%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO455^2 : 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 : n006.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 09:12:44 AM UTC 2026 % Result : Theorem 0.52s 0.77s % Output : Proof 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO455^2 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n006.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 00:09:04 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.52/0.77 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.52/0.77 % SZS status Theorem % 0.52/0.77 % SZS output start Proof % 0.52/0.77 ( % 0.52/0.77 (declare-sort $$unsorted 0) % 0.52/0.77 (declare-sort tptp.mu 0) % 0.52/0.77 (declare-const tptp.rel_d (-> $$unsorted $$unsorted Bool)) % 0.52/0.77 (declare-const tptp.p (-> $$unsorted Bool)) % 0.52/0.77 (declare-const tptp.q (-> $$unsorted Bool)) % 0.52/0.77 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.52/0.77 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.52/0.77 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.52/0.77 (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)))))) % 0.52/0.77 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.52/0.77 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.52/0.77 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.52/0.77 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.52/0.77 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.52/0.77 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.52/0.77 (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))))))) % 0.52/0.77 (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))))))) % 0.52/0.77 (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)))))) % 0.52/0.77 (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)))))) % 0.52/0.77 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.52/0.77 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.52/0.77 (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)))))) % 0.52/0.77 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.52/0.77 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.52/0.77 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.52/0.77 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.52/0.77 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.52/0.77 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.52/0.77 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.52/0.77 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.52/0.77 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.52/0.77 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.52/0.77 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.52/0.77 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.52/0.77 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.52/0.77 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.52/0.77 (define tptp.mbox_d () (let ((_let_1 (@var "V" $$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)))))))) % 0.52/0.77 (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))))) % 0.52/0.77 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ (_ tptp.mand (_ tptp.mbox_d tptp.p)) (_ tptp.mbox_d (_ (_ tptp.mor (_ tptp.mnot tptp.p)) tptp.q)))) (_ tptp.mdia_d tptp.q))))) % 0.52/0.77 (define @t2 () (@var "Y" tptp.mu)) % 0.52/0.77 (define @t3 () (@var "X" tptp.mu)) % 0.52/0.77 (define @t4 () (@var "W" $$unsorted)) % 0.52/0.77 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.52/0.77 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.52/0.77 