%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO448^1 : 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 : n014.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 09:12:40 AM UTC 2026 % Result : Theorem 0.40s 0.63s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO448^1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n014.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 00:08:13 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.51 %----Proving TH0 % 0.40/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.63 % SZS status Theorem % 0.40/0.63 % SZS output start Proof % 0.40/0.63 ( % 0.40/0.63 (declare-sort $$unsorted 0) % 0.40/0.63 (declare-sort tptp.mu 0) % 0.40/0.63 (declare-const tptp.rel_s5 (-> $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.q (-> $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.p (-> $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.40/0.63 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.40/0.63 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.40/0.63 (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)))))) % 0.40/0.63 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.40/0.63 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.40/0.63 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.40/0.63 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.40/0.63 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.40/0.63 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.40/0.63 (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))))))) % 0.40/0.63 (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))))))) % 0.40/0.63 (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)))))) % 0.40/0.63 (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)))))) % 0.40/0.63 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.40/0.63 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.40/0.63 (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)))))) % 0.40/0.63 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.40/0.63 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.40/0.63 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.40/0.63 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.40/0.63 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.40/0.63 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.40/0.63 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.40/0.63 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.40/0.63 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.40/0.63 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.40/0.63 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.40/0.63 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.40/0.63 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.40/0.63 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.40/0.63 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$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)))))))) % 0.40/0.63 (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))))) % 0.40/0.63 (define @t1 () (_ tptp.mbox_s5 tptp.p)) % 0.40/0.63 (define @t2 () (_ tptp.mbox_s5 tptp.q)) % 0.40/0.63 (define @t3 () (not (_ tptp.mvalid (_ (_ tptp.mor (_ tptp.mbox_s5 (_ (_ tptp.mimplies @t1) @t2))) (_ tptp.mbox_s5 (_ (_ tptp.mimplies @t2) @t1)))))) % 0.40/0.63 (define @t4 () (@var "Y" tptp.mu)) % 0.40/0.63 (define @t5 () (@var "X" tptp.mu)) % 0.40/0.63 (define @t6 () (@var "W" $$unsorted)) % 0.40/0.63 (define @t7 () (lambda (@list @t5 @t4 @t6) (= @t5 @t4))) % 0.40/0.63 (define @t8 () (@var "Y" (-> $$unsorted Bool))) % 0.40/0.63 (define @t9 () (@var "X" (-> $$unsorted Bool))) % 0.40/0.63 (define @t10 () (lambda (@list @t9 @t8 @t6) (= (_ @t9 @t6) (_ @t8 @t6)))) % 0.40/0.63 (define @t11 () (@var "Phi" (-> $$unsorted Bool))) % 0.40/0.63 (define @t12 () (_ @t11 @t6)) % 0.40/0.63 (define @t13 () (not @t12)) % 0.40/0.63 (define @t14 () (@list @t11 @t6)) % 0.40/0.63 (define @t15 () (lambda @t14 @t13)) % 0.40/0.63 (define @t16 () (@var "Psi" (-> $$unsorted Bool))) % 0.40/0.63 (define @t17 () (_ @t16 @t6)) % 0.40/0.63 (define @t18 () (lambda (@list @t11 @t16 @t6) (or @t12 @t17))) % 0.40/0.63 (define @t19 () (@var "__flatten_var_0" $$unsorted)) % 0.40/0.63 (define @t20 () (_ tptp.mnot @t16)) % 0.40/0.63 (define @t21 () (_ tptp.mnot @t11)) % 0.40/0.63 (define @t22 () (_ tptp.mor @t21)) % 0.40/0.63 (define @t23 () (@list @t11 @t16 @t19)) % 0.40/0.63 (define @t24 () (lambda @t23 (_ (_ tptp.mnot (_ @t22 @t20)) @t19))) % 0.40/0.63 (define @t25 () (lambda @t23 (_ (_ @t22 @t16) @t19))) % 0.40/0.63 (define @t26 () (lambda @t23 (_ (_ (_ tptp.mor @t20) @t11) @t19))) % 0.40/0.63 (define @t27 () (lambda @t23 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t11) @t16)) (_ (_ tptp.mimplies @t16) @t11)) @t19))) % 0.40/0.63 (define @t28 () (lambda @t23 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t11) @t16)) @t19))) % 0.40/0.63 (define @t29 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.40/0.63 (define @t30 () (_ @t29 @t5)) % 0.40/0.63 (define @t31 () (lambda (@list @t29 @t6) (forall (@list @t5) (_ @t30 @t6)))) % 0.40/0.63 (define @t32 () (@var "P" (-> $$unsorted Bool))) % 0.40/0.63 (define @t33 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.40/0.63 (define @t34 () (_ @t33 @t32)) % 0.40/0.63 (define @t35 () (lambda (@list @t33 @t6) (forall (@list @t32) (_ @t34 @t6)))) % 0.40/0.63 (define @t36 () (lambda (@list @t29 @t19) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t5 @t19) (_ (_ tptp.mnot @t30) @t19)))) @t19))) % 0.40/0.63 (define @t37 () (lambda (@list @t33 @t19) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t32 @t19) (_ (_ tptp.mnot @t34) @t19)))) @t19))) % 0.40/0.63 (define @t38 () (@list @t6)) % 0.40/0.63 (define @t39 () (lambda @t38 true)) % 0.40/0.63 (define @t40 () (@var "V" $$unsorted)) % 0.40/0.63 (define @t41 () (_ @t11 @t40)) % 0.40/0.63 (define @t42 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.40/0.63 (define @t43 () (@list @t40)) % 0.40/0.63 (define @t44 () (lambda (@list @t42 @t11 @t6) (forall @t43 (or (not (_ (_ @t42 @t6) @t40)) @t41)))) % 0.40/0.63 (define @t45 () (lambda (@list @t42 @t11 @t19) (_ (_ tptp.mnot (_ (_ tptp.mbox @t42) @t21)) @t19))) % 0.40/0.63 (define @t46 () (@var "S" $$unsorted)) % 0.40/0.63 (define @t47 () (_ @t42 @t46)) % 0.40/0.63 (define @t48 () (@list @t46)) % 0.40/0.63 (define @t49 () (@list @t42)) % 0.40/0.63 (define @t50 () (lambda @t49 (forall @t48 (_ @t47 @t46)))) % 0.40/0.63 (define @t51 () (@var "T" $$unsorted)) % 0.40/0.63 (define @t52 () (_ @t42 @t51)) % 0.40/0.63 (define @t53 () (_ @t52 @t46)) % 0.40/0.63 (define @t54 () (_ @t47 @t51)) % 0.40/0.63 (define @t55 () (@list @t46 @t51)) % 0.40/0.63 (define @t56 () (forall @t55 (=> @t54 @t53))) % 0.40/0.63 (define @t57 () (lambda @t49 @t56)) % 0.40/0.63 (define @t58 () (@list @t51)) % 0.40/0.63 (define @t59 () (lambda @t49 (forall @t48 (exists @t58 @t54)))) % 0.40/0.63 (define @t60 () (@var "U" $$unsorted)) % 0.40/0.63 (define @t61 () (_ @t47 @t60)) % 0.40/0.63 (define @t62 () (_ @t52 @t60)) % 0.40/0.63 (define @t63 () (and @t54 @t62)) % 0.40/0.63 (define @t64 () (@list @t46 @t51 @t60)) % 0.40/0.63 (define @t65 () (forall @t64 (=> @t63 @t61))) % 0.40/0.63 (define @t66 () (lambda @t49 @t65)) % 0.40/0.63 (define @t67 () (and @t54 @t61)) % 0.40/0.63 (define @t68 () (lambda @t49 (forall @t64 (=> @t67 @t62)))) % 0.40/0.63 (define @t69 () (= @t51 @t60)) % 0.40/0.63 (define @t70 () (lambda @t49 (forall @t64 (=> @t67 @t69)))) % 0.40/0.63 (define @t71 () (@list @t60)) % 0.40/0.63 (define @t72 () (lambda @t49 (forall @t48 (exists @t58 (and @t54 (forall @t71 (=> @t61 @t69))))))) % 0.40/0.63 (define @t73 () (_ @t42 @t60)) % 0.40/0.63 (define @t74 () (_ @t73 @t51)) % 0.40/0.63 (define @t75 () (lambda @t49 (forall @t64 (=> @t54 (exists @t71 (and @t61 @t74)))))) % 0.40/0.63 (define @t76 () (lambda @t49 (forall @t64 (=> @t67 (or @t62 @t69 @t74))))) % 0.40/0.63 (define @t77 () (lambda @t49 (forall @t64 (=> @t67 (exists @t43 (and (_ @t52 @t40) (_ @t73 @t40))))))) % 0.40/0.63 (define @t78 () (forall @t38 @t12)) % 0.40/0.63 (define @t79 () (@list @t11)) % 0.40/0.63 (define @t80 () (lambda @t79 @t78)) % 0.40/0.63 (define @t81 () (lambda @t79 (forall @t38 @t13))) % 0.40/0.63 (define @t82 () (lambda @t79 (exists @t38 @t12))) % 0.40/0.63 (define @t83 () (lambda @t79 (exists @t38 @t13))) % 0.40/0.63 (define @t84 () (_ (_ tptp.rel_s5 @t6) @t40)) % 0.40/0.63 (define @t85 () (not @t84)) % 0.40/0.63 (define @t86 () (or @t85 @t41)) % 0.40/0.63 (define @t87 () (forall @t43 @t86)) % 0.40/0.63 (define @t88 () (lambda @t14 @t87)) % 0.40/0.63 (define @t89 () (lambda (@list @t11 @t19) (_ (_ tptp.mnot (_ tptp.mbox_s5 @t21)) @t19))) % 0.40/0.63 (define @t90 () (not (tptp.rel_s5 @t46 @t51))) % 0.40/0.63 (define @t91 () (forall @t64 (or @t90 (not (tptp.rel_s5 @t51 @t60)) (tptp.rel_s5 @t46 @t60)))) % 0.40/0.63 (define @t92 () (_ @t42 @t46 @t60)) % 0.40/0.63 (define @t93 () (_ @t42 @t51 @t60)) % 0.40/0.63 (define @t94 () (_ @t42 @t46 @t51)) % 0.40/0.63 (define @t95 () (not @t94)) % 0.40/0.63 (define @t96 () (not @t62)) % 0.40/0.63 (define @t97 () (not @t54)) % 0.40/0.63 (define @t98 () (or @t97 @t96 @t61)) % 0.40/0.63 (define @t99 () (_ @t42 @t51 @t46)) % 0.40/0.63 (define @t100 () (or @t97 @t53)) % 0.40/0.63 (define @t101 () (@var "BOUND_VARIABLE_8603" $$unsorted)) % 0.40/0.63 (define @t102 () (tptp.p @t101)) % 0.40/0.63 (define @t103 () (@var "BOUND_VARIABLE_8601" $$unsorted)) % 0.40/0.63 (define @t104 () (not (tptp.rel_s5 @t103 @t101))) % 0.40/0.63 (define @t105 () (@var "BOUND_VARIABLE_8538" $$unsorted)) % 0.40/0.63 (define @t106 () (tptp.q @t105)) % 0.40/0.63 (define @t107 () (@list @t105)) % 0.40/0.63 (define @t108 () (not (forall @t107 (or (not (tptp.rel_s5 @t103 @t105)) @t106)))) % 0.40/0.63 (define @t109 () (not (tptp.rel_s5 @t6 @t103))) % 0.40/0.63 (define @t110 () (@var "BOUND_VARIABLE_8588" $$unsorted)) % 0.40/0.63 (define @t111 () (tptp.q @t110)) % 0.40/0.63 (define @t112 () (@var "BOUND_VARIABLE_8586" $$unsorted)) % 0.40/0.63 (define @t113 () (not (tptp.rel_s5 @t112 @t110))) % 0.40/0.63 (define @t114 () (@var "BOUND_VARIABLE_8469" $$unsorted)) % 0.40/0.63 (define @t115 () (tptp.p @t114)) % 0.40/0.63 (define @t116 () (@list @t114)) % 0.40/0.63 (define @t117 () (not (forall @t116 (or (not (tptp.rel_s5 @t112 @t114)) @t115)))) % 0.40/0.63 (define @t118 () (not (tptp.rel_s5 @t6 @t112))) % 0.40/0.63 (define @t119 () (or @t118 @t117 @t113 @t111 @t109 @t108 @t104 @t102)) % 0.40/0.63 (define @t120 () (@list @t6 @t112 @t110 @t103 @t101)) % 0.40/0.63 (define @t121 () (forall @t120 @t119)) % 0.40/0.63 (define @t122 () (@quantifiers_skolemize @t121 1)) % 0.40/0.63 (define @t123 () (@quantifiers_skolemize @t121 0)) % 0.40/0.63 (define @t124 () (or @t109 @t108 @t104 @t102)) % 0.40/0.63 (define @t125 () (or @t118 @t117 @t113 @t111)) % 0.40/0.63 (define @t126 () (or @t125 @t124)) % 0.40/0.63 (define @t127 () (forall @t120 @t126)) % 0.40/0.63 (define @t128 () (forall (@list @t112 @t110 @t103 @t101) @t126)) % 0.40/0.63 (define @t129 () (forall (@list @t103 @t101) @t124)) % 0.40/0.63 (define @t130 () (@var "BOUND_VARIABLE_8563" $$unsorted)) % 0.40/0.63 (define @t131 () (forall (@list @t112 @t110) @t125)) % 0.40/0.63 (define @t132 () (@var "BOUND_VARIABLE_8494" $$unsorted)) % 0.40/0.63 (define @t133 () (or @t131 @t129)) % 0.40/0.63 (define @t134 () (tptp.p @t130)) % 0.40/0.63 (define @t135 () (not (tptp.rel_s5 @t40 @t130))) % 0.40/0.63 (define @t136 () (not (forall @t107 (or (not (tptp.rel_s5 @t40 @t105)) @t106)))) % 0.40/0.63 (define @t137 () (tptp.rel_s5 @t6 @t40)) % 0.40/0.63 (define @t138 () (not @t137)) % 0.40/0.63 (define @t139 () (or @t138 @t136 @t135 @t134)) % 0.40/0.63 (define @t140 () (@list @t40 @t130)) % 0.40/0.63 (define @t141 () (forall @t140 @t139)) % 0.40/0.63 (define @t142 () (tptp.q @t132)) % 0.40/0.63 (define @t143 () (not (tptp.rel_s5 @t40 @t132))) % 0.40/0.63 (define @t144 () (not (forall @t116 (or (not (tptp.rel_s5 @t40 @t114)) @t115)))) % 0.40/0.63 (define @t145 () (or @t138 @t144 @t143 @t142)) % 0.40/0.63 (define @t146 () (@list @t40 @t132)) % 0.40/0.63 (define @t147 () (forall @t146 @t145)) % 0.40/0.63 (define @t148 () (or @t147 @t141)) % 0.40/0.63 (define @t149 () (lambda @t38 @t148)) % 0.40/0.63 (define @t150 () (_ @t149 @t6)) % 0.40/0.63 (define @t151 () (forall @t38 @t150)) % 0.40/0.63 (define @t152 () (_ @t11 @t6)) % 0.40/0.63 (define @t153 () (lambda @t79 (forall @t38 @t152))) % 0.40/0.63 (define @t154 () (lambda @t38 @t141)) % 0.40/0.63 (define @t155 () (_ @t154 @t6)) % 0.40/0.63 (define @t156 () (or @t147 @t155)) % 0.40/0.63 (define @t157 () (lambda @t38 @t156)) % 0.40/0.63 (define @t158 () (@list @t16 @t6)) % 0.40/0.63 (define @t159 () (or @t135 @t134)) % 0.40/0.63 (define @t160 () (or @t138 @t136 @t159)) % 0.40/0.63 (define @t161 () (forall @t140 @t160)) % 0.40/0.63 (define @t162 () (@list @t130)) % 0.40/0.63 (define @t163 () (forall @t162 @t160)) % 0.40/0.63 (define @t164 () (forall @t162 @t159)) % 0.40/0.63 (define @t165 () (@var "BOUND_VARIABLE_8530" $$unsorted)) % 0.40/0.63 (define @t166 () (@list @t165)) % 0.40/0.63 (define @t167 () (or @t138 @t136 @t164)) % 0.40/0.63 (define @t168 () (tptp.p @t165)) % 0.40/0.63 (define @t169 () (@list @t165)) % 0.40/0.63 (define @t170 () (forall @t169 (or (not (tptp.rel_s5 @t40 @t165)) @t168))) % 0.40/0.63 (define @t171 () (or @t138 @t136 @t170)) % 0.40/0.63 (define @t172 () (or @t136 @t170)) % 0.40/0.63 (define @t173 () (@list @t19)) % 0.40/0.63 (define @t174 () (tptp.p @t40)) % 0.40/0.63 (define @t175 () (not (tptp.rel_s5 @t19 @t40))) % 0.40/0.63 (define @t176 () (forall @t43 (or @t175 @t174))) % 0.40/0.63 (define @t177 () (@list @t40)) % 0.40/0.63 (define @t178 () (tptp.q @t40)) % 0.40/0.63 (define @t179 () (forall @t43 (or @t175 @t178))) % 0.40/0.63 (define @t180 () (not @t179)) % 0.40/0.63 (define @t181 () (or @t180 @t176)) % 0.40/0.63 (define @t182 () (lambda @t173 @t181)) % 0.40/0.63 (define @t183 () (or @t138 (_ @t182 @t40))) % 0.40/0.63 (define @t184 () (forall @t43 @t183)) % 0.40/0.63 (define @t185 () (lambda @t38 @t184)) % 0.40/0.63 (define @t186 () (_ @t11 @t40)) % 0.40/0.63 (define @t187 () (lambda @t14 (forall @t43 (or @t138 @t186)))) % 0.40/0.63 (define @t188 () (lambda @t38 (forall @t43 (or @t138 @t174)))) % 0.40/0.63 (define @t189 () (_ @t188 @t19)) % 0.40/0.63 (define @t190 () (or @t180 @t189)) % 0.40/0.63 (define @t191 () (lambda @t173 @t190)) % 0.40/0.63 (define @t192 () (_ @t16 @t19)) % 0.40/0.63 (define @t193 () (@list @t16 @t19)) % 0.40/0.63 (define @t194 () (_ @t187 tptp.p)) % 0.40/0.63 (define @t195 () (lambda @t38 (forall @t43 (or @t138 @t178)))) % 0.40/0.63 (define @t196 () (_ @t195 @t19)) % 0.40/0.63 (define @t197 () (not @t196)) % 0.40/0.63 (define @t198 () (or @t197 @t192)) % 0.40/0.63 (define @t199 () (lambda @t193 @t198)) % 0.40/0.63 (define @t200 () (or (not (_ @t11 @t19)) @t192)) % 0.40/0.63 (define @t201 () (lambda @t23 @t200)) % 0.40/0.63 (define @t202 () (_ @t187 