%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO469^6 : 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 : n026.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 09:12:53 AM UTC 2026 % Result : Theorem 0.36s 0.64s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO469^6 : 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 % 0.17/0.35 % Computer : n026.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 00:14:10 EDT 2026 % 0.17/0.36 % CPUTime : % 0.27/0.52 %----Proving TH0 % 0.36/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.64 % SZS status Theorem % 0.36/0.64 % SZS output start Proof % 0.36/0.64 ( % 0.36/0.64 (declare-sort $$unsorted 0) % 0.36/0.64 (declare-sort tptp.mu 0) % 0.36/0.64 (declare-const tptp.rel_s5 (-> $$unsorted $$unsorted Bool)) % 0.36/0.64 (declare-const tptp.p (-> $$unsorted Bool)) % 0.36/0.64 (declare-const tptp.q (-> $$unsorted Bool)) % 0.36/0.64 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.36/0.64 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.36/0.64 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.36/0.64 (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)))))) % 0.36/0.64 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.36/0.64 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.64 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.36/0.64 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.64 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.36/0.64 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.64 (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))))))) % 0.36/0.64 (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))))))) % 0.36/0.64 (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)))))) % 0.36/0.64 (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)))))) % 0.36/0.64 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.36/0.64 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.36/0.64 (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)))))) % 0.36/0.64 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.64 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.64 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.64 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.36/0.64 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.36/0.64 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.36/0.64 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.36/0.64 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.36/0.64 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.36/0.64 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.36/0.64 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.36/0.64 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.36/0.64 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.36/0.64 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.36/0.64 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s5 