%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO483^6 : 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 : n002.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 0.39s 0.60s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO483^6 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n002.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 00:16:33 EDT 2026 % 0.16/0.35 % CPUTime : % 0.30/0.51 %----Proving TH0 % 0.39/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.60 % SZS status Theorem % 0.39/0.60 % SZS output start Proof % 0.39/0.60 ( % 0.39/0.60 (declare-sort $$unsorted 0) % 0.39/0.60 (declare-sort tptp.mu 0) % 0.39/0.60 (declare-const tptp.rel_s5 (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.a tptp.mu) % 0.39/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.39/0.60 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.39/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.39/0.60 (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)))))) % 0.39/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.39/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.39/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (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))))))) % 0.39/0.60 (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))))))) % 0.39/0.60 (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)))))) % 0.39/0.60 (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)))))) % 0.39/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.39/0.60 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.39/0.60 (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)))))) % 0.39/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.39/0.60 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.39/0.60 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.39/0.60 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.39/0.60 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.39/0.60 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.39/0.60 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.39/0.60 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.39/0.60 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.39/0.60 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.39/0.60 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.39/0.60 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.39/0.60 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$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)))))))) % 0.39/0.60 (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))))) % 0.39/0.60 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.39/0.60 (define @t2 () (@var "X" tptp.mu)) % 0.39/0.60 (define @t3 () (@list @t2 @t1)) % 0.39/0.60 (define @t4 () (lambda @t3 (_ (_ tptp.mbox_s5 (_ (_ tptp.meq_ind @t2) tptp.a)) @t1))) % 0.39/0.60 (define @t5 () (not (_ tptp.mvalid (_ tptp.mexists_ind @t4)))) % 0.39/0.60 (define @t6 () (@var "Y" tptp.mu)) % 0.39/0.60 (define @t7 () (= @t2 @t6)) % 0.39/0.60 (define @t8 () (@var "W" $$unsorted)) % 0.39/0.60 (define @t9 () (lambda (@list @t2 @t6 @t8) @t7)) % 0.39/0.60 (define @t10 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.60 (define @t11 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.60 (define @t12 () (lambda (@list @t11 @t10 @t8) (= (_ @t11 @t8) (_ @t10 @t8)))) % 0.39/0.60 (define @t13 () (@var "Phi" (-> $$unsorted Bool))) % 0.39/0.60 (define @t14 () (_ @t13 @t8)) % 0.39/0.60 (define @t15 () (not @t14)) % 0.39/0.60 (define @t16 () (@list @t13 @t8)) % 0.39/0.60 (define @t17 () (lambda @t16 @t15)) % 0.39/0.60 (define @t18 () (@var "Psi" (-> $$unsorted Bool))) % 0.39/0.60 (define @t19 () (lambda (@list @t13 @t18 @t8) (or @t14 (_ @t18 @t8)))) % 0.39/0.60 (define @t20 () (_ tptp.mnot @t18)) % 0.39/0.60 (define @t21 () (_ tptp.mnot @t13)) % 0.39/0.60 (define @t22 () (_ tptp.mor @t21)) % 0.39/0.60 (define @t23 () (@list @t13 @t18 @t1)) % 0.39/0.60 (define @t24 () (lambda @t23 (_ (_ tptp.mnot (_ @t22 @t20)) @t1))) % 0.39/0.60 (define @t25 () (lambda @t23 (_ (_ @t22 @t18) @t1))) % 0.39/0.60 (define @t26 () (lambda @t23 (_ (_ (_ tptp.mor @t20) @t13) @t1))) % 0.39/0.60 (define @t27 () (lambda @t23 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t13) @t18)) (_ (_ tptp.mimplies @t18) @t13)) @t1))) % 0.39/0.60 (define @t28 () (lambda @t23 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t13) @t18)) @t1))) % 0.39/0.60 (define @t29 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.39/0.60 (define @t30 () (_ @t29 @t2)) % 0.39/0.60 (define @t31 () (_ @t30 @t8)) % 0.39/0.60 (define @t32 () (@list @t2)) % 0.39/0.60 (define @t33 () (forall @t32 @t31)) % 0.39/0.60 (define @t34 () (@list @t29 @t8)) % 0.39/0.60 (define @t35 () (lambda @t34 @t33)) % 0.39/0.60 (define @t36 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.60 (define @t37 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.39/0.60 (define @t38 () (_ @t37 @t36)) % 0.39/0.60 (define @t39 () (lambda (@list @t37 @t8) (forall (@list @t36) (_ @t38 @t8)))) % 0.39/0.60 (define @t40 () (lambda @t3 (_ (_ tptp.mnot @t30) @t1))) % 0.39/0.60 (define @t41 () (@list @t29 @t1)) % 0.39/0.60 (define @t42 () (lambda @t41 (_ (_ tptp.mnot (_ tptp.mforall_ind @t40)) @t1))) % 0.39/0.60 (define @t43 () (lambda (@list @t37 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t36 @t1) (_ (_ tptp.mnot @t38) @t1)))) @t1))) % 0.39/0.60 (define @t44 () (@list @t8)) % 0.39/0.60 (define @t45 () (lambda @t44 true)) % 0.39/0.60 (define @t46 () (@var "V" $$unsorted)) % 0.39/0.60 (define @t47 () (_ @t13 @t46)) % 0.39/0.60 (define @t48 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.39/0.60 (define @t49 () (@list @t46)) % 0.39/0.60 (define @t50 () (lambda (@list @t48 @t13 @t8) (forall @t49 (or (not (_ (_ @t48 @t8) @t46)) @t47)))) % 0.39/0.60 (define @t51 () (lambda (@list @t48 @t13 @t1) (_ (_ tptp.mnot (_ (_ tptp.mbox @t48) @t21)) @t1))) % 0.39/0.60 (define @t52 () (@var "S" $$unsorted)) % 0.39/0.60 (define @t53 () (_ @t48 @t52)) % 0.39/0.60 (define @t54 () (@list @t52)) % 0.39/0.60 (define @t55 () (@list @t48)) % 0.39/0.60 (define @t56 () (lambda @t55 (forall @t54 (_ @t53 @t52)))) % 