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.52/0.77 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.52/0.77 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.52/0.77 (define @t10 () (_ @t9 @t4)) % 0.52/0.77 (define @t11 () (not @t10)) % 0.52/0.77 (define @t12 () (@list @t9 @t4)) % 0.52/0.77 (define @t13 () (lambda @t12 @t11)) % 0.52/0.77 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.52/0.77 (define @t15 () (_ @t14 @t4)) % 0.52/0.77 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.52/0.77 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.52/0.77 (define @t18 () (_ tptp.mnot @t14)) % 0.52/0.77 (define @t19 () (_ tptp.mnot @t9)) % 0.52/0.77 (define @t20 () (_ tptp.mor @t19)) % 0.52/0.77 (define @t21 () (@list @t9 @t14 @t17)) % 0.52/0.77 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.52/0.77 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.52/0.77 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.52/0.77 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.52/0.77 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.52/0.77 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.52/0.77 (define @t28 () (_ @t27 @t3)) % 0.52/0.77 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.52/0.77 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.52/0.77 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.52/0.77 (define @t32 () (_ @t31 @t30)) % 0.52/0.77 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.52/0.77 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.52/0.77 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.52/0.77 (define @t36 () (@list @t4)) % 0.52/0.77 (define @t37 () (lambda @t36 true)) % 0.52/0.77 (define @t38 () (@var "V" $$unsorted)) % 0.52/0.77 (define @t39 () (_ @t9 @t38)) % 0.52/0.77 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.52/0.77 (define @t41 () (@list @t38)) % 0.52/0.77 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.52/0.77 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.52/0.77 (define @t44 () (@var "S" $$unsorted)) % 0.52/0.77 (define @t45 () (_ @t40 @t44)) % 0.52/0.77 (define @t46 () (@list @t44)) % 0.52/0.77 (define @t47 () (@list @t40)) % 0.52/0.77 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.52/0.77 (define @t49 () (@var "T" $$unsorted)) % 0.52/0.77 (define @t50 () (_ @t40 @t49)) % 0.52/0.77 (define @t51 () (_ @t45 @t49)) % 0.52/0.77 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.52/0.78 (define @t53 () (@list @t49)) % 0.52/0.78 (define @t54 () (exists @t53 @t51)) % 0.52/0.78 (define @t55 () (forall @t46 @t54)) % 0.52/0.78 (define @t56 () (lambda @t47 @t55)) % 0.52/0.78 (define @t57 () (@var "U" $$unsorted)) % 0.52/0.78 (define @t58 () (_ @t45 @t57)) % 0.52/0.78 (define @t59 () (_ @t50 @t57)) % 0.52/0.78 (define @t60 () (@list @t44 @t49 @t57)) % 0.52/0.78 (define @t61 () (lambda @t47 (forall @t60 (=> (and @t51 @t59) @t58)))) % 0.52/0.78 (define @t62 () (and @t51 @t58)) % 0.52/0.78 (define @t63 () (lambda @t47 (forall @t60 (=> @t62 @t59)))) % 0.52/0.78 (define @t64 () (= @t49 @t57)) % 0.52/0.78 (define @t65 () (lambda @t47 (forall @t60 (=> @t62 @t64)))) % 0.52/0.78 (define @t66 () (@list @t57)) % 0.52/0.78 (define @t67 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t66 (=> @t58 @t64))))))) % 0.52/0.78 (define @t68 () (_ @t40 @t57)) % 0.52/0.78 (define @t69 () (_ @t68 @t49)) % 0.52/0.78 (define @t70 () (lambda @t47 (forall @t60 (=> @t51 (exists @t66 (and @t58 @t69)))))) % 0.52/0.78 (define @t71 () (lambda @t47 (forall @t60 (=> @t62 (or @t59 @t64 @t69))))) % 