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.36/0.64 (define tptp.mdia_s5 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s5 (_ tptp.mnot _let_2))) _let_1))))) % 0.36/0.64 (define @t1 () (_ tptp.mimplies (_ tptp.mbox_s5 tptp.p))) % 0.36/0.64 (define @t2 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mbox_s5 (_ @t1 tptp.q))) (_ tptp.mbox_s5 (_ @t1 (_ tptp.mbox_s5 tptp.q))))))) % 0.36/0.64 (define @t3 () (@var "Y" tptp.mu)) % 0.36/0.64 (define @t4 () (@var "X" tptp.mu)) % 0.36/0.64 (define @t5 () (@var "W" $$unsorted)) % 0.36/0.64 (define @t6 () (lambda (@list @t4 @t3 @t5) (= @t4 @t3))) % 0.36/0.64 (define @t7 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.64 (define @t8 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.64 (define @t9 () (lambda (@list @t8 @t7 @t5) (= (_ @t8 @t5) (_ @t7 @t5)))) % 0.36/0.64 (define @t10 () (@var "Phi" (-> $$unsorted Bool))) % 0.36/0.64 (define @t11 () (_ @t10 @t5)) % 0.36/0.64 (define @t12 () (not @t11)) % 0.36/0.64 (define @t13 () (@list @t10 @t5)) % 0.36/0.64 (define @t14 () (lambda @t13 @t12)) % 0.36/0.64 (define @t15 () (@var "Psi" (-> $$unsorted Bool))) % 0.36/0.64 (define @t16 () (_ @t15 @t5)) % 0.36/0.64 (define @t17 () (lambda (@list @t10 @t15 @t5) (or @t11 @t16))) % 0.36/0.64 (define @t18 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.64 (define @t19 () (_ tptp.mnot @t15)) % 0.36/0.64 (define @t20 () (_ tptp.mnot @t10)) % 0.36/0.64 (define @t21 () (_ tptp.mor @t20)) % 0.36/0.64 (define @t22 () (@list @t10 @t15 @t18)) % 0.36/0.64 (define @t23 () (lambda @t22 (_ (_ tptp.mnot (_ @t21 @t19)) @t18))) % 0.36/0.64 (define @t24 () (lambda @t22 (_ (_ @t21 @t15) @t18))) % 0.36/0.64 (define @t25 () (lambda @t22 (_ (_ (_ tptp.mor @t19) @t10) @t18))) % 0.36/0.64 (define @t26 () (lambda @t22 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t10) @t15)) (_ (_ tptp.mimplies @t15) @t10)) @t18))) % 0.36/0.64 (define @t27 () (lambda @t22 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t10) @t15)) @t18))) % 0.36/0.64 (define @t28 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.36/0.64 (define @t29 () (_ @t28 @t4)) % 0.36/0.64 (define @t30 () (lambda (@list @t28 @t5) (forall (@list @t4) (_ @t29 @t5)))) % 0.36/0.64 (define @t31 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.64 (define @t32 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.36/0.64 (define @t33 () (_ @t32 @t31)) % 0.36/0.64 (define @t34 () (lambda (@list @t32 @t5) (forall (@list @t31) (_ @t33 @t5)))) % 0.36/0.64 (define @t35 () (lambda (@list @t28 @t18) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t4 @t18) (_ (_ tptp.mnot @t29) @t18)))) @t18))) % 0.36/0.64 (define @t36 () (lambda (@list @t32 @t18) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t31 @t18) (_ (_ tptp.mnot @t33) @t18)))) @t18))) % 0.36/0.64 (define @t37 () (@list @t5)) % 0.36/0.64 (define @t38 () (lambda @t37 true)) % 0.36/0.64 (define @t39 () (@var "V" $$unsorted)) % 