0.39/0.60 (define @t57 () (@var "T" $$unsorted)) % 0.39/0.60 (define @t58 () (_ @t48 @t57)) % 0.39/0.60 (define @t59 () (_ @t53 @t57)) % 0.39/0.60 (define @t60 () (lambda @t55 (forall (@list @t52 @t57) (=> @t59 (_ @t58 @t52))))) % 0.39/0.60 (define @t61 () (@list @t57)) % 0.39/0.60 (define @t62 () (lambda @t55 (forall @t54 (exists @t61 @t59)))) % 0.39/0.60 (define @t63 () (@var "U" $$unsorted)) % 0.39/0.60 (define @t64 () (_ @t53 @t63)) % 0.39/0.60 (define @t65 () (_ @t58 @t63)) % 0.39/0.60 (define @t66 () (@list @t52 @t57 @t63)) % 0.39/0.60 (define @t67 () (lambda @t55 (forall @t66 (=> (and @t59 @t65) @t64)))) % 0.39/0.60 (define @t68 () (and @t59 @t64)) % 0.39/0.60 (define @t69 () (lambda @t55 (forall @t66 (=> @t68 @t65)))) % 0.39/0.60 (define @t70 () (= @t57 @t63)) % 0.39/0.60 (define @t71 () (lambda @t55 (forall @t66 (=> @t68 @t70)))) % 0.39/0.60 (define @t72 () (@list @t63)) % 0.39/0.60 (define @t73 () (lambda @t55 (forall @t54 (exists @t61 (and @t59 (forall @t72 (=> @t64 @t70))))))) % 0.39/0.60 (define @t74 () (_ @t48 @t63)) % 0.39/0.60 (define @t75 () (_ @t74 @t57)) % 0.39/0.60 (define @t76 () (lambda @t55 (forall @t66 (=> @t59 (exists @t72 (and @t64 @t75)))))) % 0.39/0.60 (define @t77 () (lambda @t55 (forall @t66 (=> @t68 (or @t65 @t70 @t75))))) % 0.39/0.60 (define @t78 () (lambda @t55 (forall @t66 (=> @t68 (exists @t49 (and (_ @t58 @t46) (_ @t74 @t46))))))) % 0.39/0.60 (define @t79 () (forall @t44 @t14)) % 0.39/0.60 (define @t80 () (@list @t13)) % 0.39/0.60 (define @t81 () (lambda @t80 @t79)) % 0.39/0.60 (define @t82 () (lambda @t80 (forall @t44 @t15))) % 0.39/0.60 (define @t83 () (lambda @t80 (exists @t44 @t14))) % 0.39/0.60 (define @t84 () (lambda @t80 (exists @t44 @t15))) % 0.39/0.60 (define @t85 () (_ (_ tptp.rel_s5 @t8) @t46)) % 0.39/0.60 (define @t86 () (not @t85)) % 0.39/0.60 (define @t87 () (or @t86 @t47)) % 0.39/0.60 (define @t88 () (forall @t49 @t87)) % 0.39/0.60 (define @t89 () (lambda @t16 @t88)) % 0.39/0.60 (define @t90 () (lambda (@list @t13 @t1) (_ (_ tptp.mnot (_ tptp.mbox_s5 @t21)) @t1))) % 0.39/0.60 (define @t91 () (@var "BOUND_VARIABLE_8345" $$unsorted)) % 0.39/0.60 (define @t92 () (lambda (@list @t91) true)) % 0.39/0.60 (define @t93 () (_ @t92 @t8)) % 0.39/0.60 (define @t94 () (forall @t44 @t93)) % 0.39/0.60 (define @t95 () (_ @t13 @t8)) % 0.39/0.60 (define @t96 () (lambda @t80 (forall @t44 @t95))) % 0.39/0.60 (define @t97 () (@list @t1)) % 0.39/0.60 (define @t98 () (forall @t49 (not (tptp.rel_s5 @t1 @t46)))) % 0.39/0.60 (define @t99 () (not @t98)) % 0.39/0.60 (define @t100 () (not (= tptp.a tptp.a))) % 0.39/0.60 (define @t101 () (@var "BOUND_VARIABLE_8457" tptp.mu)) % 0.39/0.60 (define @t102 () (not (= tptp.a @t101))) % 0.39/0.60 (define @t103 () (not (= @t101 tptp.a))) % 0.39/0.60 (define @t104 () (@list @t101)) % 0.39/0.60 (define @t105 () (or @t102 @t102)) % 0.39/0.60 (define @t106 () (forall @t104 @t103)) % 0.39/0.60 (define @t107 () (forall @t32 @t99)) % 0.39/0.60 (define @t108 () (= @t2 tptp.a)) % 0.39/0.60 (define @t109 () (not @t108)) % 0.39/0.60 (define @t110 () (forall @t32 @t109)) % 