%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL719^1 : TPTP v9.3.1. Bugfixed v5.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n031.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:41 AM UTC 2026 % Result : Theorem 0.21s 0.53s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL719^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.10/0.36 % Computer : n031.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 21:10:10 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.45 %----Proving TH0 % 0.21/0.53 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.21/0.53 % SZS status Theorem % 0.21/0.53 % SZS output start Proof % 0.21/0.53 ( % 0.21/0.53 (declare-sort $$unsorted 0) % 0.21/0.53 (declare-sort tptp.mu 0) % 0.21/0.53 (declare-const tptp.rel_k (-> $$unsorted $$unsorted Bool)) % 0.21/0.53 (declare-const tptp.phi (-> $$unsorted Bool)) % 0.21/0.53 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.21/0.53 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.21/0.53 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.21/0.53 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.21/0.53 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.21/0.53 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.21/0.53 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.21/0.53 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.21/0.53 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.21/0.53 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.21/0.53 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.21/0.53 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.21/0.53 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.21/0.53 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.21/0.53 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.21/0.53 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.21/0.53 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.21/0.53 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.21/0.53 (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)))))))) % 0.21/0.53 (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)))))))) % 0.21/0.53 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.21/0.53 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.21/0.53 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.21/0.53 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.21/0.53 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.21/0.53 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.21/0.53 (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))))))))))))) % 0.21/0.53 (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)))))) % 0.21/0.53 (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))))))) % 0.21/0.53 (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)))))) % 0.21/0.53 (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))))))) % 0.21/0.53 (define tptp.mbox_k () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_k _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.21/0.53 (define tptp.mdia_k () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_k (_ tptp.mnot _let_2))) _let_1))))) % 0.21/0.53 (define @t1 () (=> (_ tptp.mvalid tptp.phi) (_ tptp.mvalid (_ tptp.mbox_k tptp.phi)))) % 0.21/0.53 (define @t2 () (not @t1)) % 0.21/0.53 (define @t3 () (@var "Y" tptp.mu)) % 0.21/0.53 (define @t4 () (@var "X" tptp.mu)) % 0.21/0.53 (define @t5 () (@var "W" $$unsorted)) % 0.21/0.53 (define @t6 () (lambda (@list @t4 @t3 @t5) (= @t4 @t3))) % 0.21/0.53 (define @t7 () (@var "Y" (-> $$unsorted Bool))) % 0.21/0.53 (define @t8 () (@var "X" (-> $$unsorted Bool))) % 0.21/0.53 (define @t9 () (lambda (@list @t8 @t7 @t5) (= (_ @t8 @t5) (_ @t7 @t5)))) % 0.21/0.53 (define @t10 () (@var "Phi" (-> $$unsorted Bool))) % 0.21/0.53 (define @t11 () (_ @t10 @t5)) % 