tptp.q)) % 0.40/0.63 (define @t203 () (lambda @t38 @t147)) % 0.40/0.63 (define @t204 () (_ @t203 @t6)) % 0.40/0.63 (define @t205 () (or @t204 @t17)) % 0.40/0.63 (define @t206 () (lambda @t158 @t205)) % 0.40/0.63 (define @t207 () (or @t143 @t142)) % 0.40/0.63 (define @t208 () (or @t138 @t144 @t207)) % 0.40/0.63 (define @t209 () (forall @t146 @t208)) % 0.40/0.63 (define @t210 () (@list @t132)) % 0.40/0.63 (define @t211 () (forall @t210 @t208)) % 0.40/0.63 (define @t212 () (forall @t210 @t207)) % 0.40/0.63 (define @t213 () (@var "BOUND_VARIABLE_8461" $$unsorted)) % 0.40/0.63 (define @t214 () (@list @t213)) % 0.40/0.63 (define @t215 () (or @t138 @t144 @t212)) % 0.40/0.63 (define @t216 () (tptp.q @t213)) % 0.40/0.63 (define @t217 () (@list @t213)) % 0.40/0.63 (define @t218 () (forall @t217 (or (not (tptp.rel_s5 @t40 @t213)) @t216))) % 0.40/0.63 (define @t219 () (or @t138 @t144 @t218)) % 0.40/0.63 (define @t220 () (or @t144 @t218)) % 0.40/0.63 (define @t221 () (not @t176)) % 0.40/0.63 (define @t222 () (or @t221 @t179)) % 0.40/0.63 (define @t223 () (lambda @t173 @t222)) % 0.40/0.63 (define @t224 () (or @t138 (_ @t223 @t40))) % 0.40/0.63 (define @t225 () (forall @t43 @t224)) % 0.40/0.63 (define @t226 () (lambda @t38 @t225)) % 0.40/0.63 (define @t227 () (or @t221 @t196)) % 0.40/0.63 (define @t228 () (lambda @t173 @t227)) % 0.40/0.63 (define @t229 () (not @t189)) % 0.40/0.63 (define @t230 () (or @t229 @t192)) % 0.40/0.63 (define @t231 () (lambda @t193 @t230)) % 0.40/0.63 (define @t232 () (or @t13 @t17)) % 0.40/0.63 (define @t233 () (lambda @t38 @t232)) % 0.40/0.63 (define @t234 () (lambda @t38 @t13)) % 0.40/0.63 (define @t235 () (_ @t234 @t6)) % 0.40/0.63 (define @t236 () (or @t235 @t17)) % 0.40/0.63 (define @t237 () (lambda @t158 @t236)) % 0.40/0.63 (define @t238 () (tptp.rel_s5 @t123 @t122)) % 0.40/0.63 (define @t239 () (@quantifiers_skolemize @t121 4)) % 0.40/0.63 (define @t240 () (tptp.p @t239)) % 0.40/0.63 (define @t241 () (@quantifiers_skolemize @t121 3)) % 0.40/0.63 (define @t242 () (tptp.rel_s5 @t241 @t239)) % 0.40/0.63 (define @t243 () (not @t242)) % 0.40/0.63 (define @t244 () (tptp.rel_s5 @t123 @t241)) % 0.40/0.63 (define @t245 () (not @t244)) % 0.40/0.63 (define @t246 () (@quantifiers_skolemize @t121 2)) % 0.40/0.63 (define @t247 () (forall @t116 (or (not (tptp.rel_s5 @t122 @t114)) @t115))) % 0.40/0.63 (define @t248 () (not @t247)) % 0.40/0.63 (define @t249 () (not @t238)) % 0.40/0.63 (define @t250 () (or @t249 @t248 (not (tptp.rel_s5 @t122 @t246)) (tptp.q @t246) @t245 (not (forall @t107 (or (not (tptp.rel_s5 @t241 @t105)) @t106))) @t243 @t240)) % 0.40/0.63 (define @t251 () (@list true)) % 0.40/0.63 (define @t252 () (@list @t250)) % 0.40/0.63 (define @t253 () (tptp.rel_s5 @t122 @t123)) % 0.40/0.63 (define @t254 () (or @t249 @t253)) % 0.40/0.63 (define @t255 () (tptp.rel_s5 @t123 @t239)) % 0.40/0.63 (define @t256 () (or @t245 @t243 @t255)) % 0.40/0.63 (define @t257 () (tptp.rel_s5 @t122 @t239)) % 0.40/0.63 (define @t258 () (not @t257)) % 