0.52/0.78 (define @t72 () (lambda @t47 (forall @t60 (=> @t62 (exists @t41 (and (_ @t50 @t38) (_ @t68 @t38))))))) % 0.52/0.78 (define @t73 () (forall @t36 @t10)) % 0.52/0.78 (define @t74 () (@list @t9)) % 0.52/0.78 (define @t75 () (lambda @t74 @t73)) % 0.52/0.78 (define @t76 () (lambda @t74 (forall @t36 @t11))) % 0.52/0.78 (define @t77 () (lambda @t74 (exists @t36 @t10))) % 0.52/0.78 (define @t78 () (lambda @t74 (exists @t36 @t11))) % 0.52/0.78 (define @t79 () (_ (_ tptp.rel_d @t4) @t38)) % 0.52/0.78 (define @t80 () (not @t79)) % 0.52/0.78 (define @t81 () (or @t80 @t39)) % 0.52/0.78 (define @t82 () (forall @t41 @t81)) % 0.52/0.78 (define @t83 () (lambda @t12 @t82)) % 0.52/0.78 (define @t84 () (@list @t9 @t17)) % 0.52/0.78 (define @t85 () (lambda @t84 (_ (_ tptp.mnot (_ tptp.mbox_d @t19)) @t17))) % 0.52/0.78 (define @t86 () (_ @t40 @t44 @t49)) % 0.52/0.78 (define @t87 () (not @t51)) % 0.52/0.78 (define @t88 () (forall @t53 @t87)) % 0.52/0.78 (define @t89 () (not @t88)) % 0.52/0.78 (define @t90 () (tptp.q @t38)) % 0.52/0.78 (define @t91 () (tptp.p @t38)) % 0.52/0.78 (define @t92 () (not @t91)) % 0.52/0.78 (define @t93 () (tptp.rel_d @t4 @t38)) % 0.52/0.78 (define @t94 () (not @t93)) % 0.52/0.78 (define @t95 () (forall @t41 (or @t94 @t92 @t90))) % 0.52/0.78 (define @t96 () (forall @t41 (or @t94 @t91))) % 0.52/0.78 (define @t97 () (not @t90)) % 0.52/0.78 (define @t98 () (or (not (forall @t41 (or @t94 @t97))) (not @t96) (not @t95))) % 0.52/0.78 (define @t99 () (@quantifiers_skolemize (forall @t36 @t98) 0)) % 0.52/0.78 (define @t100 () (forall @t53 (not (tptp.rel_d @t99 @t49)))) % 0.52/0.78 (define @t101 () (@quantifiers_skolemize @t100 0)) % 0.52/0.78 (define @t102 () (tptp.rel_d @t99 @t101)) % 0.52/0.78 (define @t103 () (not @t100)) % 0.52/0.78 (define @t104 () (not @t102)) % 0.52/0.78 (define @t105 () (not @t104)) % 0.52/0.78 (define @t106 () (@list true)) % 0.52/0.78 (define @t107 () (not (tptp.rel_d @t17 @t38))) % 0.52/0.78 (define @t108 () (forall @t41 (or @t107 @t92 @t90))) % 0.52/0.78 (define @t109 () (not @t108)) % 0.52/0.78 (define @t110 () (forall @t41 (or @t107 @t91))) % 0.52/0.78 (define @t111 () (not @t110)) % 0.52/0.78 (define @t112 () (not (forall @t41 (or @t107 @t97)))) % 0.52/0.78 (define @t113 () (@list @t17)) % 0.52/0.78 (define @t114 () (lambda @t113 (or @t112 @t111 @t109))) % 0.52/0.78 (define @t115 () (_ @t114 @t4)) % 0.52/0.78 (define @t116 () (forall @t36 @t115)) % 0.52/0.78 (define @t117 () (_ @t9 @t4)) % 0.52/0.78 (define @t118 () (lambda @t74 (forall @t36 @t117))) % 0.52/0.78 (define @t119 () (lambda @t113 @t112)) % 0.52/0.78 (define @t120 () (_ @t119 @t17)) % 0.52/0.78 (define @t121 () (or @t120 @t111 @t109)) % 0.52/0.78 (define @t122 () (lambda @t113 @t121)) % 0.52/0.78 (define @t123 () (_ @t14 @t17)) % 0.52/0.78 (define @t124 () (or @t123 @t111 @t109)) % 0.52/0.78 (define @t125 () (@list @t14 @t17)) % 0.52/0.78 (define @t126 () (_ @t9 @t38)) % 0.52/0.78 (define @t127 () (not @t126)) % 0.52/0.78 (define @t128 () (not (forall @t41 (or @t107 @t127)))) % 0.52/0.78 (define @t129 () (_ (lambda @t84 @t128) tptp.q)) % 0.52/0.78 (define @t130 () (or @t111 @t109)) % 0.52/0.78 (define @t131 () (not @t130)) % 0.52/0.78 (define @t132 () (lambda @t113 @t131)) % 0.52/0.78 (define @t133 () (_ @t132 @t17)) % 0.52/0.78 (define @t134 () (not @t133)) % 0.52/0.78 (define @t135 () (or @t134 @t123)) % 0.52/0.78 (define @t136 () (lambda @t125 @t135)) % 0.52/0.78 (define @t137 () (not (_ @t9 @t17))) % 0.52/0.78 (define @t138 () (or @t137 @t123)) % 0.52/0.78 (define @t139 () (lambda @t21 @t138)) % 0.52/0.78 (define @t140 () (lambda @t36 @t95)) % 0.52/0.78 (define @t141 () (_ @t140 @t17)) % 0.52/0.78 (define @t142 () (not @t141)) % 0.52/0.78 (define @t143 () (or @t111 @t142)) % 0.52/0.78 (define @t144 () (not @t143)) % 0.52/0.78 (define @t145 () (lambda @t113 @t144)) % 0.52/0.78 (define @t146 () (not @t123)) % 0.52/0.78 (define @t147 () (_ tptp.q @t38)) % 0.52/0.78 (define @t148 () (_ tptp.p @t38)) % 0.52/0.78 (define @t149 () (not @t148)) % 0.52/0.78 (define @t150 () (or @t94 @t149 @t147)) % 0.52/0.78 (define @t151 () (or @t149 @t147)) % 0.52/0.78 (define @t152 () (not (_ tptp.p @t4))) % 0.52/0.78 (define @t153 () (lambda @t36 (or @t152 (_ tptp.q @t4)))) % 0.52/0.78 (define @t154 () (_ @t153 @t38)) % 0.52/0.78 (define @t155 () (or @t94 @t154)) % 0.52/0.78 (define @t156 () (forall @t41 @t155)) % 0.52/0.78 (define @t157 () (lambda @t36 @t156)) % 0.52/0.78 (define @t158 () (lambda @t12 (forall @t41 (or @t94 @t126)))) % 0.52/0.78 (define @t159 () (@list @t14 @t4)) % 0.52/0.78 (define @t160 () (lambda @t36 @t152)) % 0.52/0.78 (define @t161 () (_ @t160 @t4)) % 0.52/0.78 (define @t162 () (or @t161 @t15)) % 0.52/0.78 (define @t163 () (lambda @t159 @t162)) % 0.52/0.78 (define @t164 () (_ @t13 tptp.p)) % 0.52/0.78 (define @t165 () (lambda @t36 @t96)) % 0.52/0.78 (define @t166 () (_ @t165 @t17)) % 0.52/0.78 (define @t167 () (not @t166)) % 0.52/0.78 (define @t168 () (or @t167 @t146)) % 0.52/0.78 (define @t169 () (not @t168)) % 0.52/0.78 (define @t170 () (lambda @t125 @t169)) % 0.52/0.78 (define @t171 () (not (or @t137 @t146))) % 0.52/0.78 (define @t172 () (lambda @t21 @t171)) % 0.52/0.78 (define @t173 () (_ @t158 tptp.p)) % 0.52/0.78 (define @t174 () (forall @t41 (or @t94 @t127))) % 0.52/0.78 (define @t175 () (lambda @t36 @t174)) % 0.52/0.78 (define @t176 () (_ @t175 @t4)) % 0.52/0.78 (define @t177 () (not @t176)) % 0.52/0.78 (define @t178 () (lambda @t36 @t177)) % 0.52/0.78 (define @t179 () (not @t39)) % 0.52/0.78 (define @t180 () (or @t94 @t179)) % 0.52/0.78 (define @t181 () (lambda @t36 @t11)) % 0.52/0.78 (define @t182 () (_ @t181 @t38)) % 0.52/0.78 (define @t183 () (or @t94 @t182)) % 0.52/0.78 (define @t184 () (forall @t41 @t183)) % 0.52/0.78 (define @t185 () (lambda @t36 @t184)) % 0.52/0.78 (define @t186 () (not @t15)) % 0.52/0.78 (define @t187 () (or @t11 @t186)) % 0.52/0.78 (define @t188 () (lambda @t36 @t187)) % 0.52/0.78 (define @t189 () (_ @t188 @t4)) % 0.52/0.78 (define @t190 () (not @t189)) % 0.52/0.78 (define @t191 () (lambda @t36 @t190)) % 0.52/0.78 (define @t192 () (lambda @t36 @t186)) % 0.52/0.78 (define @t193 () (_ @t192 @t4)) % 0.52/0.78 (define @t194 () (or @t11 @t193)) % 0.52/0.78 (define @t195 () (lambda @t36 @t194)) % 0.52/0.78 (define @t196 () (or @t11 @t15)) % 0.52/0.78 (define @t197 () (lambda @t159 @t196)) % 0.52/0.78 (define @t198 () (_ @t181 @t4)) % 0.52/0.78 (define @t199 () (or @t198 @t15)) % 0.52/0.78 (define @t200 () (lambda @t159 @t199)) % 0.52/0.78 (define @t201 () (lambda @t36 @t196)) % 0.52/0.78 (define @t202 () (not (tptp.rel_d @t99 @t38))) % 0.52/0.78 (define @t203 () (forall @t41 (or @t202 @t92 @t90))) % 0.52/0.78 (define @t204 () (not @t203)) % 0.52/0.78 (define @t205 () (forall @t41 (or @t202 @t91))) % 0.52/0.78 (define @t206 () (not @t205)) % 0.52/0.78 (define @t207 () (forall @t41 (or @t202 @t97))) % 0.52/0.78 (define @t208 () (not @t207)) % 0.52/0.78 (define @t209 () (or @t208 @t206 @t204)) % 0.52/0.78 (define @t210 () (@list @t209)) % 0.52/0.78 (define @t211 () (@list @t101)) % 0.52/0.78 (define @t212 () (tptp.q @t101)) % 0.52/0.78 (define @t213 () (not @t212)) % 0.52/0.78 (define @t214 () (or @t104 @t213)) % 0.52/0.78 (define @t215 () (@list false false)) % 0.52/0.78 (define @t216 () (tptp.p @t101)) % 0.52/0.78 (define @t217 () (or @t104 @t216)) % 0.52/0.78 (define @t218 () (not @t216)) % 0.52/0.78 (define @t219 () (or @t104 @t218 @t212)) % 0.52/0.78 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.52/0.78 (assume @p2 (_ tptp.mserial tptp.rel_d)) % 0.52/0.78 (assume @p3 @t1) % 0.52/0.78 (assume @p4 true) % 0.52/0.78 (step @p5 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.52/0.78 (step @p6 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.52/0.78 (step @p7 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.52/0.78 (step @p8 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.52/0.78 (step @p9 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.52/0.78 (step @p10 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.52/0.78 (step @p11 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.52/0.78 (step @p12 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.52/0.78 (step @p13 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.52/0.78 (step @p14 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.52/0.78 (step @p15 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.52/0.78 (step @p16 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.52/0.78 (step @p17 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.52/0.78 (step @p18 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.52/0.78 (step @p19 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.52/0.78 (step @p20 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.52/0.78 (step @p21 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.52/0.78 (step @p22 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.52/0.78 (step @p23 (= tptp.mserial @t56) :rule refl :args (@t56)) % 0.52/0.78 (step @p24 (= tptp.mtransitive @t61) :rule refl :args (@t61)) % 0.52/0.78 (step @p25 (= tptp.meuclidean @t63) :rule refl :args (@t63)) % 0.52/0.78 (step @p26 (= tptp.mpartially_functional @t65) :rule refl :args (@t65)) % 0.52/0.78 (step @p27 (= tptp.mfunctional @t67) :rule refl :args (@t67)) % 0.52/0.78 (step @p28 (= tptp.mweakly_dense @t70) :rule refl :args (@t70)) % 0.52/0.78 (step @p29 (= tptp.mweakly_connected @t71) :rule refl :args (@t71)) % 0.52/0.78 (step @p30 (= tptp.mweakly_directed @t72) :rule refl :args (@t72)) % 0.52/0.78 (step @p31 (= tptp.mvalid @t75) :rule refl :args (@t75)) % 0.52/0.78 (step @p32 (= tptp.minvalid @t76) :rule refl :args (@t76)) % 0.52/0.78 (step @p33 (= tptp.msatisfiable @t77) :rule refl :args (@t77)) % 0.52/0.78 (step @p34 (= tptp.mcountersatisfiable @t78) :rule refl :args (@t78)) % 0.52/0.78 (step @p35 (= tptp.mbox_d @t83) :rule refl :args (@t83)) % 0.52/0.78 (step @p36 (= tptp.mdia_d @t85) :rule refl :args (@t85)) % 0.52/0.78 (step @p37 :rule beta-reduce :args ((= (_ (lambda @t47 (forall @t46 (not (forall @t53 (not @t86))))) tptp.rel_d) (forall @t46 (not (forall @t53 (not (tptp.rel_d @t44 @t49)))))))) % 0.52/0.78 (step @p38 :rule refl :args (tptp.rel_d)) % 0.52/0.78 (step @p39 :rule refl :args (@t86)) % 0.52/0.78 (step @p40 :rule refl :args (@t51)) % 0.52/0.78 (step @p41 :rule cong :premises (@p40 @p39) :args ((= @t51 @t86))) % 0.52/0.78 (step @p42 :rule symm :premises (@p41)) % 0.52/0.78 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 0.52/0.78 (step @p44 :rule cong :premises (@p43) :args (@t87)) % 0.52/0.78 (step @p45 :rule cong :premises (@p44) :args (@t88)) % 0.52/0.78 (step @p46 :rule cong :premises (@p45) :args (@t89)) % 0.52/0.78 (step @p47 :rule exists-elim :args ((= @t54 @t89))) % 0.52/0.78 (step @p48 :rule trans :premises (@p47 @p46)) % 0.52/0.78 (step @p49 :rule cong :premises (@p48) :args (@t55)) % 0.52/0.78 (step @p50 :rule cong :premises (@p49) :args (@t56)) % 0.52/0.78 (step @p51 :rule trans :premises (@p23 @p50)) % 0.52/0.78 (step @p52 :rule ho_cong :premises (@p51 @p38)) % 0.52/0.78 (step @p53 :rule trans :premises (@p52 @p37)) % 0.52/0.78 (step @p54 :rule eq_resolve :premises (@p2 @p53)) % 0.52/0.78 (step @p55 :rule instantiate :premises (@p54) :args ((@list @t99))) % 0.52/0.78 (step @p56 :rule refl :args (@t102)) % 0.52/0.78 (step @p57 :rule bool-double-not-elim :args (@t100)) % 0.52/0.78 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or (not @t103) @t102))) % 0.52/0.78 (step @p59 :rule bool-double-not-elim :args (@t102)) % 0.52/0.78 (step @p60 :rule refl :args (@t103)) % 0.52/0.78 (step @p61 :rule cong :premises (@p60 @p59) :args ((=> @t103 @t105))) % 0.52/0.78 (assume-push @p313 @t103) % 0.52/0.78 (step @p63 :rule skolemize :premises (@p55)) % 0.52/0.78 (step-pop @p314 :rule scope :premises (@p63)) % 0.52/0.78 (step @p64 :rule process_scope :premises (@p314) :args (@t105)) % 0.52/0.78 (step @p66 :rule eq_resolve :premises (@p64 @p61)) % 0.52/0.78 (step @p67 :rule implies_elim :premises (@p66)) % 0.52/0.78 (step @p68 :rule eq_resolve :premises (@p67 @p58)) % 0.52/0.78 (step @p69 :rule chain_m_resolution :premises (@p68 @p55) :args (@t102 @t106 (@list @t100))) % 0.52/0.78 (step @p70 :rule beta-reduce :args ((= @t115 @t98))) % 0.52/0.78 (step @p71 :rule cong :premises (@p70) :args (@t116)) % 0.52/0.78 (step @p72 :rule beta-reduce :args ((= (_ @t118 @t114) @t116))) % 0.52/0.78 (step @p73 :rule trans :premises (@p72 @p71)) % 0.52/0.78 (step @p74 :rule refl :args (@t109)) % 0.52/0.78 (step @p75 :rule refl :args (@t111)) % 0.52/0.78 (step @p76 :rule beta-reduce :args ((= @t120 @t112))) % 0.52/0.78 (step @p77 :rule nary_cong :premises (@p76 @p75 @p74) :args (@t121)) % 0.52/0.78 (step @p78 :rule cong :premises (@p77) :args (@t122)) % 0.52/0.78 (step @p79 :rule beta-reduce :args ((= (_ (lambda @t125 @t124) @t119) @t122))) % 0.52/0.78 (step @p80 :rule trans :premises (@p79 @p78)) % 0.52/0.78 (step @p81 :rule beta-reduce :args ((= @t129 @t119))) % 0.52/0.78 (step @p82 :rule aci_norm :args ((= (or @t130 @t123) @t124))) % 0.52/0.78 (step @p83 :rule refl :args (@t123)) % 0.52/0.78 (step @p84 :rule bool-double-not-elim :args (@t130)) % 0.52/0.78 (step @p85 :rule beta-reduce :args ((= @t133 @t131))) % 0.52/0.78 (step @p86 :rule cong :premises (@p85) :args (@t134)) % 0.52/0.78 (step @p87 :rule trans :premises (@p86 @p84)) % 0.52/0.78 (step @p88 :rule nary_cong :premises (@p87 @p83) :args (@t135)) % 0.52/0.78 (step @p89 :rule trans :premises (@p88 @p82)) % 0.52/0.78 (step @p90 :rule cong :premises (@p89) :args (@t136)) % 0.52/0.78 (step @p91 :rule beta-reduce :args ((= (_ @t139 @t132) @t136))) % 0.52/0.78 (step @p92 :rule trans :premises (@p91 @p90)) % 0.52/0.78 (step @p93 :rule beta-reduce :args ((= @t141 @t108))) % 0.52/0.78 (step @p94 :rule cong :premises (@p93) :args (@t142)) % 0.52/0.78 (step @p95 :rule nary_cong :premises (@p75 @p94) :args (@t143)) % 0.52/0.78 (step @p96 :rule cong :premises (@p95) :args (@t144)) % 0.52/0.78 (step @p97 :rule cong :premises (@p96) :args (@t145)) % 0.52/0.78 (step @p98 :rule beta-reduce :args ((= (_ (lambda @t125 (not (or @t111 @t146))) @t140) @t145))) % 0.52/0.78 (step @p99 :rule trans :premises (@p98 @p97)) % 0.52/0.78 (step @p100 :rule refl :args (@t90)) % 0.52/0.78 (step @p101 :rule refl :args (@t147)) % 0.52/0.78 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t147 @t90))) % 0.52/0.78 (step @p103 :rule symm :premises (@p102)) % 0.52/0.78 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 0.52/0.78 (step @p105 :rule refl :args (@t91)) % 0.52/0.78 (step @p106 :rule refl :args (@t148)) % 0.52/0.78 (step @p107 :rule cong :premises (@p106 @p105) :args ((= @t148 @t91))) % 0.52/0.78 (step @p108 :rule symm :premises (@p107)) % 0.52/0.78 (step @p109 :rule eq_resolve :premises (@p106 @p108)) % 0.52/0.78 (step @p110 :rule cong :premises (@p109) :args (@t149)) % 0.52/0.78 (step @p111 :rule refl :args (@t94)) % 0.52/0.78 (step @p112 :rule nary_cong :premises (@p111 @p110 @p104) :args (@t150)) % 0.52/0.78 (step @p113 :rule cong :premises (@p112) :args ((forall @t41 @t150))) % 0.52/0.78 (step @p114 :rule aci_norm :args ((= (or @t94 @t151) @t150))) % 0.52/0.78 (step @p115 :rule beta-reduce :args ((= @t154 @t151))) % 0.52/0.78 (step @p116 :rule refl :args (@t94)) % 0.52/0.78 (step @p117 :rule nary_cong :premises (@p116 @p115) :args (@t155)) % 0.52/0.78 (step @p118 :rule trans :premises (@p117 @p114)) % 0.52/0.78 (step @p119 :rule cong :premises (@p118) :args (@t156)) % 0.52/0.78 (step @p120 :rule trans :premises (@p119 @p113)) % 0.52/0.78 (step @p121 :rule cong :premises (@p120) :args (@t157)) % 0.52/0.78 (step @p122 :rule beta-reduce :args ((= (_ @t158 @t153) @t157))) % 0.52/0.78 (step @p123 :rule trans :premises (@p122 @p121)) % 0.52/0.78 (step @p124 :rule beta-reduce :args ((= (_ (lambda @t159 (or @t152 @t15)) tptp.q) @t153))) % 0.52/0.78 (step @p125 :rule refl :args (tptp.q)) % 0.52/0.78 (step @p126 :rule refl :args (@t15)) % 0.52/0.78 (step @p127 :rule beta-reduce :args ((= @t161 @t152))) % 0.52/0.78 (step @p128 :rule nary_cong :premises (@p127 @p126) :args (@t162)) % 0.52/0.78 (step @p129 :rule cong :premises (@p128) :args (@t163)) % 0.52/0.78 (step @p130 :rule beta-reduce :args ((= (_ @t16 @t160) @t163))) % 0.52/0.78 (step @p131 :rule trans :premises (@p130 @p129)) % 0.52/0.78 (step @p132 :rule beta-reduce :args ((= @t164 @t160))) % 0.52/0.78 (step @p133 :rule refl :args (@t16)) % 0.52/0.78 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.52/0.78 (step @p135 :rule trans :premises (@p134 @p131)) % 0.52/0.78 (step @p136 :rule ho_cong :premises (@p135 @p125)) % 0.52/0.78 (step @p137 :rule trans :premises (@p136 @p124)) % 0.52/0.78 (step @p138 :rule refl :args (@t158)) % 0.52/0.78 (step @p139 :rule ho_cong :premises (@p138 @p137)) % 0.52/0.78 (step @p140 :rule trans :premises (@p139 @p123)) % 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(@p304 @p281) :args (@t205 @t106 @t210)) % 0.52/0.78 (step @p306 :rule instantiate :premises (@p305) :args (@t211)) % 0.52/0.78 (step @p307 :rule cnf_or_pos :args (@t217)) % 0.52/0.78 (step @p308 :rule reordering :premises (@p307) :args ((or @t104 @t216 (not @t217)))) % 0.52/0.78 (step @p309 :rule chain_m_resolution :premises (@p308 @p69 @p306) :args (@t216 @t215 (@list @t102 @t217))) % 0.52/0.78 (step @p310 :rule cnf_or_pos :args (@t219)) % 0.52/0.78 (step @p311 :rule reordering :premises (@p310) :args ((or @t104 @t212 @t218 (not @t219)))) % 0.52/0.78 (step @p312 false :rule chain_m_resolution :premises (@p311 @p309 @p299 @p289 @p69) :args (false (@list false true false false) (@list @t216 @t212 @t219 @t102))) % 0.52/0.78 ) % 0.52/0.78 % SZS output end Proof % 0.52/0.78 % cvc5 exiting %------------------------------------------------------------------------------