0.21/0.53 (define @t12 () (not @t11)) % 0.21/0.53 (define @t13 () (@list @t10 @t5)) % 0.21/0.53 (define @t14 () (lambda @t13 @t12)) % 0.21/0.53 (define @t15 () (@var "Psi" (-> $$unsorted Bool))) % 0.21/0.53 (define @t16 () (lambda (@list @t10 @t15 @t5) (or @t11 (_ @t15 @t5)))) % 0.21/0.53 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.21/0.53 (define @t18 () (_ tptp.mnot @t15)) % 0.21/0.53 (define @t19 () (_ tptp.mnot @t10)) % 0.21/0.53 (define @t20 () (_ tptp.mor @t19)) % 0.21/0.53 (define @t21 () (@list @t10 @t15 @t17)) % 0.21/0.53 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.21/0.53 (define @t23 () (lambda @t21 (_ (_ @t20 @t15) @t17))) % 0.21/0.53 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t10) @t17))) % 0.21/0.53 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t10) @t15)) (_ (_ tptp.mimplies @t15) @t10)) @t17))) % 0.21/0.53 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t10) @t15)) @t17))) % 0.21/0.53 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.21/0.53 (define @t28 () (_ @t27 @t4)) % 0.21/0.53 (define @t29 () (lambda (@list @t27 @t5) (forall (@list @t4) (_ @t28 @t5)))) % 0.21/0.53 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.21/0.53 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.21/0.53 (define @t32 () (_ @t31 @t30)) % 0.21/0.53 (define @t33 () (lambda (@list @t31 @t5) (forall (@list @t30) (_ @t32 @t5)))) % 0.21/0.53 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t4 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.21/0.53 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.21/0.53 (define @t36 () (@list @t5)) % 0.21/0.53 (define @t37 () (lambda @t36 true)) % 0.21/0.53 (define @t38 () (@var "V" $$unsorted)) % 0.21/0.53 (define @t39 () (_ @t10 @t38)) % 0.21/0.53 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.21/0.53 (define @t41 () (@list @t38)) % 0.21/0.53 (define @t42 () (lambda (@list @t40 @t10 @t5) (forall @t41 (or (not (_ (_ @t40 @t5) @t38)) @t39)))) % 0.21/0.53 (define @t43 () (lambda (@list @t40 @t10 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.21/0.53 (define @t44 () (@var "S" $$unsorted)) % 0.21/0.53 (define @t45 () (_ @t40 @t44)) % 0.21/0.53 (define @t46 () (@list @t44)) % 0.21/0.53 (define @t47 () (@list @t40)) % 0.21/0.53 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.21/0.53 (define @t49 () (@var "T" $$unsorted)) % 0.21/0.53 (define @t50 () (_ @t40 @t49)) % 0.21/0.53 (define @t51 () (_ @t45 @t49)) % 0.21/0.53 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.21/0.53 (define @t53 () (@list @t49)) % 0.21/0.53 (define @t54 () (lambda @t47 (forall @t46 (exists @t53 @t51)))) % 0.21/0.53 (define @t55 () (@var "U" $$unsorted)) % 0.21/0.53 (define @t56 () (_ @t45 @t55)) % 0.21/0.53 (define @t57 () (_ @t50 @t55)) % 0.21/0.53 (define @t58 () (@list @t44 @t49 @t55)) % 0.21/0.53 (define @t59 () (lambda @t47 (forall @t58 (=> (and @t51 @t57) @t56)))) % 0.21/0.53 (define @t60 () (and @t51 @t56)) % 0.21/0.53 (define @t61 () (lambda @t47 (forall @t58 (=> @t60 @t57)))) % 0.21/0.53 (define @t62 () (= @t49 @t55)) % 0.21/0.53 (define @t63 () (lambda @t47 (forall @t58 (=> @t60 @t62)))) % 0.21/0.53 (define @t64 () (@list @t55)) % 0.21/0.53 (define @t65 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t64 (=> @t56 @t62))))))) % 0.21/0.53 (define @t66 () (_ @t40 @t55)) % 0.21/0.53 (define @t67 () (_ @t66 @t49)) % 0.21/0.53 (define @t68 () (lambda @t47 (forall @t58 (=> @t51 (exists @t64 (and @t56 @t67)))))) % 0.21/0.53 (define @t69 () (lambda @t47 (forall @t58 (=> @t60 (or @t57 @t62 @t67))))) % 0.21/0.53 (define @t70 () (lambda @t47 (forall @t58 (=> @t60 (exists @t41 (and (_ @t50 @t38) (_ @t66 @t38))))))) % 0.21/0.53 (define @t71 () (forall @t36 @t11)) % 0.21/0.53 (define @t72 () (@list @t10)) % 0.21/0.53 (define @t73 () (lambda @t72 @t71)) % 