%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO432^1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n027.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:12:38 AM UTC 2026 % Result : Theorem 0.38s 0.64s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO432^1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n027.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Wed Jun 3 00:07:51 EDT 2026 % 0.19/0.35 % CPUTime : % 0.29/0.52 %----Proving TH0 % 0.38/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.64 % SZS status Theorem % 0.38/0.64 % SZS output start Proof % 0.38/0.64 ( % 0.38/0.64 (declare-sort $$unsorted 0) % 0.38/0.64 (declare-sort tptp.mu 0) % 0.38/0.64 (declare-const tptp.rel_b (-> $$unsorted $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.q (-> $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.p (-> $$unsorted Bool)) % 0.38/0.64 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.38/0.64 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.38/0.64 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.38/0.64 (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)))))) % 0.38/0.64 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.64 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.64 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.64 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.64 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.38/0.64 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.64 (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))))))) % 0.38/0.64 (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))))))) % 0.38/0.64 (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)))))) % 0.38/0.64 (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)))))) % 0.38/0.64 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.38/0.64 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.38/0.64 (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)))))) % 0.38/0.64 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.64 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.64 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.64 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.38/0.64 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.38/0.64 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.38/0.64 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.38/0.64 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.38/0.64 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.38/0.64 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.38/0.64 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.64 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.64 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.64 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.64 (define tptp.mbox_b () (let ((_let_1 (@var "V" $$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_b _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.38/0.64 (define tptp.mdia_b () (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_b (_ tptp.mnot _let_2))) _let_1))))) % 0.38/0.64 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ (_ tptp.mand (_ tptp.mbox_b tptp.p)) (_ tptp.mbox_b (_ tptp.mdia_b (_ tptp.mbox_b (_ (_ tptp.mimplies tptp.p) tptp.q)))))) (_ tptp.mbox_b tptp.q))))) % 0.38/0.64 (define @t2 () (@var "Y" tptp.mu)) % 0.38/0.64 (define @t3 () (@var "X" tptp.mu)) % 0.38/0.64 (define @t4 () (@var "W" $$unsorted)) % 0.38/0.64 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.38/0.64 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.64 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.64 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.38/0.64 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.38/0.64 (define @t10 () (_ @t9 @t4)) % 0.38/0.64 (define @t11 () (not @t10)) % 0.38/0.64 (define @t12 () (@list @t9 @t4)) % 0.38/0.64 (define @t13 () (lambda @t12 @t11)) % 0.38/0.64 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.38/0.64 (define @t15 () (_ @t14 @t4)) % 0.38/0.64 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.38/0.64 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.64 (define @t18 () (_ tptp.mnot @t14)) % 0.38/0.64 (define @t19 () (_ tptp.mnot @t9)) % 0.38/0.64 (define @t20 () (_ tptp.mor @t19)) % 0.38/0.64 (define @t21 () (@list @t9 @t14 @t17)) % 0.38/0.64 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.38/0.64 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.38/0.64 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.38/0.64 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.38/0.64 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.38/0.64 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.38/0.64 (define @t28 () (_ @t27 @t3)) % 0.38/0.64 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.38/0.64 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.64 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.38/0.64 (define @t32 () (_ @t31 @t30)) % 0.38/0.64 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.38/0.64 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.38/0.64 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.38/0.64 (define @t36 () (@list @t4)) % 0.38/0.64 (define @t37 () (lambda @t36 true)) % 0.38/0.64 (define @t38 () (@var "V" $$unsorted)) % 0.38/0.64 (define @t39 () (_ @t9 @t38)) % 0.38/0.64 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.64 (define @t41 () (@list @t38)) % 0.38/0.64 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.38/0.64 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.38/0.64 (define @t44 () (@var "S" $$unsorted)) % 0.38/0.64 (define @t45 () (_ @t40 @t44)) % 0.38/0.64 (define @t46 () (@list @t44)) % 0.38/0.64 (define @t47 () (@list @t40)) % 0.38/0.64 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.38/0.64 (define @t49 () (@var "T" $$unsorted)) % 0.38/0.64 (define @t50 () (_ @t40 @t49)) % 0.38/0.64 (define @t51 () (_ @t50 @t44)) % 0.38/0.64 (define @t52 () (_ @t45 @t49)) % 0.38/0.64 (define @t53 () (@list @t44 @t49)) % 0.38/0.64 (define @t54 () (forall @t53 (=> @t52 @t51))) % 0.38/0.64 (define @t55 () (lambda @t47 @t54)) % 0.38/0.64 (define @t56 () (@list @t49)) % 0.38/0.64 (define @t57 () (lambda @t47 (forall @t46 (exists @t56 @t52)))) % 0.38/0.64 (define @t58 () (@var "U" $$unsorted)) % 0.38/0.64 (define @t59 () (_ @t45 @t58)) % 0.38/0.64 (define @t60 () (_ @t50 @t58)) % 0.38/0.64 (define @t61 () (@list @t44 @t49 @t58)) % 0.38/0.64 (define @t62 () (lambda @t47 (forall @t61 (=> (and @t52 @t60) @t59)))) % 0.38/0.64 (define @t63 () (and @t52 @t59)) % 0.38/0.64 (define @t64 () (lambda @t47 (forall @t61 (=> @t63 @t60)))) % 0.38/0.64 (define @t65 () (= @t49 @t58)) % 0.38/0.64 (define @t66 () (lambda @t47 (forall @t61 (=> @t63 @t65)))) % 0.38/0.64 (define @t67 () (@list @t58)) % 0.38/0.64 (define @t68 () (lambda @t47 (forall @t46 (exists @t56 (and @t52 (forall @t67 (=> @t59 @t65))))))) % 0.38/0.64 (define @t69 () (_ @t40 @t58)) % 0.38/0.64 (define @t70 () (_ @t69 @t49)) % 0.38/0.64 (define @t71 () (lambda @t47 (forall @t61 (=> @t52 (exists @t67 (and @t59 @t70)))))) % 0.38/0.64 (define @t72 () (lambda @t47 (forall @t61 (=> @t63 (or @t60 @t65 @t70))))) % 0.38/0.64 (define @t73 () (lambda @t47 (forall @t61 (=> @t63 (exists @t41 (and (_ @t50 @t38) (_ @t69 @t38))))))) % 0.38/0.64 (define @t74 () (forall @t36 @t10)) % 0.38/0.64 (define @t75 () (@list @t9)) % 0.38/0.64 (define @t76 () (lambda @t75 @t74)) % 0.38/0.64 (define @t77 () (lambda @t75 (forall @t36 @t11))) % 0.38/0.64 (define @t78 () (lambda @t75 (exists @t36 @t10))) % 0.38/0.64 (define @t79 () (lambda @t75 (exists @t36 @t11))) % 0.38/0.64 (define @t80 () (_ (_ tptp.rel_b @t4) @t38)) % 0.38/0.64 (define @t81 () (not @t80)) % 0.38/0.64 (define @t82 () (or @t81 @t39)) % 0.38/0.64 (define @t83 () (forall @t41 @t82)) % 0.38/0.64 (define @t84 () (lambda @t12 @t83)) % 0.38/0.64 (define @t85 () (@list @t9 @t17)) % 0.38/0.64 (define @t86 () (lambda @t85 (_ (_ tptp.mnot (_ tptp.mbox_b @t19)) @t17))) % 0.38/0.64 (define @t87 () (@var "BOUND_VARIABLE_8563" $$unsorted)) % 0.38/0.64 (define @t88 () (tptp.q @t87)) % 0.38/0.64 (define @t89 () (not (tptp.rel_b @t4 @t87))) % 0.38/0.64 (define @t90 () (@var "BOUND_VARIABLE_8473" $$unsorted)) % 0.38/0.64 (define @t91 () (tptp.q @t90)) % 0.38/0.64 (define @t92 () (not (tptp.p @t90))) % 0.38/0.64 (define @t93 () (@var "BOUND_VARIABLE_8499" $$unsorted)) % 0.38/0.64 (define @t94 () (@list @t90)) % 0.38/0.64 (define @t95 () (not (forall @t94 (or (not (tptp.rel_b @t93 @t90)) @t92 @t91)))) % 0.38/0.64 (define @t96 () (@list @t93)) % 0.38/0.64 (define @t97 () (not (forall @t96 (or (not (tptp.rel_b @t38 @t93)) @t95)))) % 0.38/0.64 (define @t98 () (tptp.rel_b @t4 @t38)) % 0.38/0.64 (define @t99 () (not @t98)) % 0.38/0.64 (define @t100 () (forall @t41 (or @t99 @t97))) % 0.38/0.64 (define @t101 () (not @t100)) % 0.38/0.64 (define @t102 () (tptp.p @t38)) % 0.38/0.64 (define @t103 () (forall @t41 (or @t99 @t102))) % 0.38/0.64 (define @t104 () (not @t103)) % 0.38/0.64 (define @t105 () (or @t104 @t101 @t89 @t88)) % 0.38/0.64 (define @t106 () (or @t89 @t88)) % 0.38/0.64 (define @t107 () (or @t106 @t104 @t101)) % 0.38/0.64 (define @t108 () (@list @t4 @t87)) % 0.38/0.64 (define @t109 () (forall @t108 @t107)) % 0.38/0.64 (define @t110 () (@list @t87)) % 0.38/0.64 (define @t111 () (forall @t110 @t107)) % 0.38/0.64 (define @t112 () (forall @t110 @t106)) % 0.38/0.64 (define @t113 () (@list @t38)) % 0.38/0.64 (define @t114 () (or @t112 @t104 @t101)) % 0.38/0.64 (define @t115 () (tptp.q @t38)) % 0.38/0.64 (define @t116 () (forall @t41 (or @t99 @t115))) % 0.38/0.64 (define @t117 () (or @t116 @t104 @t101)) % 0.38/0.64 (define @t118 () (not (tptp.rel_b @t17 @t38))) % 0.38/0.64 (define @t119 () (forall @t41 (or @t118 @t97))) % 0.38/0.64 (define @t120 () (not @t119)) % 0.38/0.64 (define @t121 () (forall @t41 (or @t118 @t102))) % 0.38/0.64 (define @t122 () (not @t121)) % 0.38/0.64 (define @t123 () (forall @t41 (or @t118 @t115))) % 0.38/0.64 (define @t124 () (@list @t17)) % 0.38/0.64 (define @t125 () (lambda @t124 (or @t123 @t122 @t120))) % 0.38/0.64 (define @t126 () (_ @t125 @t4)) % 0.38/0.64 (define @t127 () (forall @t36 @t126)) % 0.38/0.64 (define @t128 () (_ @t9 @t4)) % 0.38/0.64 (define @t129 () (lambda @t75 (forall @t36 @t128))) % 0.38/0.64 (define @t130 () (lambda @t36 @t116)) % 0.38/0.64 (define @t131 () (_ @t130 @t17)) % 0.38/0.64 (define @t132 () (or @t131 @t122 @t120)) % 0.38/0.64 (define @t133 () (lambda @t124 @t132)) % 0.38/0.64 (define @t134 () (_ @t14 @t17)) % 0.38/0.64 (define @t135 () (or @t134 @t122 @t120)) % 0.38/0.64 (define @t136 () (@list @t14 @t17)) % 0.38/0.64 (define @t137 () (_ @t9 @t38)) % 0.38/0.64 (define @t138 () (lambda @t12 (forall @t41 (or @t99 @t137)))) % 0.38/0.64 (define @t139 () (_ @t138 tptp.q)) % 0.38/0.64 (define @t140 () (or @t122 @t120)) % 0.38/0.64 (define @t141 () (not @t140)) % 0.38/0.64 (define @t142 () (lambda @t124 @t141)) % 0.38/0.64 (define @t143 () (_ @t142 @t17)) % 0.38/0.64 (define @t144 () (not @t143)) % 0.38/0.64 (define @t145 () (or @t144 @t134)) % 0.38/0.64 (define @t146 () (lambda @t136 @t145)) % 0.38/0.64 (define @t147 () (not (_ @t9 @t17))) % 0.38/0.64 (define @t148 () (or @t147 @t134)) % 0.38/0.64 (define @t149 () (lambda @t21 @t148)) % 0.38/0.64 (define @t150 () (lambda @t36 @t100)) % 0.38/0.64 (define @t151 () (_ @t150 @t17)) % 0.38/0.64 (define @t152 () (not @t151)) % 0.38/0.64 (define @t153 () (or @t122 @t152)) % 0.38/0.64 (define @t154 () (not @t153)) % 0.38/0.64 (define @t155 () (lambda @t124 @t154)) % 0.38/0.64 (define @t156 () (not @t134)) % 0.38/0.64 (define @t157 () (forall @t94 (or (not (tptp.rel_b @t38 @t90)) @t92 @t91))) % 0.38/0.64 (define @t158 () (forall @t41 (or @t118 (not @t157)))) % 0.38/0.64 (define @t159 () (not @t158)) % 0.38/0.64 (define @t160 () (lambda @t124 @t159)) % 0.38/0.64 (define @t161 () (or @t99 (_ @t160 @t38))) % 0.38/0.64 (define @t162 () (forall @t41 @t161)) % 0.38/0.64 (define @t163 () (lambda @t36 @t162)) % 0.38/0.64 (define @t164 () (forall @t41 (or @t99 (not @t102) @t115))) % 0.38/0.64 (define @t165 () (lambda @t36 @t164)) % 0.38/0.64 (define @t166 () (not (_ @t165 @t38))) % 0.38/0.64 (define @t167 () (or @t118 @t166)) % 0.38/0.64 (define @t168 () (forall @t41 @t167)) % 0.38/0.64 (define @t169 () (not @t168)) % 0.38/0.64 (define @t170 () (lambda @t124 @t169)) % 0.38/0.64 (define @t171 () (not @t137)) % 0.38/0.64 (define @t172 () (not (forall @t41 (or @t118 @t171)))) % 0.38/0.64 (define @t173 () (lambda @t85 @t172)) % 0.38/0.64 (define @t174 () (_ tptp.q @t38)) % 0.38/0.64 (define @t175 () (_ tptp.p @t38)) % 0.38/0.64 (define @t176 () (not @t175)) % 0.38/0.64 (define @t177 () (or @t99 @t176 @t174)) % 0.38/0.64 (define @t178 () (or @t176 @t174)) % 0.38/0.64 (define @t179 () (not (_ tptp.p @t17))) % 0.38/0.64 (define @t180 () (lambda @t124 (or @t179 (_ tptp.q @t17)))) % 0.38/0.64 (define @t181 () (_ @t180 @t38)) % 0.38/0.64 (define @t182 () (or @t99 @t181)) % 0.38/0.64 (define @t183 () (forall @t41 @t182)) % 0.38/0.64 (define @t184 () (lambda @t36 @t183)) % 0.38/0.64 (define @t185 () (lambda @t136 (or @t179 @t134))) % 0.38/0.64 (define @t186 () (_ @t149 tptp.p)) % 0.38/0.64 (define @t187 () (lambda @t36 @t103)) % 0.38/0.64 (define @t188 () (_ @t187 @t17)) % 0.38/0.64 (define @t189 () (not @t188)) % 0.38/0.64 (define @t190 () (or @t189 @t156)) % 0.38/0.64 (define @t191 () (not @t190)) % 0.38/0.64 (define @t192 () (lambda @t136 @t191)) % 0.38/0.64 (define @t193 () (not (or @t147 @t156))) % 0.38/0.64 (define @t194 () (lambda @t21 @t193)) % 0.38/0.64 (define @t195 () (_ @t138 tptp.p)) % 