :rule cong :premises (@p147) :args ((forall @t35 @t176))) % 0.38/0.60 (step @p149 :rule beta-reduce :args ((= @t179 @t176))) % 0.38/0.60 (step @p150 :rule cong :premises (@p149) :args (@t180)) % 0.38/0.60 (step @p151 :rule trans :premises (@p150 @p148)) % 0.38/0.60 (step @p152 :rule cong :premises (@p151) :args (@t181)) % 0.38/0.60 (step @p153 :rule beta-reduce :args ((= (_ @t182 @t178) @t181))) % 0.38/0.60 (step @p154 :rule trans :premises (@p153 @p152)) % 0.38/0.60 (step @p155 :rule beta-reduce :args ((= (_ @t183 @t1) @t177))) % 0.38/0.60 (step @p156 :rule beta-reduce :args ((= @t184 @t183))) % 0.38/0.60 (step @p157 :rule ho_cong :premises (@p156 @p104)) % 0.38/0.60 (step @p158 :rule trans :premises (@p157 @p155)) % 0.38/0.60 (step @p159 :rule cong :premises (@p158) :args ((lambda @t5 (_ @t184 @t1)))) % 0.38/0.60 (step @p160 :rule refl :args (@t182)) % 0.38/0.60 (step @p161 :rule ho_cong :premises (@p160 @p159)) % 0.38/0.60 (step @p162 :rule trans :premises (@p161 @p154)) % 0.38/0.60 (step @p163 :rule refl :args (@t19)) % 0.38/0.60 (step @p164 :rule ho_cong :premises (@p163 @p162)) % 0.38/0.60 (step @p165 :rule trans :premises (@p164 @p141)) % 0.38/0.60 (step @p166 :rule ho_cong :premises (@p165 @p104)) % 0.38/0.60 (step @p167 :rule trans :premises (@p166 @p136)) % 0.38/0.60 (step @p168 :rule refl :args (@t33)) % 0.38/0.60 (step @p169 :rule ho_cong :premises (@p9 @p168)) % 0.38/0.60 (step @p170 :rule ho_cong :premises (@p169 @p104)) % 0.38/0.60 (step @p171 :rule cong :premises (@p170) :args (@t43)) % 0.38/0.60 (step @p172 :rule cong :premises (@p146) :args (@t36)) % 0.38/0.60 (step @p173 :rule cong :premises (@p172) :args (@t38)) % 0.38/0.60 (step @p174 :rule trans :premises (@p16 @p173)) % 0.38/0.60 (step @p175 :rule ho_cong :premises (@p174 @p171)) % 0.38/0.60 (step @p176 :rule ho_cong :premises (@p9 @p175)) % 0.38/0.60 (step @p177 :rule ho_cong :premises (@p176 @p104)) % 0.38/0.60 (step @p178 :rule trans :premises (@p177 @p167)) % 0.38/0.60 (step @p179 :rule cong :premises (@p178) :args (@t45)) % 0.38/0.60 (step @p180 :rule trans :premises (@p18 @p179)) % 0.38/0.60 (step @p181 :rule ho_cong :premises (@p180 @p135)) % 0.38/0.60 (step @p182 :rule refl :args (@t137)) % 0.38/0.60 (step @p183 :rule refl :args (@t50)) % 0.38/0.60 (step @p184 :rule cong :premises (@p183 @p182) :args ((= @t50 @t137))) % 0.38/0.60 (step @p185 :rule symm :premises (@p184)) % 0.38/0.60 (step @p186 :rule eq_resolve :premises (@p183 @p185)) % 0.38/0.60 (step @p187 :rule refl :args (@t98)) % 0.38/0.60 (step @p188 :rule refl :args (@t88)) % 0.38/0.60 (step @p189 :rule cong :premises (@p188 @p187) :args ((= @t88 @t98))) % 0.38/0.60 (step @p190 :rule symm :premises (@p189)) % 0.38/0.60 (step @p191 :rule eq_resolve :premises (@p188 @p190)) % 0.38/0.60 (step @p192 :rule cong :premises (@p191) :args (@t89)) % 0.38/0.60 (step @p193 :rule nary_cong :premises (@p192 @p186) :args (@t90)) % 0.38/0.60 (step @p194 :rule cong :premises (@p193) :args (@t91)) % 0.38/0.60 (step @p195 :rule cong :premises (@p194) :args (@t92)) % 0.38/0.60 (step @p196 :rule trans :premises (@p37 @p195)) % 0.38/0.60 (step @p197 :rule ho_cong :premises (@p196 @p181)) % 0.38/0.60 (step @p198 :rule refl :args (@t3)) % 0.38/0.60 (step @p199 :rule ho_cong :premises (@p196 @p198)) % 0.38/0.60 (step @p200 :rule ho_cong :premises (@p199 @p104)) % 0.38/0.60 (step @p201 :rule cong :premises (@p200) :args (@t7)) % 0.38/0.60 (step @p202 :rule ho_cong :premises (@p180 @p201)) % 0.38/0.60 (step @p203 :rule beta-reduce :args ((= (_ @t186 @t1) @t154))) % 0.38/0.60 (step @p204 :rule beta-reduce :args ((= (_ (lambda @t187 @t185) @t20) @t186))) % 0.38/0.60 (step @p205 :rule refl :args (@t20)) % 0.38/0.60 (step @p206 :rule refl :args (@t21)) % 0.38/0.60 (step @p207 :rule beta-reduce :args ((= @t189 @t17))) % 0.38/0.60 (step @p208 :rule nary_cong :premises (@p207 @p206) :args (@t190)) % 0.38/0.60 (step @p209 :rule cong :premises (@p208) :args (@t191)) % 0.38/0.60 (step @p210 :rule beta-reduce :args ((= (_ @t22 @t188) @t191))) % 0.38/0.60 (step @p211 :rule trans :premises (@p210 @p209)) % 0.38/0.60 (step @p212 :rule beta-reduce :args ((= (_ @t19 @t15) @t188))) % 0.38/0.60 (step @p213 :rule refl :args (@t22)) % 0.38/0.60 (step @p214 :rule ho_cong :premises (@p213 @p212)) % 0.38/0.60 (step @p215 :rule trans :premises (@p214 @p211)) % 0.38/0.60 (step @p216 :rule ho_cong :premises (@p215 @p205)) % 0.38/0.60 (step @p217 :rule trans :premises (@p216 @p204)) % 0.38/0.60 (step @p218 :rule ho_cong :premises (@p217 @p104)) % 0.38/0.60 (step @p219 :rule trans :premises (@p218 @p203)) % 0.38/0.60 (step @p220 :rule refl :args (@t15)) % 0.38/0.60 (step @p221 :rule ho_cong :premises (@p9 @p220)) % 0.38/0.60 (step @p222 :rule ho_cong :premises (@p10 @p221)) % 0.38/0.60 (step @p223 :rule ho_cong :premises (@p222 @p205)) % 0.38/0.60 (step @p224 :rule ho_cong :premises (@p223 @p104)) % 0.38/0.60 (step @p225 :rule trans :premises (@p224 @p219)) % 0.38/0.60 (step @p226 :rule cong :premises (@p225) :args (@t28)) % 0.38/0.60 (step @p227 :rule trans :premises (@p12 @p226)) % 0.38/0.60 (step @p228 :rule ho_cong :premises (@p227 @p202)) % 0.38/0.60 (step @p229 :rule ho_cong :premises (@p228 @p197)) % 0.38/0.60 (step @p230 :rule refl :args (@t123)) % 0.38/0.60 (step @p231 :rule refl :args (@t16)) % 0.38/0.60 (step @p232 :rule cong :premises (@p231 @p230) :args ((= @t16 @t123))) % 0.38/0.60 (step @p233 :rule symm :premises (@p232)) % 0.38/0.60 (step @p234 :rule eq_resolve :premises (@p231 @p233)) % 0.38/0.60 (step @p235 :rule cong :premises (@p234) :args (@t82)) % 0.38/0.60 (step @p236 :rule cong :premises (@p235) :args (@t84)) % 0.38/0.60 (step @p237 :rule trans :premises (@p33 @p236)) % 0.38/0.60 (step @p238 :rule ho_cong :premises (@p237 @p229)) % 0.38/0.60 (step @p239 :rule cong :premises (@p238) :args (@t8)) % 0.38/0.60 (step @p240 :rule trans :premises (@p239 @p134)) % 0.38/0.60 (step @p241 :rule eq_resolve :premises (@p5 @p240)) % 0.38/0.60 (step @p242 :rule skolemize :premises (@p241)) % 0.38/0.60 (step @p243 :rule bool-double-not-elim :args (@t194)) % 0.38/0.60 (step @p244 :rule refl :args (@t202)) % 0.38/0.60 (step @p245 :rule nary_cong :premises (@p244 @p243) :args ((or @t202 (not @t195)))) % 0.38/0.60 (step @p246 :rule cnf_or_neg :args (@t202 2)) % 0.38/0.60 (step @p247 :rule eq_resolve :premises (@p246 @p245)) % 0.38/0.60 (step @p248 :rule reordering :premises (@p247) :args ((or @t194 @t202))) % 0.38/0.60 (step @p249 :rule chain_m_resolution :premises (@p248 @p242) :args (@t194 @t203 @t204)) % 0.38/0.60 (step @p250 :rule bool-double-not-elim :args (@t200)) % 0.38/0.60 (step @p251 :rule nary_cong :premises (@p244 @p250) :args ((or @t202 (not @t201)))) % 0.38/0.60 (step @p252 :rule cnf_or_neg :args (@t202 0)) % 0.38/0.60 (step @p253 :rule eq_resolve :premises (@p252 @p251)) % 0.38/0.60 (step @p254 :rule reordering :premises (@p253) :args ((or @t200 @t202))) % 0.38/0.60 (step @p255 :rule chain_m_resolution :premises (@p254 @p242) :args (@t200 @t203 @t204)) % 0.38/0.60 (step @p256 :rule instantiate :premises (@p255) :args ((@list @t193))) % 0.38/0.60 (step @p257 :rule bool-double-not-elim :args (@t197)) % 0.38/0.60 (step @p258 :rule nary_cong :premises (@p244 @p257) :args ((or @t202 (not @t198)))) % 0.38/0.60 (step @p259 :rule cnf_or_neg :args (@t202 1)) % 0.38/0.60 (step @p260 :rule eq_resolve :premises (@p259 @p258)) % 0.38/0.60 (step @p261 :rule reordering :premises (@p260) :args ((or @t197 @t202))) % 0.38/0.60 (step @p262 :rule chain_m_resolution :premises (@p261 @p242) :args (@t197 @t203 @t204)) % 0.38/0.60 (step @p263 :rule cnf_or_pos :args (@t206)) % 0.38/0.61 (step @p264 :rule reordering :premises (@p263) :args ((or @t198 @t205 (not @t206)))) % 0.38/0.61 (step @p265 :rule chain_m_resolution :premises (@p264 @p262 @p256) :args (@t205 @t207 (@list @t197 @t206))) % 0.38/0.61 (assume-push @p272 @t194) % 0.38/0.61 (step @p267 :rule instantiate :premises (@p249) :args ((@list @t199))) % 0.38/0.61 (step-pop @p273 :rule scope :premises (@p267)) % 0.38/0.61 (step @p268 :rule process_scope :premises (@p273) :args ((not @t205))) % 0.38/0.61 (step @p270 :rule implies_elim :premises (@p268)) % 0.38/0.61 (step @p271 false :rule chain_m_resolution :premises (@p270 @p265 @p249) :args (false @t207 (@list @t205 @t194))) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------