0.21/0.53 (define @t74 () (lambda @t72 (forall @t36 @t12))) % 0.21/0.53 (define @t75 () (lambda @t72 (exists @t36 @t11))) % 0.21/0.53 (define @t76 () (lambda @t72 (exists @t36 @t12))) % 0.21/0.53 (define @t77 () (_ (_ tptp.rel_k @t5) @t38)) % 0.21/0.53 (define @t78 () (not @t77)) % 0.21/0.53 (define @t79 () (or @t78 @t39)) % 0.21/0.53 (define @t80 () (forall @t41 @t79)) % 0.21/0.53 (define @t81 () (lambda @t13 @t80)) % 0.21/0.53 (define @t82 () (lambda (@list @t10 @t17) (_ (_ tptp.mnot (_ tptp.mbox_k @t19)) @t17))) % 0.21/0.53 (define @t83 () (tptp.rel_k @t5 @t38)) % 0.21/0.53 (define @t84 () (not @t83)) % 0.21/0.53 (define @t85 () (or @t84 (tptp.phi @t38))) % 0.21/0.53 (define @t86 () (forall (@list @t5 @t38) @t85)) % 0.21/0.53 (define @t87 () (forall @t41 @t85)) % 0.21/0.53 (define @t88 () (lambda @t36 @t87)) % 0.21/0.53 (define @t89 () (_ @t88 @t5)) % 0.21/0.53 (define @t90 () (forall @t36 @t89)) % 0.21/0.53 (define @t91 () (_ @t10 @t5)) % 0.21/0.53 (define @t92 () (lambda @t72 (forall @t36 @t91))) % 0.21/0.53 (define @t93 () (_ @t10 @t38)) % 0.21/0.53 (define @t94 () (_ (lambda @t13 (forall @t41 (or @t84 @t93))) tptp.phi)) % 0.21/0.53 (define @t95 () (forall @t36 (tptp.phi @t5))) % 0.21/0.53 (define @t96 () (_ @t92 tptp.phi)) % 0.21/0.53 (define @t97 () (=> @t96 (_ @t92 @t94))) % 0.21/0.53 (define @t98 () (@quantifiers_skolemize @t86 1)) % 0.21/0.53 (define @t99 () (tptp.phi @t98)) % 0.21/0.53 (define @t100 () (or (not (tptp.rel_k (@quantifiers_skolemize @t86 0) @t98)) @t99)) % 0.21/0.53 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.21/0.53 (assume @p2 @t2) % 0.21/0.53 (assume @p3 true) % 0.21/0.53 (step @p4 (= tptp.meq_ind @t6) :rule refl :args (@t6)) % 0.21/0.53 (step @p5 (= tptp.meq_prop @t9) :rule refl :args (@t9)) % 0.21/0.53 (step @p6 (= tptp.mnot @t14) :rule refl :args (@t14)) % 0.21/0.53 (step @p7 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.21/0.53 (step @p8 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.21/0.53 (step @p9 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.21/0.53 (step @p10 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.21/0.53 (step @p11 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.21/0.53 (step @p12 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.21/0.53 (step @p13 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.21/0.53 (step @p14 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.21/0.53 (step @p15 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.21/0.53 (step @p16 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.21/0.53 (step @p17 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.21/0.53 (step @p18 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.21/0.53 (step @p19 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.21/0.53 (step @p20 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.21/0.53 (step @p21 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.21/0.53 (step @p22 (= tptp.mserial @t54) :rule refl :args (@t54)) % 0.21/0.53 (step @p23 (= tptp.mtransitive @t59) :rule refl :args (@t59)) % 0.21/0.53 (step @p24 (= tptp.meuclidean @t61) :rule refl :args (@t61)) % 0.21/0.53 (step @p25 (= tptp.mpartially_functional @t63) :rule refl :args (@t63)) % 0.21/0.53 (step @p26 (= tptp.mfunctional @t65) :rule refl :args (@t65)) % 0.21/0.53 (step @p27 (= tptp.mweakly_dense @t68) :rule refl :args (@t68)) % 0.21/0.53 (step @p28 (= tptp.mweakly_connected @t69) :rule refl :args (@t69)) % 0.21/0.53 (step @p29 (= tptp.mweakly_directed @t70) :rule refl :args (@t70)) % 0.21/0.53 (step @p30 (= tptp.mvalid @t73) :rule refl :args (@t73)) % 0.21/0.53 (step @p31 (= tptp.minvalid @t74) :rule refl :args (@t74)) % 0.21/0.53 (step @p32 (= tptp.msatisfiable @t75) :rule refl :args (@t75)) % 0.21/0.53 (step @p33 (= tptp.mcountersatisfiable @t76) :rule refl :args (@t76)) % 0.21/0.53 (step @p34 (= tptp.mbox_k @t81) :rule refl :args (@t81)) % 0.21/0.53 (step @p35 (= tptp.mdia_k @t82) :rule refl :args (@t82)) % 0.21/0.53 (step @p36 :rule quant-merge-prenex :args ((= (forall @t36 @t87) @t86))) % 0.21/0.53 (step @p37 :rule beta-reduce :args ((= @t89 @t87))) % 0.21/0.53 (step @p38 :rule cong :premises (@p37) :args (@t90)) % 0.21/0.53 (step @p39 :rule trans :premises (@p38 @p36)) % 0.21/0.53 (step @p40 :rule beta-reduce :args ((= (_ @t92 @t88) @t90))) % 0.21/0.53 (step @p41 :rule trans :premises (@p40 @p39)) % 0.21/0.53 (step @p42 :rule beta-reduce :args ((= @t94 @t88))) % 0.21/0.53 (step @p43 :rule refl :args (@t92)) % 0.21/0.53 (step @p44 :rule ho_cong :premises (@p43 @p42)) % 0.21/0.53 (step @p45 :rule trans :premises (@p44 @p41)) % 0.21/0.53 (step @p46 :rule beta-reduce :args ((= @t96 @t95))) % 0.21/0.53 (step @p47 :rule cong :premises (@p46 @p45) :args (@t97)) % 0.21/0.53 (step @p48 :rule cong :premises (@p47) :args ((not @t97))) % 0.21/0.53 (step @p49 :rule refl :args (tptp.phi)) % 0.21/0.53 (step @p50 :rule refl :args (@t93)) % 0.21/0.53 (step @p51 :rule refl :args (@t39)) % 0.21/0.53 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t39 @t93))) % 0.21/0.53 (step @p53 :rule symm :premises (@p52)) % 0.21/0.53 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 0.21/0.53 (step @p55 :rule refl :args (@t83)) % 0.21/0.53 (step @p56 :rule refl :args (@t77)) % 0.21/0.53 (step @p57 :rule cong :premises (@p56 @p55) :args ((= @t77 @t83))) % 0.21/0.53 (step @p58 :rule symm :premises (@p57)) % 0.21/0.53 (step @p59 :rule eq_resolve :premises (@p56 @p58)) % 0.21/0.53 (step @p60 :rule cong :premises (@p59) :args (@t78)) % 0.21/0.53 (step @p61 :rule nary_cong :premises (@p60 @p54) :args (@t79)) % 0.21/0.53 (step @p62 :rule cong :premises (@p61) :args (@t80)) % 0.21/0.53 (step @p63 :rule cong :premises (@p62) :args (@t81)) % 0.21/0.53 (step @p64 :rule trans :premises (@p34 @p63)) % 0.21/0.53 (step @p65 :rule ho_cong :premises (@p64 @p49)) % 0.21/0.53 (step @p66 :rule refl :args (@t91)) % 0.21/0.53 (step @p67 :rule refl :args (@t11)) % 0.21/0.53 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t11 @t91))) % 0.21/0.53 (step @p69 :rule symm :premises (@p68)) % 0.21/0.53 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.21/0.53 (step @p71 :rule cong :premises (@p70) :args (@t71)) % 0.21/0.53 (step @p72 :rule cong :premises (@p71) :args (@t73)) % 0.21/0.53 (step @p73 :rule trans :premises (@p30 @p72)) % 0.21/0.53 (step @p74 :rule ho_cong :premises (@p73 @p65)) % 0.21/0.53 (step @p75 :rule ho_cong :premises (@p73 @p49)) % 0.21/0.53 (step @p76 :rule cong :premises (@p75 @p74) :args (@t1)) % 0.21/0.53 (step @p77 :rule cong :premises (@p76) :args (@t2)) % 0.21/0.53 (step @p78 :rule trans :premises (@p77 @p48)) % 0.21/0.53 (step @p79 :rule eq_resolve :premises (@p2 @p78)) % 0.21/0.53 (step @p80 :rule not_implies_elim1 :premises (@p79)) % 0.21/0.53 (step @p81 :rule not_implies_elim2 :premises (@p79)) % 0.21/0.53 (step @p82 :rule skolemize :premises (@p81)) % 0.21/0.53 (step @p83 :rule cnf_or_neg :args (@t100 1)) % 0.21/0.53 (step @p84 :rule chain_m_resolution :premises (@p83 @p82) :args ((not @t99) (@list true) (@list @t100))) % 0.21/0.53 (assume-push @p91 @t95) % 0.21/0.53 (step @p86 :rule instantiate :premises (@p80) :args ((@list @t98))) % 0.21/0.53 (step-pop @p92 :rule scope :premises (@p86)) % 0.21/0.53 (step @p87 :rule process_scope :premises (@p92) :args (@t99)) % 0.21/0.53 (step @p89 :rule implies_elim :premises (@p87)) % 0.21/0.53 (step @p90 false :rule chain_m_resolution :premises (@p89 @p84 @p80) :args (false (@list true false) (@list @t99 @t95))) % 0.21/0.53 ) % 0.21/0.53 % SZS output end Proof % 0.21/0.53 % cvc5 exiting %------------------------------------------------------------------------------