0.36/0.64 (define @t40 () (_ @t10 @t39)) % 0.36/0.64 (define @t41 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.64 (define @t42 () (@list @t39)) % 0.36/0.64 (define @t43 () (lambda (@list @t41 @t10 @t5) (forall @t42 (or (not (_ (_ @t41 @t5) @t39)) @t40)))) % 0.36/0.64 (define @t44 () (lambda (@list @t41 @t10 @t18) (_ (_ tptp.mnot (_ (_ tptp.mbox @t41) @t20)) @t18))) % 0.36/0.64 (define @t45 () (@var "S" $$unsorted)) % 0.36/0.64 (define @t46 () (_ @t41 @t45)) % 0.36/0.64 (define @t47 () (@list @t45)) % 0.36/0.64 (define @t48 () (@list @t41)) % 0.36/0.64 (define @t49 () (lambda @t48 (forall @t47 (_ @t46 @t45)))) % 0.36/0.64 (define @t50 () (@var "T" $$unsorted)) % 0.36/0.64 (define @t51 () (_ @t41 @t50)) % 0.36/0.64 (define @t52 () (_ @t51 @t45)) % 0.36/0.64 (define @t53 () (_ @t46 @t50)) % 0.36/0.64 (define @t54 () (@list @t45 @t50)) % 0.36/0.64 (define @t55 () (forall @t54 (=> @t53 @t52))) % 0.36/0.64 (define @t56 () (lambda @t48 @t55)) % 0.36/0.64 (define @t57 () (@list @t50)) % 0.36/0.64 (define @t58 () (lambda @t48 (forall @t47 (exists @t57 @t53)))) % 0.36/0.64 (define @t59 () (@var "U" $$unsorted)) % 0.36/0.64 (define @t60 () (_ @t46 @t59)) % 0.36/0.64 (define @t61 () (_ @t51 @t59)) % 0.36/0.64 (define @t62 () (and @t53 @t61)) % 0.36/0.64 (define @t63 () (@list @t45 @t50 @t59)) % 0.36/0.64 (define @t64 () (forall @t63 (=> @t62 @t60))) % 0.36/0.64 (define @t65 () (lambda @t48 @t64)) % 0.36/0.64 (define @t66 () (and @t53 @t60)) % 0.36/0.64 (define @t67 () (lambda @t48 (forall @t63 (=> @t66 @t61)))) % 0.36/0.64 (define @t68 () (= @t50 @t59)) % 0.36/0.64 (define @t69 () (lambda @t48 (forall @t63 (=> @t66 @t68)))) % 0.36/0.64 (define @t70 () (@list @t59)) % 0.36/0.64 (define @t71 () (lambda @t48 (forall @t47 (exists @t57 (and @t53 (forall @t70 (=> @t60 @t68))))))) % 0.36/0.64 (define @t72 () (_ @t41 @t59)) % 0.36/0.64 (define @t73 () (_ @t72 @t50)) % 0.36/0.64 (define @t74 () (lambda @t48 (forall @t63 (=> @t53 (exists @t70 (and @t60 @t73)))))) % 0.36/0.64 (define @t75 () (lambda @t48 (forall @t63 (=> @t66 (or @t61 @t68 @t73))))) % 0.36/0.64 (define @t76 () (lambda @t48 (forall @t63 (=> @t66 (exists @t42 (and (_ @t51 @t39) (_ @t72 @t39))))))) % 0.36/0.64 (define @t77 () (forall @t37 @t11)) % 0.36/0.64 (define @t78 () (@list @t10)) % 0.36/0.64 (define @t79 () (lambda @t78 @t77)) % 0.36/0.64 (define @t80 () (lambda @t78 (forall @t37 @t12))) % 0.36/0.64 (define @t81 () (lambda @t78 (exists @t37 @t11))) % 0.36/0.64 (define @t82 () (lambda @t78 (exists @t37 @t12))) % 0.36/0.64 (define @t83 () (_ (_ tptp.rel_s5 @t5) @t39)) % 0.36/0.64 (define @t84 () (not @t83)) % 0.36/0.64 (define @t85 () (or @t84 @t40)) % 0.36/0.64 (define @t86 () (forall @t42 @t85)) % 0.36/0.64 (define @t87 () (lambda @t13 @t86)) % 0.36/0.64 (define @t88 () (lambda (@list @t10 @t18) (_ (_ tptp.mnot (_ tptp.mbox_s5 @t20)) @t18))) % 0.36/0.64 (define @t89 () (not (tptp.rel_s5 @t45 @t50))) % 0.36/0.64 (define @t90 () (forall @t63 (or @t89 (not (tptp.rel_s5 @t50 @t59)) (tptp.rel_s5 @t45 @t59)))) % 0.36/0.64 (define @t91 () (_ @t41 @t45 @t59)) % 0.36/0.64 (define @t92 () (_ @t41 @t50 @t59)) % 0.36/0.64 (define @t93 () (_ @t41 @t45 @t50)) % 0.36/0.64 (define @t94 () (not @t93)) % 0.36/0.64 (define @t95 () (not @t61)) % 0.36/0.64 (define @t96 () (not @t53)) % 0.36/0.64 (define @t97 () (or @t96 @t95 @t60)) % 0.36/0.64 (define @t98 () (@var "BOUND_VARIABLE_8451" $$unsorted)) % 0.36/0.64 (define @t99 () (tptp.p @t98)) % 0.36/0.64 (define @t100 () (@var "BOUND_VARIABLE_8565" $$unsorted)) % 0.36/0.64 (define @t101 () (tptp.q @t100)) % 0.36/0.64 (define @t102 () (@var "BOUND_VARIABLE_8563" $$unsorted)) % 0.36/0.64 (define @t103 () (not (tptp.rel_s5 @t102 @t100))) % 0.36/0.64 (define @t104 () (@var "BOUND_VARIABLE_8511" $$unsorted)) % 0.36/0.64 (define @t105 () (tptp.p @t104)) % 0.36/0.64 (define @t106 () (@list @t104)) % 0.36/0.64 (define @t107 () (not (forall @t106 (or (not (tptp.rel_s5 @t102 @t104)) @t105)))) % 0.36/0.64 (define @t108 () (not (tptp.rel_s5 @t5 @t102))) % 0.36/0.64 (define @t109 () (tptp.q @t39)) % 0.36/0.64 (define @t110 () (@list @t98)) % 0.36/0.64 (define @t111 () (not (forall @t110 (or (not (tptp.rel_s5 @t39 @t98)) @t99)))) % 0.36/0.64 (define @t112 () (tptp.rel_s5 @t5 @t39)) % 0.36/0.64 (define @t113 () (not @t112)) % 0.36/0.64 (define @t114 () (forall @t42 (or @t113 @t111 @t109))) % 0.36/0.64 (define @t115 () (not @t114)) % 0.36/0.64 (define @t116 () (or @t115 @t108 @t107 @t103 @t101)) % 0.36/0.64 (define @t117 () (@list @t5 @t102 @t100)) % 0.36/0.64 (define @t118 () (forall @t117 @t116)) % 0.36/0.64 (define @t119 () (@quantifiers_skolemize @t118 2)) % 0.36/0.64 (define @t120 () (forall @t110 (or (not (tptp.rel_s5 @t119 @t98)) @t99))) % 0.36/0.64 (define @t121 () (@quantifiers_skolemize @t120 0)) % 0.36/0.64 (define @t122 () (@quantifiers_skolemize @t118 0)) % 0.36/0.64 (define @t123 () (or @t108 @t107 @t103 @t101)) % 0.36/0.64 (define @t124 () (or @t115 @t123)) % 0.36/0.64 (define @t125 () (forall @t117 @t124)) % 0.36/0.64 (define @t126 () (@list @t102 @t100)) % 0.36/0.64 (define @t127 () (forall @t126 @t124)) % 0.36/0.64 (define @t128 () (forall @t126 @t123)) % 0.36/0.64 (define @t129 () (@var "BOUND_VARIABLE_8536" $$unsorted)) % 0.36/0.64 (define @t130 () (or @t115 @t128)) % 0.36/0.64 (define @t131 () (tptp.q @t129)) % 0.36/0.64 (define @t132 () (not (tptp.rel_s5 @t39 @t129))) % 0.36/0.64 (define @t133 () (not (forall @t106 (or (not (tptp.rel_s5 @t39 @t104)) @t105)))) % 0.36/0.64 (define @t134 () (or @t113 @t133 @t132 @t131)) % 0.36/0.64 (define @t135 () (@list @t39 @t129)) % 0.36/0.64 (define @t136 () (forall @t135 @t134)) % 0.36/0.64 (define @t137 () (or @t115 @t136)) % 0.36/0.64 (define @t138 () (not (tptp.rel_s5 @t18 @t39))) % 0.36/0.64 (define @t139 () (forall @t135 (or @t138 @t133 @t132 @t131))) % 0.36/0.64 (define @t140 () (forall @t42 (or @t138 @t111 @t109))) % 