0.39/0.60 (define @t111 () (and @t110 @t107)) % 0.39/0.60 (define @t112 () (or @t108 @t98)) % 0.39/0.60 (define @t113 () (lambda @t3 @t112)) % 0.39/0.60 (define @t114 () (_ @t113 @t2 @t1)) % 0.39/0.60 (define @t115 () (not @t114)) % 0.39/0.60 (define @t116 () (forall @t32 @t115)) % 0.39/0.60 (define @t117 () (not @t116)) % 0.39/0.60 (define @t118 () (lambda @t97 @t117)) % 0.39/0.60 (define @t119 () (not (forall @t32 (not (_ @t29 @t2 @t1))))) % 0.39/0.60 (define @t120 () (lambda @t41 @t119)) % 0.39/0.60 (define @t121 () (tptp.rel_s5 @t8 @t46)) % 0.39/0.60 (define @t122 () (not @t121)) % 0.39/0.60 (define @t123 () (or @t108 (forall @t49 @t122))) % 0.39/0.60 (define @t124 () (or @t108 @t122)) % 0.39/0.60 (define @t125 () (or @t122 @t108)) % 0.39/0.60 (define @t126 () (lambda @t44 @t108)) % 0.39/0.60 (define @t127 () (_ @t126 @t46)) % 0.39/0.60 (define @t128 () (or @t122 @t127)) % 0.39/0.60 (define @t129 () (forall @t49 @t128)) % 0.39/0.60 (define @t130 () (lambda @t44 @t129)) % 0.39/0.60 (define @t131 () (_ @t13 @t46)) % 0.39/0.60 (define @t132 () (lambda @t16 (forall @t49 (or @t122 @t131)))) % 0.39/0.60 (define @t133 () (lambda (@list @t6 @t8) @t7)) % 0.39/0.60 (define @t134 () (_ @t9 @t2)) % 0.39/0.60 (define @t135 () (lambda @t3 (_ (_ @t132 (_ @t134 tptp.a)) @t1))) % 0.39/0.60 (define @t136 () (_ @t29 @t2 @t8)) % 0.39/0.60 (define @t137 () (forall @t32 (not @t136))) % 0.39/0.60 (define @t138 () (lambda @t44 @t137)) % 0.39/0.60 (define @t139 () (_ @t138 @t8)) % 0.39/0.60 (define @t140 () (not @t139)) % 0.39/0.60 (define @t141 () (lambda @t44 @t140)) % 0.39/0.60 (define @t142 () (not @t31)) % 0.39/0.60 (define @t143 () (not (_ @t30 @t1))) % 0.39/0.60 (define @t144 () (lambda @t3 @t143)) % 0.39/0.60 (define @t145 () (_ @t144 @t2 @t8)) % 0.39/0.60 (define @t146 () (forall @t32 @t145)) % 0.39/0.60 (define @t147 () (lambda @t44 @t146)) % 0.39/0.60 (define @t148 () (lambda @t34 (forall @t32 @t136))) % 0.39/0.60 (define @t149 () (lambda @t44 @t142)) % 0.39/0.60 (define @t150 () (_ @t17 @t30)) % 0.39/0.60 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.39/0.60 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.39/0.60 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.39/0.60 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.39/0.60 (assume @p5 @t5) % 0.39/0.60 (assume @p6 true) % 0.39/0.60 (step @p7 (= tptp.meq_ind @t9) :rule refl :args (@t9)) % 0.39/0.60 (step @p8 (= tptp.meq_prop @t12) :rule refl :args (@t12)) % 0.39/0.60 (step @p9 (= tptp.mnot @t17) :rule refl :args (@t17)) % 0.39/0.60 (step @p10 (= tptp.mor @t19) :rule refl :args (@t19)) % 0.39/0.60 (step @p11 (= tptp.mand @t24) :rule refl :args (@t24)) % 0.39/0.60 (step @p12 (= tptp.mimplies @t25) :rule refl :args (@t25)) % 0.39/0.60 (step @p13 (= tptp.mimplied @t26) :rule refl :args (@t26)) % 0.39/0.60 (step @p14 (= tptp.mequiv @t27) :rule refl :args (@t27)) % 0.39/0.60 (step @p15 (= tptp.mxor @t28) :rule refl :args (@t28)) % 0.39/0.60 (step @p16 (= tptp.mforall_ind @t35) :rule refl :args (@t35)) % 0.39/0.60 (step @p17 (= tptp.mforall_prop @t39) :rule