%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO419^1 : 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 : n025.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 09:12:37 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO419^1 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n025.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Wed Jun 3 00:07:16 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.37/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-sort tptp.mu 0) % 0.37/0.58 (declare-const tptp.rel_d (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.p (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.37/0.58 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.37/0.58 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.58 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.58 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.58 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.37/0.58 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.58 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.58 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.37/0.58 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.37/0.58 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.58 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.58 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.37/0.58 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.37/0.58 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.37/0.58 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.37/0.58 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.37/0.58 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.37/0.58 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.58 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.58 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.37/0.58 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.37/0.58 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.37/0.58 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.37/0.58 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.37/0.58 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.37/0.58 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.37/0.58 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.58 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.58 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.58 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.58 (define tptp.mbox_d () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_d _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.37/0.58 (define tptp.mdia_d () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_d (_ tptp.mnot _let_2))) _let_1))))) % 0.37/0.58 (define @t1 () (not (_ tptp.mvalid (_ tptp.mnot (_ tptp.mbox_d (_ (_ tptp.mand tptp.p) (_ tptp.mnot tptp.p))))))) % 0.37/0.58 (define @t2 () (@var "Y" tptp.mu)) % 0.37/0.58 (define @t3 () (@var "X" tptp.mu)) % 0.37/0.58 (define @t4 () (@var "W" $$unsorted)) % 0.37/0.58 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.37/0.58 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.58 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.58 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.37/0.58 