0.40/0.63 (define @t259 () (or @t258 @t240)) % 0.40/0.63 (define @t260 () (@list true false)) % 0.40/0.63 (define @t261 () (not @t255)) % 0.40/0.63 (define @t262 () (not @t253)) % 0.40/0.63 (define @t263 () (or @t262 @t261 @t257)) % 0.40/0.63 (define @t264 () (not @t263)) % 0.40/0.63 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.40/0.63 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.40/0.63 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.40/0.63 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.40/0.63 (assume @p5 @t3) % 0.40/0.63 (assume @p6 true) % 0.40/0.63 (step @p7 (= tptp.meq_ind @t7) :rule refl :args (@t7)) % 0.40/0.63 (step @p8 (= tptp.meq_prop @t10) :rule refl :args (@t10)) % 0.40/0.63 (step @p9 (= tptp.mnot @t15) :rule refl :args (@t15)) % 0.40/0.63 (step @p10 (= tptp.mor @t18) :rule refl :args (@t18)) % 0.40/0.63 (step @p11 (= tptp.mand @t24) :rule refl :args (@t24)) % 0.40/0.63 (step @p12 (= tptp.mimplies @t25) :rule refl :args (@t25)) % 0.40/0.63 (step @p13 (= tptp.mimplied @t26) :rule refl :args (@t26)) % 0.40/0.63 (step @p14 (= tptp.mequiv @t27) :rule refl :args (@t27)) % 0.40/0.63 (step @p15 (= tptp.mxor @t28) :rule refl :args (@t28)) % 0.40/0.63 (step @p16 (= tptp.mforall_ind @t31) :rule refl :args (@t31)) % 0.40/0.63 (step @p17 (= tptp.mforall_prop @t35) :rule refl :args (@t35)) % 0.40/0.63 (step @p18 (= tptp.mexists_ind @t36) :rule refl :args (@t36)) % 0.40/0.63 (step @p19 (= tptp.mexists_prop @t37) :rule refl :args (@t37)) % 0.40/0.63 (step @p20 (= tptp.mtrue @t39) :rule refl :args (@t39)) % 0.40/0.63 (step @p21 (= tptp.mbox @t44) :rule refl :args (@t44)) % 0.40/0.63 (step @p22 (= tptp.mdia @t45) :rule refl :args (@t45)) % 0.40/0.63 (step @p23 (= tptp.mreflexive @t50) :rule refl :args (@t50)) % 0.40/0.63 (step @p24 (= tptp.msymmetric @t57) :rule refl :args (@t57)) % 0.40/0.63 (step @p25 (= tptp.mserial @t59) :rule refl :args (@t59)) % 0.40/0.63 (step @p26 (= tptp.mtransitive @t66) :rule refl :args (@t66)) % 0.40/0.63 (step @p27 (= tptp.meuclidean @t68) :rule refl :args (@t68)) % 0.40/0.63 (step @p28 (= tptp.mpartially_functional @t70) :rule refl :args (@t70)) % 0.40/0.63 (step @p29 (= tptp.mfunctional @t72) :rule refl :args (@t72)) % 0.40/0.63 (step @p30 (= tptp.mweakly_dense @t75) :rule refl :args (@t75)) % 0.40/0.63 (step @p31 (= tptp.mweakly_connected @t76) :rule refl :args (@t76)) % 0.40/0.63 (step @p32 (= tptp.mweakly_directed @t77) :rule refl :args (@t77)) % 0.40/0.63 (step @p33 (= tptp.mvalid @t80) :rule refl :args (@t80)) % 0.40/0.63 (step @p34 (= tptp.minvalid @t81) :rule refl :args (@t81)) % 0.40/0.63 (step @p35 (= tptp.msatisfiable @t82) :rule refl :args (@t82)) % 0.40/0.63 (step @p36 (= tptp.mcountersatisfiable @t83) :rule refl :args (@t83)) % 0.40/0.63 (step @p37 (= tptp.mbox_s5 @t88) :rule refl :args (@t88)) % 0.40/0.63 (step @p38 (= tptp.mdia_s5 @t89) :rule refl :args (@t89)) % 0.40/0.63 (step @p39 :rule beta-reduce :args ((= (_ (lambda @t49 (forall @t64 (or @t95 (not @t93) @t92))) tptp.rel_s5) @t91))) % 0.40/0.63 (step @p40 :rule refl :args (tptp.rel_s5)) % 0.40/0.63 (step @p41 :rule refl :args (@t92)) % 0.40/0.63 (step @p42 :rule refl :args (@t61)) % 0.40/0.63 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t61 @t92))) % 0.40/0.63 (step @p44 :rule symm :premises (@p43)) % 0.40/0.63 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.40/0.63 (step @p46 :rule refl :args (@t93)) % 0.40/0.63 (step @p47 :rule refl :args (@t62)) % 0.40/0.63 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t62 @t93))) % 0.40/0.63 (step @p49 :rule symm :premises (@p48)) % 0.40/0.63 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.40/0.63 (step @p51 :rule cong :premises (@p50) :args (@t96)) % 0.40/0.63 (step @p52 :rule refl :args (@t94)) % 0.40/0.63 (step @p53 :rule refl :args (@t54)) % 0.40/0.63 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t54 @t94))) % 0.40/0.63 (step @p55 :rule symm :premises (@p54)) % 0.40/0.63 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.40/0.63 (step @p57 :rule cong :premises (@p56) :args (@t97)) % 0.40/0.63 (step @p58 :rule nary_cong :premises (@p57 @p51 @p45) :args (@t98)) % 0.40/0.63 (step @p59 :rule cong :premises (@p58) :args ((forall @t64 @t98))) % 0.40/0.63 (step @p60 :rule aci_norm :args ((= (or (or @t97 @t96) @t61) @t98))) % 0.40/0.63 (step @p61 :rule bool-and-de-morgan :args (@t54 @t62 true)) % 0.40/0.63 (step @p62 :rule nary_cong :premises (@p61 @p42) :args ((or (not @t63) @t61))) % 0.40/0.63 (step @p63 :rule trans :premises (@p62 @p60)) % 0.40/0.63 (step @p64 :rule bool-impl-elim :args (@t63 @t61)) % 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:rule cnf_or_neg :args (@t250 7)) % 0.40/0.63 (step @p324 :rule chain_m_resolution :premises (@p323 @p289) :args ((not @t240) @t251 @t252)) % 0.40/0.63 (step @p325 :rule cnf_or_pos :args (@t259)) % 0.40/0.63 (step @p326 :rule reordering :premises (@p325) :args ((or @t240 @t258 (not @t259)))) % 0.40/0.63 (step @p327 :rule chain_m_resolution :premises (@p326 @p324 @p322) :args (@t258 @t260 (@list @t240 @t259))) % 0.40/0.63 (step @p328 :rule cnf_or_pos :args (@t263)) % 0.40/0.63 (step @p329 :rule reordering :premises (@p328) :args ((or @t257 @t261 @t262 @t264))) % 0.40/0.63 (step @p330 :rule chain_m_resolution :premises (@p329 @p327 @p315 @p299) :args (@t264 (@list true false false) (@list @t257 @t255 @t253))) % 0.40/0.63 (assume-push @p337 @t91) % 0.40/0.63 (step @p332 :rule instantiate :premises (@p72) :args ((@list @t122 @t123 @t239))) % 0.40/0.63 (step-pop @p338 :rule scope :premises (@p332)) % 0.40/0.63 (step @p333 :rule process_scope :premises (@p338) :args (@t263)) % 0.40/0.63 (step @p335 :rule implies_elim :premises (@p333)) % 0.40/0.63 (step @p336 false :rule chain_m_resolution :premises (@p335 @p330 @p72) :args (false @t260 (@list @t263 @t91))) % 0.40/0.63 ) % 0.40/0.63 % SZS output end Proof % 0.40/0.63 % cvc5 exiting %------------------------------------------------------------------------------