0.36/0.64 (define @t141 () (not @t140)) % 0.36/0.64 (define @t142 () (@list @t18)) % 0.36/0.64 (define @t143 () (lambda @t142 (or @t141 @t139))) % 0.36/0.64 (define @t144 () (_ @t143 @t5)) % 0.36/0.64 (define @t145 () (forall @t37 @t144)) % 0.36/0.64 (define @t146 () (_ @t10 @t5)) % 0.36/0.64 (define @t147 () (lambda @t78 (forall @t37 @t146))) % 0.36/0.64 (define @t148 () (lambda @t37 @t136)) % 0.36/0.64 (define @t149 () (_ @t148 @t18)) % 0.36/0.64 (define @t150 () (or @t141 @t149)) % 0.36/0.64 (define @t151 () (lambda @t142 @t150)) % 0.36/0.64 (define @t152 () (_ @t15 @t18)) % 0.36/0.64 (define @t153 () (@list @t15 @t18)) % 0.36/0.64 (define @t154 () (or @t132 @t131)) % 0.36/0.64 (define @t155 () (or @t113 @t133 @t154)) % 0.36/0.64 (define @t156 () (forall @t135 @t155)) % 0.36/0.64 (define @t157 () (@list @t129)) % 0.36/0.64 (define @t158 () (forall @t157 @t155)) % 0.36/0.64 (define @t159 () (forall @t157 @t154)) % 0.36/0.64 (define @t160 () (@var "BOUND_VARIABLE_8503" $$unsorted)) % 0.36/0.64 (define @t161 () (@list @t160)) % 0.36/0.64 (define @t162 () (or @t113 @t133 @t159)) % 0.36/0.64 (define @t163 () (tptp.q @t160)) % 0.36/0.64 (define @t164 () (@list @t160)) % 0.36/0.64 (define @t165 () (forall @t164 (or (not (tptp.rel_s5 @t39 @t160)) @t163))) % 0.36/0.64 (define @t166 () (or @t113 @t133 @t165)) % 0.36/0.64 (define @t167 () (or @t133 @t165)) % 0.36/0.64 (define @t168 () (forall @t42 (or @t138 @t109))) % 0.36/0.64 (define @t169 () (@list @t39)) % 0.36/0.64 (define @t170 () (tptp.p @t39)) % 0.36/0.64 (define @t171 () (forall @t42 (or @t138 @t170))) % 0.36/0.64 (define @t172 () (not @t171)) % 0.36/0.64 (define @t173 () (or @t172 @t168)) % 0.36/0.64 (define @t174 () (lambda @t142 @t173)) % 0.36/0.64 (define @t175 () (or @t113 (_ @t174 @t39))) % 0.36/0.64 (define @t176 () (forall @t42 @t175)) % 0.36/0.64 (define @t177 () (lambda @t37 @t176)) % 0.36/0.64 (define @t178 () (_ @t10 @t39)) % 0.36/0.64 (define @t179 () (lambda @t13 (forall @t42 (or @t113 @t178)))) % 0.36/0.64 (define @t180 () (lambda @t37 (forall @t42 (or @t113 @t109)))) % 0.36/0.64 (define @t181 () (_ @t180 @t18)) % 0.36/0.64 (define @t182 () (or @t172 @t181)) % 0.36/0.64 (define @t183 () (lambda @t142 @t182)) % 0.36/0.64 (define @t184 () (lambda @t153 (or @t172 @t152))) % 0.36/0.64 (define @t185 () (_ @t179 tptp.q)) % 0.36/0.64 (define @t186 () (lambda @t37 (forall @t42 (or @t113 @t170)))) % 0.36/0.64 (define @t187 () (_ @t186 @t18)) % 0.36/0.64 (define @t188 () (not @t187)) % 0.36/0.64 (define @t189 () (or @t188 @t152)) % 0.36/0.64 (define @t190 () (lambda @t153 @t189)) % 0.36/0.64 (define @t191 () (or (not (_ @t10 @t18)) @t152)) % 0.36/0.64 (define @t192 () (lambda @t22 @t191)) % 0.36/0.64 (define @t193 () (_ @t179 tptp.p)) % 0.36/0.64 (define @t194 () (lambda @t37 @t114)) % 0.36/0.64 (define @t195 () (_ @t194 @t18)) % 0.36/0.64 (define @t196 () (not @t195)) % 0.36/0.64 (define @t197 () (or @t196 @t152)) % 