refl :args (@t39)) % 0.39/0.60 (step @p18 (= tptp.mexists_ind @t42) :rule refl :args (@t42)) % 0.39/0.60 (step @p19 (= tptp.mexists_prop @t43) :rule refl :args (@t43)) % 0.39/0.60 (step @p20 (= tptp.mtrue @t45) :rule refl :args (@t45)) % 0.39/0.60 (step @p21 (= tptp.mbox @t50) :rule refl :args (@t50)) % 0.39/0.60 (step @p22 (= tptp.mdia @t51) :rule refl :args (@t51)) % 0.39/0.60 (step @p23 (= tptp.mreflexive @t56) :rule refl :args (@t56)) % 0.39/0.60 (step @p24 (= tptp.msymmetric @t60) :rule refl :args (@t60)) % 0.39/0.60 (step @p25 (= tptp.mserial @t62) :rule refl :args (@t62)) % 0.39/0.60 (step @p26 (= tptp.mtransitive @t67) :rule refl :args (@t67)) % 0.39/0.60 (step @p27 (= tptp.meuclidean @t69) :rule refl :args (@t69)) % 0.39/0.60 (step @p28 (= tptp.mpartially_functional @t71) :rule refl :args (@t71)) % 0.39/0.60 (step @p29 (= tptp.mfunctional @t73) :rule refl :args (@t73)) % 0.39/0.60 (step @p30 (= tptp.mweakly_dense @t76) :rule refl :args (@t76)) % 0.39/0.60 (step @p31 (= tptp.mweakly_connected @t77) :rule refl :args (@t77)) % 0.39/0.60 (step @p32 (= tptp.mweakly_directed @t78) :rule refl :args (@t78)) % 0.39/0.60 (step @p33 (= tptp.mvalid @t81) :rule refl :args (@t81)) % 0.39/0.60 (step @p34 (= tptp.minvalid @t82) :rule refl :args (@t82)) % 0.39/0.60 (step @p35 (= tptp.msatisfiable @t83) :rule refl :args (@t83)) % 0.39/0.60 (step @p36 (= tptp.mcountersatisfiable @t84) :rule refl :args (@t84)) % 0.39/0.60 (step @p37 (= tptp.mbox_s5 @t89) :rule refl :args (@t89)) % 0.39/0.60 (step @p38 (= tptp.mdia_s5 @t90) :rule refl :args (@t90)) % 0.39/0.60 (step @p39 :rule evaluate :args ((not true))) % 0.39/0.60 (step @p40 :rule quant-unused-vars :args ((= (forall @t44 true) true))) % 0.39/0.60 (step @p41 :rule beta-reduce :args ((= @t93 true))) % 0.39/0.60 (step @p42 :rule cong :premises (@p41) :args (@t94)) % 0.39/0.60 (step @p43 :rule trans :premises (@p42 @p40)) % 0.39/0.60 (step @p44 :rule beta-reduce :args ((= (_ @t96 @t92) @t94))) % 0.39/0.60 (step @p45 :rule trans :premises (@p44 @p43)) % 0.39/0.60 (step @p46 :rule refl :args (@t92)) % 0.39/0.60 (step @p47 :rule symm :premises (@p46)) % 0.39/0.60 (step @p48 :rule alpha_equiv :args ((lambda @t97 true) (@list @t1) (@list @t91))) % 0.39/0.60 (step @p49 :rule trans :premises (@p48 @p47)) % 0.39/0.60 (step @p50 :rule evaluate :args ((not false))) % 0.39/0.60 (step @p51 :rule absorb :args ((= (and false @t99) false))) % 0.39/0.60 (step @p52 :rule refl :args (@t99)) % 0.39/0.60 (step @p53 :rule eq-refl :args (tptp.a)) % 0.39/0.60 (step @p54 :rule cong :premises (@p53) :args (@t100)) % 0.39/0.60 (step @p55 :rule trans :premises (@p54 @p39)) % 0.39/0.60 (step @p56 :rule quant-var-elim-eq :args ((= (forall @t104 (or @t103 @t102)) @t100))) % 0.39/0.60 (step @p57 :rule refl :args (@t102)) % 0.39/0.60 (step @p58 :rule eq-symm :args (tptp.a @t101)) % 0.39/0.60 (step @p59 :rule cong :premises (@p58) :args (@t102)) % 0.39/0.60 (step @p60 :rule nary_cong :premises (@p59 @p57) :args (@t105)) % 0.39/0.60 (step @p61 :rule aci_norm :args ((= @t102 @t105))) % 0.39/0.60 (step @p62 :rule trans :premises (@p61 @p60)) % 0.39/0.60 (step @p63 :rule cong :premises (@p62) :args ((forall @t104 @t102))) % 0.39/0.60 (step @p64 :rule trans :premises (@p63 @p56)) % 0.39/0.60 (step @p65 :rule trans :premises (@p64 @p55)) % 0.39/0.60 (step @p66 :rule eq-symm :args (@t101 tptp.a)) % 0.39/0.60 (step @p67 :rule cong :premises (@p66) :args (@t103)) % 0.39/0.60 (step @p68 :rule cong :premises (@p67) :args (@t106)) % 0.39/0.60 (step @p69 :rule trans :premises (@p68 @p65)) % 0.39/0.60 (step @p70 :rule nary_cong :premises (@p69 @p52) :args ((and @t106 @t99))) % 0.39/0.60 (step @p71 :rule trans :premises (@p70 @p51)) % 0.39/0.60 (step @p72 :rule quant-unused-vars :args ((= @t107 @t99))) % 0.39/0.60 (step @p73 :rule alpha_equiv :args (@t110 (@list @t2) (@list @t101))) % 0.39/0.60 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t111)) % 0.39/0.60 (step @p75 :rule quant-miniscope-and :args ((= (forall @t32 (and @t109 @t99)) @t111))) % 0.39/0.60 (step @p76 :rule trans :premises (@p75 @p74)) % 0.39/0.60 (step @p77 :rule trans :premises (@p76 @p71)) % 0.39/0.60 (step @p78 :rule bool-or-de-morgan :args (@t108 @t98 false)) % 0.39/0.60 (step @p79 :rule cong :premises (@p78) :args ((forall @t32 (not @t112)))) % 0.39/0.60 (step @p80 :rule trans :premises (@p79 @p77)) % 0.39/0.60 (step @p81 :rule beta-reduce :args ((= @t114 @t112))) % 0.39/0.60 (step @p82 :rule cong :premises (@p81) :args (@t115)) % 0.39/0.60 (step @p83 :rule cong :premises (@p82) :args (@t116)) % 0.39/0.60 (step @p84 :rule trans :premises (@p83 @p80)) % 0.39/0.60 (step @p85 :rule cong :premises (@p84) :args (@t117)) % 0.39/0.60 (step @p86 :rule trans :premises (@p85 @p50)) % 0.39/0.60 (step @p87 :rule cong :premises (@p86) :args (@t118)) % 0.39/0.60 (step @p88 :rule trans :premises (@p87 @p49)) % 0.39/0.60 (step @p89 :rule beta-reduce :args ((= (_ @t120 @t113) @t118))) % 0.39/0.60 (step @p90 :rule trans :premises (@p89 @p88)) % 0.39/0.60 (step @p91 :rule beta-reduce :args ((= (_ (lambda @t44 @t123) @t1) @t112))) % 0.39/0.60 (step @p92 :rule refl :args (@t1)) % 0.39/0.60 (step @p93 :rule quant-miniscope-or :args ((= (forall @t49 @t124) @t123))) % 0.39/0.60 (step @p94 :rule aci_norm :args ((= @t125 @t124))) % 0.39/0.60 (step @p95 :rule cong :premises (@p94) :args ((forall @t49 @t125))) % 0.39/0.60 (step @p96 :rule trans :premises (@p95 @p93)) % 0.39/0.60 (step @p97 :rule beta-reduce :args ((= @t127 @t108))) % 0.39/0.60 (step @p98 :rule refl :args (@t122)) % 0.39/0.60 (step @p99 :rule nary_cong :premises (@p98 @p97) :args (@t128)) % 0.39/0.60 (step @p100 :rule cong :premises (@p99) :args (@t129)) % 0.39/0.60 (step @p101 :rule trans :premises (@p100 @p96)) % 0.39/0.60 (step @p102 :rule cong :premises (@p101) :args (@t130)) % 0.39/0.60 (step @p103 :rule beta-reduce :args ((= (_ @t132 @t126) @t130))) % 0.39/0.60 (step @p104 :rule trans :premises (@p103 @p102)) % 0.39/0.60 (step @p105 :rule beta-reduce :args ((= (_ @t133 tptp.a) @t126))) % 0.39/0.60 (step @p106 :rule refl :args (tptp.a)) % 0.39/0.60 (step @p107 :rule beta-reduce :args ((= @t134 @t133))) % 0.39/0.60 (step @p108 :rule ho_cong :premises (@p107 @p106)) % 0.39/0.60 (step @p109 :rule trans :premises (@p108 @p105)) % 0.39/0.60 (step @p110 :rule refl :args (@t132)) % 0.39/0.60 (step @p111 :rule ho_cong :premises (@p110 @p109)) % 0.39/0.60 (step @p112 :rule trans :premises (@p111 @p104)) % 0.39/0.60 (step @p113 :rule ho_cong :premises (@p112 @p92)) % 0.39/0.60 (step @p114 :rule trans :premises (@p113 @p91)) % 0.39/0.60 (step @p115 :rule cong :premises (@p114) :args (@t135)) % 0.39/0.60 (step @p116 :rule refl :args (@t120)) % 0.39/0.60 (step @p117 :rule ho_cong :premises (@p116 @p115)) % 0.39/0.60 (step @p118 :rule trans :premises (@p117 @p90)) % 0.39/0.60 (step @p119 :rule refl :args (@t96)) % 0.39/0.60 (step @p120 :rule ho_cong :premises (@p119 @p118)) % 0.39/0.60 (step @p121 :rule trans :premises (@p120 @p45)) % 0.39/0.60 (step @p122 :rule cong :premises (@p121) :args ((not (_ @t96 (_ @t120 @t135))))) % 0.39/0.60 (step @p123 :rule trans :premises (@p122 @p39)) % 0.39/0.60 (step @p124 :rule refl :args (@t2)) % 0.39/0.60 (step @p125 :rule ho_cong :premises (@p7 @p124)) % 0.39/0.60 (step @p126 :rule ho_cong :premises (@p125 @p106)) % 0.39/0.60 (step @p127 :rule refl :args (@t131)) % 0.39/0.60 (step @p128 :rule refl :args (@t47)) % 0.39/0.60 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t47 @t131))) % 0.39/0.60 (step @p130 :rule symm :premises (@p129)) % 0.39/0.60 (step @p131 :rule eq_resolve :premises (@p128 @p130)) % 0.39/0.60 (step @p132 :rule refl :args (@t121)) % 0.39/0.60 (step @p133 :rule refl :args (@t85)) % 0.39/0.60 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t85 @t121))) % 0.39/0.60 (step @p135 :rule symm :premises (@p134)) % 0.39/0.60 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 0.39/0.60 (step @p137 :rule cong :premises (@p136) :args (@t86)) % 0.39/0.60 (step @p138 :rule nary_cong :premises (@p137 @p131) :args (@t87)) % 0.39/0.60 (step @p139 :rule cong :premises (@p138) :args (@t88)) % 0.39/0.60 (step @p140 :rule cong :premises (@p139) :args (@t89)) % 0.39/0.60 (step @p141 :rule trans :premises (@p37 @p140)) % 0.39/0.60 (step @p142 :rule ho_cong :premises (@p141 @p126)) % 0.39/0.60 (step @p143 :rule ho_cong :premises (@p142 @p92)) % 0.39/0.60 (step @p144 :rule cong :premises (@p143) :args (@t4)) % 0.39/0.60 (step @p145 :rule beta-reduce :args ((= (_ (lambda @t44 (not @t137)) @t1) @t119))) % 0.39/0.60 (step @p146 :rule beta-reduce :args ((= @t139 @t137))) % 0.39/0.60 (step @p147 :rule cong :premises (@p146) :args (@t140)) % 0.39/0.60 (step @p148 :rule cong :premises (@p147) :args (@t141)) % 0.39/0.60 (step @p149 :rule beta-reduce :args ((= (_ @t17 @t138) @t141))) % 0.39/0.60 (step @p150 :rule trans :premises (@p149 @p148)) % 0.39/0.60 (step @p151 :rule refl :args (@t136)) % 0.39/0.60 (step @p152 :rule refl :args (@t31)) % 0.39/0.60 (step @p153 :rule cong :premises (@p152 @p151) :args ((= @t31 @t136))) % 0.39/0.60 (step @p154 :rule symm :premises (@p153)) % 0.39/0.60 (step @p155 :rule eq_resolve :premises (@p152 @p154)) % 0.39/0.60 (step @p156 :rule cong :premises (@p155) :args (@t142)) % 0.39/0.60 (step @p157 :rule cong :premises (@p156) :args ((forall @t32 @t142))) % 0.39/0.60 (step @p158 :rule beta-reduce :args ((= @t145 @t142))) % 0.39/0.60 (step @p159 :rule cong :premises (@p158) :args (@t146)) % 0.39/0.60 (step @p160 :rule trans :premises (@p159 @p157)) % 0.39/0.60 (step @p161 :rule cong :premises (@p160) :args (@t147)) % 0.39/0.60 (step @p162 :rule beta-reduce :args ((= (_ @t148 @t144) @t147))) % 0.39/0.60 (step @p163 :rule trans :premises (@p162 @p161)) % 0.39/0.60 (step @p164 :rule beta-reduce :args ((= (_ @t149 @t1) @t143))) % 0.39/0.60 (step @p165 :rule beta-reduce :args ((= @t150 @t149))) % 0.39/0.60 (step @p166 :rule ho_cong :premises (@p165 @p92)) % 0.39/0.60 (step @p167 :rule trans :premises (@p166 @p164)) % 0.39/0.60 (step @p168 :rule cong :premises (@p167) :args ((lambda @t3 (_ @t150 @t1)))) % 0.39/0.60 (step @p169 :rule refl :args (@t148)) % 0.39/0.60 (step @p170 :rule ho_cong :premises (@p169 @p168)) % 0.39/0.60 (step @p171 :rule trans :premises (@p170 @p163)) % 0.39/0.60 (step @p172 :rule refl :args (@t17)) % 0.39/0.60 (step @p173 :rule ho_cong :premises (@p172 @p171)) % 0.39/0.60 (step @p174 :rule trans :premises (@p173 @p150)) % 0.39/0.60 (step @p175 :rule ho_cong :premises (@p174 @p92)) % 0.39/0.60 (step @p176 :rule trans :premises (@p175 @p145)) % 0.39/0.60 (step @p177 :rule refl :args (@t30)) % 0.39/0.60 (step @p178 :rule ho_cong :premises (@p9 @p177)) % 0.39/0.60 (step @p179 :rule ho_cong :premises (@p178 @p92)) % 0.39/0.60 (step @p180 :rule cong :premises (@p179) :args (@t40)) % 0.39/0.60 (step @p181 :rule cong :premises (@p155) :args (@t33)) % 0.39/0.60 (step @p182 :rule cong :premises (@p181) :args (@t35)) % 0.39/0.60 (step @p183 :rule trans :premises (@p16 @p182)) % 0.39/0.60 (step @p184 :rule ho_cong :premises (@p183 @p180)) % 0.39/0.60 (step @p185 :rule ho_cong :premises (@p9 @p184)) % 0.39/0.60 (step @p186 :rule ho_cong :premises (@p185 @p92)) % 0.39/0.60 (step @p187 :rule trans :premises (@p186 @p176)) % 0.39/0.60 (step @p188 :rule cong :premises (@p187) :args (@t42)) % 0.39/0.60 (step @p189 :rule trans :premises (@p18 @p188)) % 0.39/0.60 (step @p190 :rule ho_cong :premises (@p189 @p144)) % 0.39/0.60 (step @p191 :rule refl :args (@t95)) % 0.39/0.60 (step @p192 :rule refl :args (@t14)) % 0.39/0.60 (step @p193 :rule cong :premises (@p192 @p191) :args ((= @t14 @t95))) % 0.39/0.60 (step @p194 :rule symm :premises (@p193)) % 0.39/0.60 (step @p195 :rule eq_resolve :premises (@p192 @p194)) % 0.39/0.60 (step @p196 :rule cong :premises (@p195) :args (@t79)) % 0.39/0.60 (step @p197 :rule cong :premises (@p196) :args (@t81)) % 0.39/0.60 (step @p198 :rule trans :premises (@p33 @p197)) % 0.39/0.60 (step @p199 :rule ho_cong :premises (@p198 @p190)) % 0.39/0.60 (step @p200 :rule cong :premises (@p199) :args (@t5)) % 0.39/0.60 (step @p201 :rule trans :premises (@p200 @p123)) % 0.39/0.60 (step @p202 false :rule eq_resolve :premises (@p5 @p201)) % 0.39/0.60 ) % 0.39/0.60 % SZS output end Proof % 0.39/0.60 % cvc5 exiting %------------------------------------------------------------------------------