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.37/0.58 (define @t10 () (_ @t9 @t4)) % 0.37/0.58 (define @t11 () (not @t10)) % 0.37/0.58 (define @t12 () (@list @t9 @t4)) % 0.37/0.58 (define @t13 () (lambda @t12 @t11)) % 0.37/0.58 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.37/0.58 (define @t15 () (_ @t14 @t4)) % 0.37/0.58 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.37/0.58 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.58 (define @t18 () (_ tptp.mnot @t14)) % 0.37/0.58 (define @t19 () (_ tptp.mnot @t9)) % 0.37/0.58 (define @t20 () (_ tptp.mor @t19)) % 0.37/0.58 (define @t21 () (@list @t9 @t14 @t17)) % 0.37/0.58 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.37/0.58 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.37/0.58 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.37/0.58 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.37/0.58 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.37/0.58 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.37/0.58 (define @t28 () (_ @t27 @t3)) % 0.37/0.58 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.37/0.58 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.58 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.37/0.58 (define @t32 () (_ @t31 @t30)) % 0.37/0.58 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.37/0.58 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.37/0.58 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.37/0.58 (define @t36 () (@list @t4)) % 0.37/0.58 (define @t37 () (lambda @t36 true)) % 0.37/0.58 (define @t38 () (@var "V" $$unsorted)) % 0.37/0.58 (define @t39 () (_ @t9 @t38)) % 0.37/0.58 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.58 (define @t41 () (@list @t38)) % 0.37/0.58 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.37/0.58 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.37/0.58 (define @t44 () (@var "S" $$unsorted)) % 0.37/0.58 (define @t45 () (_ @t40 @t44)) % 0.37/0.58 (define @t46 () (@list @t44)) % 0.37/0.58 (define @t47 () (@list @t40)) % 0.37/0.58 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.37/0.58 (define @t49 () (@var "T" $$unsorted)) % 0.37/0.58 (define @t50 () (_ @t40 @t49)) % 0.37/0.58 (define @t51 () (_ @t45 @t49)) % 0.37/0.58 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.37/0.58 (define @t53 () (@list @t49)) % 0.37/0.58 (define @t54 () (exists @t53 @t51)) % 0.37/0.58 (define @t55 () (forall @t46 @t54)) % 0.37/0.58 (define @t56 () (lambda @t47 @t55)) % 0.37/0.58 (define @t57 () (@var "U" $$unsorted)) % 0.37/0.58 (define @t58 () (_ @t45 @t57)) % 0.37/0.58 (define @t59 () (_ @t50 @t57)) % 0.37/0.58 (define @t60 () (@list @t44 @t49 @t57)) % 0.37/0.58 (define @t61 () (lambda @t47 (forall @t60 (=> (and @t51 @t59) @t58)))) % 0.37/0.58 (define @t62 () (and @t51 @t58)) % 0.37/0.58 (define @t63 () (lambda @t47 (forall @t60 (=> @t62 @t59)))) % 0.37/0.58 (define @t64 () (= @t49 @t57)) % 0.37/0.58 (define @t65 () (lambda @t47 (forall @t60 (=> @t62 @t64)))) % 0.37/0.58 (define @t66 () (@list @t57)) % 0.37/0.58 (define @t67 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t66 (=> @t58 @t64))))))) % 0.37/0.58 (define @t68 () (_ @t40 @t57)) % 0.37/0.58 (define @t69 () (_ @t68 @t49)) % 0.37/0.58 (define @t70 () (lambda @t47 (forall @t60 (=> @t51 (exists @t66 (and @t58 @t69)))))) % 0.37/0.58 (define @t71 () (lambda @t47 (forall @t60 (=> @t62 (or @t59 @t64 @t69))))) % 0.37/0.58 (define @t72 () (lambda @t47 (forall @t60 (=> @t62 (exists @t41 (and (_ @t50 @t38) (_ @t68 @t38))))))) % 0.37/0.58 (define @t73 () (forall @t36 @t10)) % 0.37/0.58 (define @t74 () (@list @t9)) % 0.37/0.58 (define @t75 () (lambda @t74 @t73)) % 0.37/0.58 (define @t76 () (lambda @t74 (forall @t36 @t11))) % 0.37/0.58 (define @t77 () (lambda @t74 (exists @t36 @t10))) % 0.37/0.58 (define @t78 () (lambda @t74 (exists @t36 @t11))) % 0.37/0.58 (define @t79 () (_ (_ tptp.rel_d @t4) @t38)) % 0.37/0.58 (define @t80 () (not @t79)) % 0.37/0.58 (define @t81 () (or @t80 @t39)) % 0.37/0.58 (define @t82 () (forall @t41 @t81)) % 0.37/0.58 (define @t83 () (lambda @t12 @t82)) % 0.37/0.58 (define @t84 () (lambda (@list @t9 @t17) (_ (_ tptp.mnot (_ tptp.mbox_d @t19)) @t17))) % 0.37/0.58 (define @t85 () (forall @t46 (not (forall @t53 (not (tptp.rel_d @t44 @t49)))))) % 0.37/0.58 (define @t86 () (_ @t40 @t44 @t49)) % 0.37/0.58 (define @t87 () (not @t51)) % 0.37/0.58 (define @t88 () (forall @t53 @t87)) % 0.37/0.58 (define @t89 () (not @t88)) % 0.37/0.58 (define @t90 () (tptp.rel_d @t4 @t38)) % 0.37/0.58 (define @t91 () (not @t90)) % 0.37/0.58 (define @t92 () (forall @t41 @t91)) % 0.37/0.58 (define @t93 () (not @t92)) % 0.37/0.58 (define @t94 () (forall @t36 @t93)) % 0.37/0.58 (define @t95 () (@list false)) % 0.37/0.58 (define @t96 () (lambda @t36 @t93)) % 0.37/0.58 (define @t97 () (_ @t96 @t4)) % 0.37/0.58 (define @t98 () (forall @t36 @t97)) % 0.37/0.58 (define @t99 () (_ @t9 @t4)) % 0.37/0.58 (define @t100 () (lambda @t74 (forall @t36 @t99))) % 0.37/0.58 (define @t101 () (lambda @t36 @t92)) % 0.37/0.58 (define @t102 () (_ @t101 @t4)) % 0.37/0.58 (define @t103 () (not @t102)) % 0.37/0.58 (define @t104 () (lambda @t36 @t103)) % 0.37/0.58 (define @t105 () (or @t91 false)) % 0.37/0.58 (define @t106 () (_ tptp.p @t38)) % 0.37/0.58 (define @t107 () (not @t106)) % 0.37/0.58 (define @t108 () (not (or @t107 @t106))) % 0.37/0.58 (define @t109 () (or @t91 @t108)) % 0.37/0.58 (define @t110 () (_ tptp.p @t17)) % 0.37/0.58 (define @t111 () (not @t110)) % 0.37/0.58 (define @t112 () (@list @t17)) % 0.37/0.58 (define @t113 () (lambda @t112 (not (or @t111 @t110)))) % 0.37/0.58 (define @t114 () (_ @t113 @t38)) % 0.37/0.58 (define @t115 () (or @t91 @t114)) % 0.37/0.58 (define @t116 () (forall @t41 @t115)) % 0.37/0.58 (define @t117 () (lambda @t36 @t116)) % 0.37/0.58 (define @t118 () (_ @t9 @t38)) % 0.37/0.58 (define @t119 () (lambda @t12 (forall @t41 (or @t91 @t118)))) % 0.37/0.58 (define @t120 () (lambda @t36 (not (_ tptp.p @t4)))) % 0.37/0.58 (define @t121 () (_ @t120 @t17)) % 0.37/0.58 (define @t122 () (not @t121)) % 0.37/0.58 (define @t123 () (or @t111 @t122)) % 0.37/0.58 (define @t124 () (not @t123)) % 0.37/0.58 (define @t125 () (lambda @t112 @t124)) % 0.37/0.58 (define @t126 () (not (_ @t14 @t17))) % 0.37/0.58 (define @t127 () (lambda (@list @t14 @t17) (not (or @t111 @t126)))) % 0.37/0.58 (define @t128 () (_ @t13 tptp.p)) % 0.37/0.58 (define @t129 () (not (or (not (_ @t9 @t17)) @t126))) % 0.37/0.58 (define @t130 () (_ (lambda @t21 @t129) tptp.p)) % 0.37/0.58 (define @t131 () (not @t15)) % 0.37/0.58 (define @t132 () (or @t11 @t131)) % 0.37/0.58 (define @t133 () (lambda @t36 @t132)) % 0.37/0.58 (define @t134 () (_ @t133 @t4)) % 0.37/0.58 (define @t135 () (not @t134)) % 0.37/0.58 (define @t136 () (lambda @t36 @t135)) % 0.37/0.58 (define @t137 () (lambda @t36 @t131)) % 0.37/0.58 (define @t138 () (_ @t137 @t4)) % 0.37/0.58 (define @t139 () (or @t11 @t138)) % 0.37/0.58 (define @t140 () (lambda @t36 @t139)) % 0.37/0.58 (define @t141 () (@list @t14 @t4)) % 0.37/0.58 (define @t142 () (lambda @t36 @t11)) % 0.37/0.58 (define @t143 () (_ @t142 @t4)) % 0.37/0.58 (define @t144 () (or @t143 @t15)) % 0.37/0.58 (define @t145 () (lambda @t141 @t144)) % 0.37/0.58 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.37/0.58 (assume @p2 (_ tptp.mserial tptp.rel_d)) % 0.37/0.58 (assume @p3 @t1) % 0.37/0.58 (assume @p4 true) % 0.37/0.58 (step @p5 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.37/0.58 (step @p6 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.37/0.58 (step @p7 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.37/0.58 (step @p8 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.37/0.58 (step @p9 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.37/0.58 (step @p10 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.37/0.58 (step @p11 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.37/0.58 (step @p12 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.37/0.58 (step @p13 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.37/0.58 (step @p14 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.37/0.58 (step @p15 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.37/0.58 (step @p16 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.37/0.58 (step @p17 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.37/0.58 (step @p18 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.37/0.58 (step @p19 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.37/0.58 (step @p20 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.37/0.58 (step @p21 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.37/0.58 (step @p22 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.37/0.58 (step @p23 (= tptp.mserial @t56) :rule refl :args (@t56)) % 0.37/0.58 (step @p24 (= tptp.mtransitive @t61) :rule refl :args (@t61)) % 0.37/0.58 (step @p25 (= tptp.meuclidean @t63) :rule refl :args (@t63)) % 0.37/0.58 (step @p26 (= tptp.mpartially_functional @t65) :rule refl :args (@t65)) % 0.37/0.58 (step @p27 (= tptp.mfunctional @t67) :rule refl :args (@t67)) % 0.37/0.58 (step @p28 (= tptp.mweakly_dense @t70) :rule refl :args (@t70)) % 0.37/0.58 (step @p29 (= tptp.mweakly_connected @t71) :rule refl :args (@t71)) % 0.37/0.58 (step @p30 (= tptp.mweakly_directed @t72) :rule refl :args (@t72)) % 0.37/0.58 (step @p31 (= tptp.mvalid @t75) :rule refl :args (@t75)) % 0.37/0.58 (step @p32 (= tptp.minvalid @t76) :rule refl :args (@t76)) % 0.37/0.58 (step @p33 (= tptp.msatisfiable @t77) :rule refl :args (@t77)) % 0.37/0.58 (step @p34 (= tptp.mcountersatisfiable @t78) :rule refl :args (@t78)) % 0.37/0.58 (step @p35 (= tptp.mbox_d @t83) :rule refl :args (@t83)) % 0.37/0.58 (step @p36 (= tptp.mdia_d @t84) :rule refl :args (@t84)) % 0.37/0.58 (step @p37 :rule beta-reduce :args ((= (_ (lambda @t47 (forall @t46 (not (forall @t53 (not @t86))))) tptp.rel_d) @t85))) % 0.37/0.58 (step @p38 :rule refl :args (tptp.rel_d)) % 0.37/0.58 (step @p39 :rule refl :args (@t86)) % 0.37/0.58 (step @p40 :rule refl :args (@t51)) % 0.37/0.58 (step @p41 :rule cong :premises (@p40 @p39) :args ((= @t51 @t86))) % 0.37/0.58 (step @p42 :rule symm :premises (@p41)) % 0.37/0.58 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 0.37/0.58 (step @p44 :rule cong :premises (@p43) :args (@t87)) % 0.37/0.58 (step @p45 :rule cong :premises (@p44) :args (@t88)) % 0.37/0.58 (step @p46 :rule cong :premises (@p45) :args (@t89)) % 0.37/0.58 (step @p47 :rule exists-elim :args ((= @t54 @t89))) % 0.37/0.58 (step @p48 :rule trans :premises (@p47 @p46)) % 0.37/0.58 (step @p49 :rule cong :premises (@p48) :args (@t55)) % 0.37/0.58 (step @p50 :rule cong :premises (@p49) :args (@t56)) % 0.37/0.58 (step @p51 :rule trans :premises (@p23 @p50)) % 0.37/0.58 (step @p52 :rule ho_cong :premises (@p51 @p38)) % 0.37/0.58 (step @p53 :rule trans :premises (@p52 @p37)) % 0.37/0.58 (step @p54 :rule eq_resolve :premises (@p2 @p53)) % 0.37/0.58 (step @p55 :rule alpha_equiv :args (@t85 (@list @t49 @t44) (@list @t38 @t4))) % 0.37/0.58 (step @p56 :rule equiv_elim1 :premises (@p55)) % 0.37/0.58 (step @p57 :rule reordering :premises (@p56) :args ((or @t94 (not @t85)))) % 0.37/0.58 (step @p58 :rule chain_m_resolution :premises (@p57 @p54) :args (@t94 @t95 (@list @t85))) % 0.37/0.58 (step @p59 :rule beta-reduce :args ((= @t97 @t93))) % 0.37/0.58 (step @p60 :rule cong :premises (@p59) :args (@t98)) % 0.37/0.58 (step @p61 :rule beta-reduce :args ((= (_ @t100 @t96) @t98))) % 0.37/0.58 (step @p62 :rule trans :premises (@p61 @p60)) % 0.37/0.58 (step @p63 :rule beta-reduce :args ((= @t102 @t92))) % 0.37/0.58 (step @p64 :rule cong :premises (@p63) :args (@t103)) % 0.37/0.58 (step @p65 :rule cong :premises (@p64) :args (@t104)) % 0.37/0.58 (step @p66 :rule beta-reduce :args ((= (_ @t13 @t101) @t104))) % 0.37/0.58 (step @p67 :rule trans :premises (@p66 @p65)) % 0.37/0.58 (step @p68 :rule aci_norm :args ((= @t105 @t91))) % 0.37/0.58 (step @p69 :rule cong :premises (@p68) :args ((forall @t41 @t105))) % 0.37/0.58 (step @p70 :rule bool-and-conf :args (true @t106 true true)) % 0.37/0.58 (step @p71 :rule refl :args (@t107)) % 0.37/0.58 (step @p72 :rule bool-double-not-elim :args (@t106)) % 0.37/0.58 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((and (not @t107) @t107))) % 0.37/0.58 (step @p74 :rule bool-or-de-morgan :args (@t107 @t106 false)) % 0.37/0.58 (step @p75 :rule trans :premises (@p74 @p73)) % 0.37/0.58 (step @p76 :rule trans :premises (@p75 @p70)) % 0.37/0.58 (step @p77 :rule refl :args (@t91)) % 0.37/0.58 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t109)) % 0.37/0.58 (step @p79 :rule cong :premises (@p78) :args ((forall @t41 @t109))) % 0.37/0.58 (step @p80 :rule trans :premises (@p79 @p69)) % 0.37/0.58 (step @p81 :rule beta-reduce :args ((= @t114 @t108))) % 0.37/0.58 (step @p82 :rule refl :args (@t91)) % 0.37/0.58 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t115)) % 0.37/0.58 (step @p84 :rule cong :premises (@p83) :args (@t116)) % 0.37/0.58 (step @p85 :rule trans :premises (@p84 @p80)) % 0.37/0.58 (step @p86 :rule cong :premises (@p85) :args (@t117)) % 0.37/0.58 (step @p87 :rule beta-reduce :args ((= (_ @t119 @t113) @t117))) % 0.37/0.58 (step @p88 :rule trans :premises (@p87 @p86)) % 0.37/0.58 (step @p89 :rule bool-double-not-elim :args (@t110)) % 0.37/0.58 (step @p90 :rule beta-reduce :args ((= @t121 @t111))) % 0.37/0.58 (step @p91 :rule cong :premises (@p90) :args (@t122)) % 0.37/0.58 (step @p92 :rule trans :premises (@p91 @p89)) % 0.37/0.58 (step @p93 :rule refl :args (@t111)) % 0.37/0.58 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t123)) % 0.37/0.58 (step @p95 :rule cong :premises (@p94) :args (@t124)) % 0.37/0.58 (step @p96 :rule cong :premises (@p95) :args (@t125)) % 0.37/0.58 (step @p97 :rule beta-reduce :args ((= (_ @t127 @t120) @t125))) % 0.37/0.58 (step @p98 :rule trans :premises (@p97 @p96)) % 0.37/0.58 (step @p99 :rule beta-reduce :args ((= @t128 @t120))) % 0.37/0.58 (step @p100 :rule beta-reduce :args ((= @t130 @t127))) % 0.37/0.58 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 0.37/0.58 (step @p102 :rule trans :premises (@p101 @p98)) % 0.37/0.58 (step @p103 :rule refl :args (@t119)) % 0.37/0.58 (step @p104 :rule ho_cong :premises (@p103 @p102)) % 0.37/0.58 (step @p105 :rule trans :premises (@p104 @p88)) % 0.37/0.58 (step @p106 :rule refl :args (@t13)) % 0.37/0.58 (step @p107 :rule ho_cong :premises (@p106 @p105)) % 0.37/0.58 (step @p108 :rule trans :premises (@p107 @p67)) % 0.37/0.58 (step @p109 :rule refl :args (@t100)) % 0.37/0.58 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 0.37/0.58 (step @p111 :rule trans :premises (@p110 @p62)) % 0.37/0.58 (step @p112 :rule cong :premises (@p111) :args ((not (_ @t100 (_ @t13 (_ @t119 (_ @t130 @t128))))))) % 0.37/0.58 (step @p113 :rule refl :args (tptp.p)) % 0.37/0.58 (step @p114 :rule ho_cong :premises (@p7 @p113)) % 0.37/0.58 (step @p115 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t132)) @t17) @t129))) % 0.37/0.58 (step @p116 :rule refl :args (@t17)) % 0.37/0.58 (step @p117 :rule beta-reduce :args ((= @t134 @t132))) % 0.37/0.58 (step @p118 :rule cong :premises (@p117) :args (@t135)) % 0.37/0.58 (step @p119 :rule cong :premises (@p118) :args (@t136)) % 0.37/0.58 (step @p120 :rule beta-reduce :args ((= (_ @t13 @t133) @t136))) % 0.37/0.58 (step @p121 :rule trans :premises (@p120 @p119)) % 0.37/0.58 (step @p122 :rule beta-reduce :args ((= @t138 @t131))) % 0.37/0.58 (step @p123 :rule refl :args (@t11)) % 0.37/0.58 (step @p124 :rule nary_cong :premises (@p123 @p122) :args (@t139)) % 0.37/0.58 (step @p125 :rule cong :premises (@p124) :args (@t140)) % 0.37/0.58 (step @p126 :rule beta-reduce :args ((= (_ (lambda @t141 (or @t11 @t15)) @t137) @t140))) % 0.37/0.58 (step @p127 :rule trans :premises (@p126 @p125)) % 0.37/0.58 (step @p128 :rule beta-reduce :args ((= (_ @t13 @t14) @t137))) % 0.37/0.58 (step @p129 :rule refl :args (@t15)) % 0.37/0.58 (step @p130 :rule beta-reduce :args ((= @t143 @t11))) % 0.37/0.58 (step @p131 :rule nary_cong :premises (@p130 @p129) :args (@t144)) % 0.37/0.58 (step @p132 :rule cong :premises (@p131) :args (@t145)) % 0.37/0.58 (step @p133 :rule beta-reduce :args ((= (_ @t16 @t142) @t145))) % 0.37/0.58 (step @p134 :rule trans :premises (@p133 @p132)) % 0.37/0.58 (step @p135 :rule beta-reduce :args ((= (_ @t13 @t9) @t142))) % 0.37/0.58 (step @p136 :rule refl :args (@t16)) % 0.37/0.58 (step @p137 :rule ho_cong :premises (@p136 @p135)) % 0.37/0.58 (step @p138 :rule trans :premises (@p137 @p134)) % 0.37/0.58 (step @p139 :rule ho_cong :premises (@p138 @p128)) % 0.37/0.58 (step @p140 :rule trans :premises (@p139 @p127)) % 0.37/0.58 (step @p141 :rule ho_cong :premises (@p106 @p140)) % 0.37/0.58 (step @p142 :rule trans :premises (@p141 @p121)) % 0.37/0.58 (step @p143 :rule ho_cong :premises (@p142 @p116)) % 0.37/0.58 (step @p144 :rule trans :premises (@p143 @p115)) % 0.37/0.58 (step @p145 :rule refl :args (@t14)) % 0.37/0.58 (step @p146 :rule ho_cong :premises (@p7 @p145)) % 0.37/0.58 (step @p147 :rule refl :args (@t9)) % 0.37/0.58 (step @p148 :rule ho_cong :premises (@p7 @p147)) % 0.37/0.58 (step @p149 :rule ho_cong :premises (@p8 @p148)) % 0.37/0.58 (step @p150 :rule ho_cong :premises (@p149 @p146)) % 0.37/0.58 (step @p151 :rule ho_cong :premises (@p7 @p150)) % 0.37/0.58 (step @p152 :rule ho_cong :premises (@p151 @p116)) % 0.37/0.58 (step @p153 :rule trans :premises (@p152 @p144)) % 0.37/0.58 (step @p154 :rule cong :premises (@p153) :args (@t22)) % 0.37/0.58 (step @p155 :rule trans :premises (@p9 @p154)) % 0.37/0.58 (step @p156 :rule ho_cong :premises (@p155 @p113)) % 0.37/0.58 (step @p157 :rule ho_cong :premises (@p156 @p114)) % 0.37/0.58 (step @p158 :rule refl :args (@t118)) % 0.37/0.58 (step @p159 :rule refl :args (@t39)) % 0.37/0.58 (step @p160 :rule cong :premises (@p159 @p158) :args ((= @t39 @t118))) % 0.37/0.58 (step @p161 :rule symm :premises (@p160)) % 0.37/0.58 (step @p162 :rule eq_resolve :premises (@p159 @p161)) % 0.37/0.58 (step @p163 :rule refl :args (@t90)) % 0.37/0.58 (step @p164 :rule refl :args (@t79)) % 0.37/0.58 (step @p165 :rule cong :premises (@p164 @p163) :args ((= @t79 @t90))) % 0.37/0.58 (step @p166 :rule symm :premises (@p165)) % 0.37/0.58 (step @p167 :rule eq_resolve :premises (@p164 @p166)) % 0.37/0.58 (step @p168 :rule cong :premises (@p167) :args (@t80)) % 0.37/0.58 (step @p169 :rule nary_cong :premises (@p168 @p162) :args (@t81)) % 0.37/0.58 (step @p170 :rule cong :premises (@p169) :args (@t82)) % 0.37/0.58 (step @p171 :rule cong :premises (@p170) :args (@t83)) % 0.37/0.58 (step @p172 :rule trans :premises (@p35 @p171)) % 0.37/0.58 (step @p173 :rule ho_cong :premises (@p172 @p157)) % 0.37/0.58 (step @p174 :rule ho_cong :premises (@p7 @p173)) % 0.37/0.58 (step @p175 :rule refl :args (@t99)) % 0.37/0.58 (step @p176 :rule refl :args (@t10)) % 0.37/0.58 (step @p177 :rule cong :premises (@p176 @p175) :args ((= @t10 @t99))) % 0.37/0.58 (step @p178 :rule symm :premises (@p177)) % 0.37/0.58 (step @p179 :rule eq_resolve :premises (@p176 @p178)) % 0.37/0.58 (step @p180 :rule cong :premises (@p179) :args (@t73)) % 0.37/0.58 (step @p181 :rule cong :premises (@p180) :args (@t75)) % 0.37/0.58 (step @p182 :rule trans :premises (@p31 @p181)) % 0.37/0.58 (step @p183 :rule ho_cong :premises (@p182 @p174)) % 0.37/0.58 (step @p184 :rule cong :premises (@p183) :args (@t1)) % 0.37/0.58 (step @p185 :rule trans :premises (@p184 @p112)) % 0.37/0.58 (step @p186 :rule eq_resolve :premises (@p3 @p185)) % 0.37/0.58 (step @p187 false :rule chain_m_resolution :premises (@p186 @p58) :args (false @t95 (@list @t94))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------