0.36/0.64 (define @t198 () (lambda @t153 @t197)) % 0.36/0.64 (define @t199 () (_ tptp.q @t39)) % 0.36/0.64 (define @t200 () (or @t113 @t111 @t199)) % 0.36/0.64 (define @t201 () (or @t111 @t199)) % 0.36/0.64 (define @t202 () (_ tptp.q @t18)) % 0.36/0.64 (define @t203 () (or @t172 @t202)) % 0.36/0.64 (define @t204 () (lambda @t142 @t203)) % 0.36/0.64 (define @t205 () (or @t113 (_ @t204 @t39))) % 0.36/0.64 (define @t206 () (forall @t42 @t205)) % 0.36/0.64 (define @t207 () (lambda @t37 @t206)) % 0.36/0.64 (define @t208 () (_ @t192 @t193)) % 0.36/0.64 (define @t209 () (or @t12 @t16)) % 0.36/0.64 (define @t210 () (lambda @t37 @t209)) % 0.36/0.64 (define @t211 () (@list @t15 @t5)) % 0.36/0.64 (define @t212 () (lambda @t37 @t12)) % 0.36/0.64 (define @t213 () (_ @t212 @t5)) % 0.36/0.64 (define @t214 () (or @t213 @t16)) % 0.36/0.64 (define @t215 () (lambda @t211 @t214)) % 0.36/0.64 (define @t216 () (forall @t42 (or (not (tptp.rel_s5 @t122 @t39)) @t111 @t109))) % 0.36/0.64 (define @t217 () (tptp.q @t119)) % 0.36/0.64 (define @t218 () (@quantifiers_skolemize @t118 1)) % 0.36/0.64 (define @t219 () (tptp.rel_s5 @t218 @t119)) % 0.36/0.64 (define @t220 () (not @t219)) % 0.36/0.64 (define @t221 () (forall @t106 (or (not (tptp.rel_s5 @t218 @t104)) @t105))) % 0.36/0.64 (define @t222 () (not @t221)) % 0.36/0.64 (define @t223 () (tptp.rel_s5 @t122 @t218)) % 0.36/0.64 (define @t224 () (not @t223)) % 0.36/0.64 (define @t225 () (not @t216)) % 0.36/0.64 (define @t226 () (or @t225 @t224 @t222 @t220 @t217)) % 0.36/0.64 (define @t227 () (@list true)) % 0.36/0.64 (define @t228 () (@list @t226)) % 0.36/0.64 (define @t229 () (tptp.rel_s5 @t122 @t119)) % 0.36/0.64 (define @t230 () (or @t224 @t220 @t229)) % 0.36/0.64 (define @t231 () (@list false false false)) % 0.36/0.64 (define @t232 () (not @t120)) % 0.36/0.64 (define @t233 () (not @t229)) % 0.36/0.64 (define @t234 () (or @t233 @t232 @t217)) % 0.36/0.64 (define @t235 () (tptp.rel_s5 @t119 @t121)) % 0.36/0.64 (define @t236 () (tptp.p @t121)) % 0.36/0.64 (define @t237 () (not @t235)) % 0.36/0.64 (define @t238 () (or @t237 @t236)) % 0.36/0.64 (define @t239 () (@list @t238)) % 0.36/0.64 (define @t240 () (tptp.rel_s5 @t122 @t121)) % 0.36/0.64 (define @t241 () (or @t233 @t237 @t240)) % 0.36/0.64 (define @t242 () (tptp.rel_s5 @t218 @t121)) % 0.36/0.64 (define @t243 () (not @t242)) % 0.36/0.64 (define @t244 () (or @t243 @t236)) % 0.36/0.64 (define @t245 () (@list true false)) % 0.36/0.64 (define @t246 () (_ @t41 @t50 @t45)) % 0.36/0.64 (define @t247 () (or @t96 @t52)) % 0.36/0.64 (define @t248 () (tptp.rel_s5 @t218 @t122)) % 0.36/0.64 (define @t249 () (or @t224 @t248)) % 0.36/0.64 (define @t250 () (not @t240)) % 0.36/0.64 (define @t251 () (not @t248)) % 0.36/0.64 (define @t252 () (or @t251 @t250 @t242)) % 0.36/0.64 (define @t253 () (not @t252)) % 0.36/0.64 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.36/0.64 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.36/0.64 