0.38/0.64 (define @t196 () (or @t11 @t15)) % 0.38/0.64 (define @t197 () (lambda @t36 @t196)) % 0.38/0.64 (define @t198 () (@list @t14 @t4)) % 0.38/0.64 (define @t199 () (lambda @t198 @t196)) % 0.38/0.64 (define @t200 () (lambda @t36 @t11)) % 0.38/0.64 (define @t201 () (_ @t200 @t4)) % 0.38/0.64 (define @t202 () (or @t201 @t15)) % 0.38/0.64 (define @t203 () (lambda @t198 @t202)) % 0.38/0.64 (define @t204 () (forall @t41 (or @t99 @t171))) % 0.38/0.64 (define @t205 () (lambda @t36 @t204)) % 0.38/0.64 (define @t206 () (_ @t205 @t4)) % 0.38/0.64 (define @t207 () (not @t206)) % 0.38/0.64 (define @t208 () (lambda @t36 @t207)) % 0.38/0.64 (define @t209 () (not @t39)) % 0.38/0.64 (define @t210 () (or @t99 @t209)) % 0.38/0.64 (define @t211 () (_ @t200 @t38)) % 0.38/0.64 (define @t212 () (or @t99 @t211)) % 0.38/0.64 (define @t213 () (forall @t41 @t212)) % 0.38/0.64 (define @t214 () (lambda @t36 @t213)) % 0.38/0.64 (define @t215 () (not @t15)) % 0.38/0.64 (define @t216 () (or @t11 @t215)) % 0.38/0.64 (define @t217 () (lambda @t36 @t216)) % 0.38/0.64 (define @t218 () (_ @t217 @t4)) % 0.38/0.64 (define @t219 () (not @t218)) % 0.38/0.64 (define @t220 () (lambda @t36 @t219)) % 0.38/0.64 (define @t221 () (lambda @t36 @t215)) % 0.38/0.64 (define @t222 () (_ @t221 @t4)) % 0.38/0.64 (define @t223 () (or @t11 @t222)) % 0.38/0.64 (define @t224 () (lambda @t36 @t223)) % 0.38/0.64 (define @t225 () (forall @t108 @t105)) % 0.38/0.64 (define @t226 () (@quantifiers_skolemize @t225 1)) % 0.38/0.64 (define @t227 () (tptp.q @t226)) % 0.38/0.64 (define @t228 () (@quantifiers_skolemize @t225 0)) % 0.38/0.64 (define @t229 () (tptp.rel_b @t228 @t226)) % 0.38/0.64 (define @t230 () (not @t229)) % 0.38/0.64 (define @t231 () (not (tptp.rel_b @t228 @t38))) % 0.38/0.64 (define @t232 () (forall @t41 (or @t231 @t97))) % 0.38/0.64 (define @t233 () (not @t232)) % 0.38/0.64 (define @t234 () (forall @t41 (or @t231 @t102))) % 0.38/0.64 (define @t235 () (not @t234)) % 0.38/0.64 (define @t236 () (or @t235 @t233 @t230 @t227)) % 0.38/0.64 (define @t237 () (@list true)) % 0.38/0.64 (define @t238 () (@list @t236)) % 0.38/0.64 (define @t239 () (@list @t226)) % 0.38/0.64 (define @t240 () (tptp.p @t226)) % 0.38/0.64 (define @t241 () (or @t230 @t240)) % 0.38/0.64 (define @t242 () (@list false false)) % 0.38/0.64 (define @t243 () (forall @t96 (or (not (tptp.rel_b @t226 @t93)) @t95))) % 0.38/0.64 (define @t244 () (not @t243)) % 0.38/0.64 (define @t245 () (or @t230 @t244)) % 0.38/0.64 (define @t246 () (@quantifiers_skolemize @t243 0)) % 0.38/0.64 (define @t247 () (forall @t94 (or (not (tptp.rel_b @t246 @t90)) @t92 @t91))) % 0.38/0.64 (define @t248 () (not @t247)) % 0.38/0.64 (define @t249 () (tptp.rel_b @t226 @t246)) % 0.38/0.64 (define @t250 () (not @t249)) % 0.38/0.64 (define @t251 () (or @t250 @t248)) % 0.38/0.64 (define @t252 () (@list @t251)) % 0.38/0.64 (define @t253 () (_ @t40 @t49 @t44)) % 0.38/0.64 (define @t254 () (_ @t40 @t44 @t49)) % 0.38/0.64 (define @t255 () (not @t52)) % 0.38/0.64 (define @t256 () (or @t255 @t51)) % 0.38/0.64 (define @t257 () (tptp.rel_b @t246 @t226)) % 0.38/0.64 (define @t258 () (or @t250 @t257)) % 0.38/0.64 (define @t259 () (not @t240)) % 0.38/0.64 (define @t260 () (not @t257)) % 0.38/0.64 (define @t261 () (or @t260 @t259 @t227)) % 0.38/0.64 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.38/0.64 (assume @p2 (_ tptp.mreflexive tptp.rel_b)) % 0.38/0.64 (assume @p3 (_ tptp.msymmetric tptp.rel_b)) % 0.38/0.64 (assume @p4 @t1) % 0.38/0.64 (assume @p5 true) % 0.38/0.64 (step @p6 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.38/0.64 (step @p7 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.38/0.64 (step @p8 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.38/0.64 (step @p9 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.38/0.64 (step @p10 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.38/0.64 (step @p11 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.38/0.64 (step @p12 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.38/0.64 (step @p13 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.38/0.64 (step @p14 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.38/0.64 (step @p15 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.38/0.64 (step @p16 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.38/0.64 (step @p17 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.38/0.64 (step @p18 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.38/0.64 (step @p19 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.38/0.64 (step @p20 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.38/0.64 (step @p21 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.38/0.64 (step @p22 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.38/0.64 (step @p23 (= tptp.msymmetric @t55) :rule refl :args (@t55)) % 0.38/0.64 (step @p24 (= tptp.mserial @t57) :rule refl :args (@t57)) % 0.38/0.64 (step @p25 (= tptp.mtransitive @t62) :rule refl :args (@t62)) % 0.38/0.64 (step @p26 (= tptp.meuclidean @t64) :rule refl :args (@t64)) % 0.38/0.64 (step @p27 (= tptp.mpartially_functional @t66) :rule refl :args (@t66)) % 0.38/0.64 (step @p28 (= tptp.mfunctional @t68) :rule refl :args (@t68)) % 0.38/0.64 (step @p29 (= tptp.mweakly_dense @t71) :rule refl :args (@t71)) % 0.38/0.64 (step @p30 (= tptp.mweakly_connected @t72) :rule refl :args (@t72)) % 0.38/0.64 (step @p31 (= tptp.mweakly_directed @t73) :rule refl :args (@t73)) % 0.38/0.64 (step @p32 (= tptp.mvalid @t76) :rule refl :args (@t76)) % 0.38/0.64 (step @p33 (= tptp.minvalid @t77) :rule refl :args (@t77)) % 0.38/0.64 (step @p34 (= tptp.msatisfiable @t78) :rule refl :args (@t78)) % 0.38/0.64 (step @p35 (= tptp.mcountersatisfiable @t79) :rule refl :args (@t79)) % 0.38/0.64 (step @p36 (= tptp.mbox_b @t84) :rule refl :args (@t84)) % 0.38/0.64 (step @p37 (= tptp.mdia_b @t86) :rule refl :args (@t86)) % 0.38/0.64 (step @p38 :rule aci_norm :args ((= @t107 @t105))) % 0.38/0.64 (step @p39 :rule cong :premises (@p38) :args (@t109)) % 0.38/0.64 (step @p40 :rule quant-merge-prenex :args ((= (forall @t36 @t111) @t109))) % 0.38/0.64 (step @p41 :rule refl :args (@t101)) % 0.38/0.64 (step @p42 :rule refl :args (@t104)) % 0.38/0.64 (step @p43 :rule alpha_equiv :args (@t112 (@list @t87) @t113)) % 0.38/0.64 (step @p44 :rule nary_cong :premises (@p43 @p42 @p41) :args (@t114)) % 0.38/0.64 (step @p45 :rule quant-miniscope-or :args ((= @t111 @t114))) % 0.38/0.64 (step @p46 :rule trans :premises (@p45 @p44)) % 0.38/0.64 (step @p47 :rule symm :premises (@p46)) % 0.38/0.64 (step @p48 :rule cong :premises (@p47) :args ((forall @t36 @t117))) % 0.38/0.64 (step @p49 :rule trans :premises (@p48 @p40)) % 0.38/0.64 (step @p50 :rule trans :premises (@p49 @p39)) % 0.38/0.64 (step @p51 :rule beta-reduce :args ((= @t126 @t117))) % 0.38/0.64 (step @p52 :rule cong :premises (@p51) :args (@t127)) % 0.38/0.64 (step @p53 :rule trans :premises (@p52 @p50)) % 0.38/0.64 (step @p54 :rule beta-reduce :args ((= (_ @t129 @t125) @t127))) % 0.38/0.64 (step @p55 :rule trans :premises (@p54 @p53)) % 0.38/0.64 (step @p56 :rule refl :args (@t120)) % 0.38/0.64 (step @p57 :rule refl :args (@t122)) % 0.38/0.64 (step @p58 :rule beta-reduce :args ((= @t131 @t123))) % 0.38/0.64 (step @p59 :rule nary_cong :premises (@p58 @p57 @p56) :args (@t132)) % 0.38/0.64 (step @p60 :rule cong :premises (@p59) :args (@t133)) % 0.38/0.64 (step @p61 :rule beta-reduce :args ((= (_ (lambda @t136 @t135) @t130) @t133))) % 0.38/0.64 (step @p62 :rule trans :premises (@p61 @p60)) % 0.38/0.64 (step @p63 :rule beta-reduce :args ((= @t139 @t130))) % 0.38/0.64 (step @p64 :rule aci_norm :args ((= (or @t140 @t134) @t135))) % 0.38/0.64 (step @p65 :rule refl :args (@t134)) % 0.38/0.64 (step @p66 :rule bool-double-not-elim :args (@t140)) % 0.38/0.64 (step @p67 :rule beta-reduce :args ((= @t143 @t141))) % 0.38/0.64 (step @p68 :rule cong :premises (@p67) :args (@t144)) % 0.38/0.64 (step @p69 :rule trans :premises (@p68 @p66)) % 0.38/0.64 (step @p70 :rule nary_cong :premises (@p69 @p65) :args (@t145)) % 0.38/0.64 (step @p71 :rule trans :premises (@p70 @p64)) % 0.38/0.64 (step @p72 :rule cong :premises (@p71) :args (@t146)) % 0.38/0.64 (step @p73 :rule beta-reduce :args ((= (_ @t149 @t142) @t146))) % 0.38/0.64 (step @p74 :rule trans :premises (@p73 @p72)) % 0.38/0.64 (step @p75 :rule beta-reduce :args ((= @t151 @t119))) % 0.38/0.64 (step 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@p341 :rule bool-impl-elim :args (@t52 @t51)) % 0.38/0.64 (step @p342 :rule cong :premises (@p341) :args (@t54)) % 0.38/0.64 (step @p343 :rule trans :premises (@p342 @p340)) % 0.38/0.64 (step @p344 :rule cong :premises (@p343) :args (@t55)) % 0.38/0.64 (step @p345 :rule trans :premises (@p23 @p344)) % 0.38/0.64 (step @p346 :rule ho_cong :premises (@p345 @p327)) % 0.38/0.64 (step @p347 :rule trans :premises (@p346 @p326)) % 0.38/0.64 (step @p348 :rule eq_resolve :premises (@p3 @p347)) % 0.38/0.64 (step @p349 :rule instantiate :premises (@p348) :args ((@list @t226 @t246))) % 0.38/0.64 (step @p350 :rule bool-double-not-elim :args (@t249)) % 0.38/0.64 (step @p351 :rule nary_cong :premises (@p319 @p350) :args ((or @t251 (not @t250)))) % 0.38/0.64 (step @p352 :rule cnf_or_neg :args (@t251 0)) % 0.38/0.64 (step @p353 :rule eq_resolve :premises (@p352 @p351)) % 0.38/0.64 (step @p354 :rule reordering :premises (@p353) :args ((or @t249 @t251))) % 0.38/0.64 (step @p355 :rule chain_m_resolution :premises (@p354 @p317) :args (@t249 @t237 @t252)) % 0.38/0.64 (step @p356 :rule cnf_or_pos :args (@t258)) % 0.38/0.64 (step @p357 :rule reordering :premises (@p356) :args ((or @t250 @t257 (not @t258)))) % 0.38/0.64 (step @p358 :rule chain_m_resolution :premises (@p357 @p355 @p349) :args (@t257 @t242 (@list @t249 @t258))) % 0.38/0.64 (step @p359 :rule cnf_or_pos :args (@t261)) % 0.38/0.64 (step @p360 :rule reordering :premises (@p359) :args ((or @t227 @t259 @t260 (not @t261)))) % 0.38/0.64 (step @p361 false :rule chain_m_resolution :premises (@p360 @p358 @p325 @p306 @p289) :args (false (@list false false false true) (@list @t257 @t261 @t240 @t227))) % 0.38/0.64 ) % 0.38/0.64 % SZS output end Proof % 0.38/0.64 % cvc5 exiting %------------------------------------------------------------------------------