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.36/0.64 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.36/0.64 (assume @p5 @t2) % 0.36/0.64 (assume @p6 true) % 0.36/0.64 (step @p7 (= tptp.meq_ind @t6) :rule refl :args (@t6)) % 0.36/0.64 (step @p8 (= tptp.meq_prop @t9) :rule refl :args (@t9)) % 0.36/0.64 (step @p9 (= tptp.mnot @t14) :rule refl :args (@t14)) % 0.36/0.64 (step @p10 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.36/0.64 (step @p11 (= tptp.mand @t23) :rule refl :args (@t23)) % 0.36/0.64 (step @p12 (= tptp.mimplies @t24) :rule refl :args (@t24)) % 0.36/0.64 (step @p13 (= tptp.mimplied @t25) :rule refl :args (@t25)) % 0.36/0.64 (step @p14 (= tptp.mequiv @t26) :rule refl :args (@t26)) % 0.36/0.64 (step @p15 (= tptp.mxor @t27) :rule refl :args (@t27)) % 0.36/0.64 (step @p16 (= tptp.mforall_ind @t30) :rule refl :args (@t30)) % 0.36/0.64 (step @p17 (= tptp.mforall_prop @t34) :rule refl :args (@t34)) % 0.36/0.64 (step @p18 (= tptp.mexists_ind @t35) :rule refl :args (@t35)) % 0.36/0.64 (step @p19 (= tptp.mexists_prop @t36) :rule refl :args (@t36)) % 0.36/0.64 (step @p20 (= tptp.mtrue @t38) :rule refl :args (@t38)) % 0.36/0.64 (step @p21 (= tptp.mbox @t43) :rule refl :args (@t43)) % 0.36/0.64 (step @p22 (= tptp.mdia @t44) :rule refl :args (@t44)) % 0.36/0.64 (step @p23 (= tptp.mreflexive @t49) :rule refl :args (@t49)) % 0.36/0.64 (step @p24 (= tptp.msymmetric @t56) :rule refl :args (@t56)) % 0.36/0.64 (step @p25 (= tptp.mserial @t58) :rule refl :args (@t58)) % 0.36/0.64 (step @p26 (= tptp.mtransitive @t65) :rule refl :args (@t65)) % 0.36/0.64 (step @p27 (= tptp.meuclidean @t67) :rule refl :args (@t67)) % 0.36/0.64 (step @p28 (= tptp.mpartially_functional @t69) :rule refl :args (@t69)) % 0.36/0.64 (step @p29 (= tptp.mfunctional @t71) :rule refl :args (@t71)) % 0.36/0.64 (step @p30 (= tptp.mweakly_dense @t74) :rule refl :args (@t74)) % 0.36/0.64 (step @p31 (= tptp.mweakly_connected @t75) :rule refl :args (@t75)) % 0.36/0.64 (step @p32 (= tptp.mweakly_directed @t76) :rule refl :args (@t76)) % 0.36/0.64 (step @p33 (= tptp.mvalid @t79) :rule refl :args (@t79)) % 0.36/0.64 (step @p34 (= tptp.minvalid @t80) :rule refl :args (@t80)) % 0.36/0.64 (step @p35 (= tptp.msatisfiable @t81) :rule refl :args (@t81)) % 0.36/0.64 (step @p36 (= tptp.mcountersatisfiable @t82) :rule refl :args (@t82)) % 0.36/0.64 (step @p37 (= tptp.mbox_s5 @t87) :rule refl :args (@t87)) % 0.36/0.64 (step @p38 (= tptp.mdia_s5 @t88) :rule refl :args (@t88)) % 0.36/0.64 (step @p39 :rule beta-reduce :args ((= (_ (lambda @t48 (forall @t63 (or @t94 (not @t92) @t91))) tptp.rel_s5) @t90))) % 0.36/0.64 (step @p40 :rule refl :args (tptp.rel_s5)) % 0.36/0.64 (step @p41 :rule refl :args (@t91)) % 0.36/0.64 (step @p42 :rule refl :args (@t60)) % 0.36/0.64 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t60 @t91))) % 0.36/0.64 (step @p44 :rule symm :premises (@p43)) % 0.36/0.64 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.36/0.64 (step @p46 :rule refl :args (@t92)) % 0.36/0.64 (step @p47 :rule refl :args (@t61)) % 0.36/0.64 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t61 @t92))) % 0.36/0.64 (step @p49 :rule symm :premises (@p48)) % 0.36/0.64 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.36/0.64 (step @p51 :rule cong :premises (@p50) :args (@t95)) % 0.36/0.64 (step @p52 :rule refl :args (@t93)) % 0.36/0.64 (step @p53 :rule refl :args (@t53)) % 0.36/0.64 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t53 @t93))) % 0.36/0.64 (step @p55 :rule symm :premises (@p54)) % 0.36/0.64 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.36/0.64 (step @p57 :rule cong :premises (@p56) :args (@t96)) % 0.36/0.64 (step @p58 :rule nary_cong :premises (@p57 @p51 @p45) :args (@t97)) % 0.36/0.64 (step @p59 :rule cong :premises (@p58) :args ((forall @t63 @t97))) % 0.36/0.64 (step @p60 :rule aci_norm :args ((= (or (or @t96 @t95) @t60) @t97))) % 0.36/0.64 (step @p61 :rule bool-and-de-morgan :args (@t53 @t61 true)) % 0.36/0.64 (step @p62 :rule nary_cong :premises (@p61 @p42) :args ((or (not @t62) @t60))) % 0.36/0.64 (step @p63 :rule trans :premises (@p62 @p60)) % 0.36/0.64 (step @p64 :rule bool-impl-elim :args (@t62 @t60)) % 0.36/0.64 (step @p65 :rule trans :premises (@p64 @p63)) % 0.36/0.64 (step @p66 :rule cong :premises (@p65) :args (@t64)) % 0.36/0.64 (step @p67 :rule trans :premises (@p66 @p59)) % 0.36/0.64 (step @p68 :rule cong :premises (@p67) :args (@t65)) % 0.36/0.64 (step @p69 :rule trans :premises (@p26 @p68)) % 0.36/0.64 (step @p70 :rule ho_cong :premises (@p69 @p40)) % 0.36/0.64 (step @p71 :rule trans :premises (@p70 @p39)) % 0.36/0.64 (step @p72 :rule eq_resolve :premises (@p3 @p71)) % 0.36/0.64 (step @p73 :rule instantiate :premises (@p72) :args ((@list @t122 @t119 @t121))) % 0.36/0.64 (step @p74 :rule aci_norm :args ((= @t124 @t116))) % 0.36/0.64 (step @p75 :rule cong :premises (@p74) :args (@t125)) % 0.36/0.64 (step @p76 :rule quant-merge-prenex :args ((= (forall @t37 @t127) 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:rule reordering :premises (@p331) :args ((or @t251 @t242 @t250 @t253))) % 0.36/0.64 (step @p333 :rule chain_m_resolution :premises (@p332 @p330 @p310 @p298) :args (@t253 (@list false true false) (@list @t248 @t242 @t240))) % 0.36/0.64 (assume-push @p340 @t90) % 0.36/0.64 (step @p335 :rule instantiate :premises (@p72) :args ((@list @t218 @t122 @t121))) % 0.36/0.64 (step-pop @p341 :rule scope :premises (@p335)) % 0.36/0.64 (step @p336 :rule process_scope :premises (@p341) :args (@t252)) % 0.36/0.64 (step @p338 :rule implies_elim :premises (@p336)) % 0.36/0.64 (step @p339 false :rule chain_m_resolution :premises (@p338 @p333 @p72) :args (false @t245 (@list @t252 @t90))) % 0.36/0.64 ) % 0.36/0.64 % SZS output end Proof % 0.36/0.64 % cvc5 exiting %------------------------------------------------------------------------------