%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO457^6 : 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 : n004.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 09:12:46 AM UTC 2026 % Result : Theorem 0.39s 0.60s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO457^6 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n004.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 00:09:22 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.39/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.60 % SZS status Theorem % 0.39/0.60 % SZS output start Proof % 0.39/0.60 ( % 0.39/0.60 (declare-sort $$unsorted 0) % 0.39/0.60 (declare-sort tptp.mu 0) % 0.39/0.60 (declare-const tptp.rel_s5 (-> $$unsorted $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.q (-> $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.p (-> $$unsorted Bool)) % 0.39/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.39/0.60 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.39/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.39/0.60 (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)))))) % 0.39/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.39/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.39/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.60 (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))))))) % 0.39/0.60 (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))))))) % 0.39/0.60 (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)))))) % 0.39/0.60 (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)))))) % 0.39/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.39/0.60 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.39/0.60 (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)))))) % 0.39/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.39/0.60 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.39/0.60 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.39/0.60 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.39/0.60 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.39/0.60 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.39/0.60 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.39/0.60 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.39/0.60 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.39/0.60 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.39/0.60 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.39/0.60 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.39/0.60 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$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)))))))) % 0.39/0.60 (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))))) % 0.39/0.60 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mdia_s5 (_ tptp.mbox_s5 tptp.p))) (_ tptp.mdia_s5 (_ (_ tptp.mimplies tptp.q) tptp.p)))))) % 0.39/0.60 (define @t2 () (@var "Y" tptp.mu)) % 0.39/0.60 (define @t3 () (@var "X" tptp.mu)) % 0.39/0.60 (define @t4 () (@var "W" $$unsorted)) % 0.39/0.60 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.39/0.60 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.60 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.60 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.39/0.60 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.39/0.60 (define @t10 () (_ @t9 @t4)) % 0.39/0.60 (define @t11 () (not @t10)) % 0.39/0.60 (define @t12 () (@list @t9 @t4)) % 0.39/0.60 (define @t13 () (lambda @t12 @t11)) % 0.39/0.60 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.39/0.60 (define @t15 () (_ @t14 @t4)) % 0.39/0.60 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.39/0.60 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.39/0.60 (define @t18 () (_ tptp.mnot @t14)) % 0.39/0.60 (define @t19 () (_ tptp.mnot @t9)) % 0.39/0.60 (define @t20 () (_ tptp.mor @t19)) % 0.39/0.60 (define @t21 () (@list @t9 @t14 @t17)) % 0.39/0.60 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.39/0.60 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.39/0.60 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.39/0.60 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.39/0.60 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.39/0.60 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.39/0.60 (define @t28 () (_ @t27 @t3)) % 0.39/0.60 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.39/0.60 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.60 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.39/0.60 (define @t32 () (_ @t31 @t30)) % 0.39/0.60 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.39/0.60 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.39/0.60 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.39/0.60 (define @t36 () (@list @t4)) % 0.39/0.60 (define @t37 () (lambda @t36 true)) % 0.39/0.60 (define @t38 () (@var "V" $$unsorted)) % 0.39/0.60 (define @t39 () (_ @t9 @t38)) % 0.39/0.60 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.39/0.60 (define @t41 () (@list @t38)) % 0.39/0.60 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.39/0.60 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.39/0.60 (define @t44 () (@var "S" $$unsorted)) % 0.39/0.60 (define @t45 () (_ @t40 @t44)) % 0.39/0.60 (define @t46 () (@list @t44)) % 0.39/0.60 (define @t47 () (@list @t40)) % 0.39/0.60 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.39/0.60 (define @t49 () (@var "T" $$unsorted)) % 0.39/0.60 (define @t50 () (_ @t40 @t49)) % 0.39/0.60 (define @t51 () (_ @t50 @t44)) % 0.39/0.60 (define @t52 () (_ @t45 @t49)) % 0.39/0.60 (define @t53 () (@list @t44 @t49)) % 0.39/0.60 (define @t54 () (forall @t53 (=> @t52 @t51))) % 0.39/0.60 (define @t55 () (lambda @t47 @t54)) % 0.39/0.60 (define @t56 () (@list @t49)) % 0.39/0.60 (define @t57 () (lambda @t47 (forall @t46 (exists @t56 @t52)))) % 0.39/0.60 (define @t58 () (@var "U" $$unsorted)) % 0.39/0.60 (define @t59 () (_ @t45 @t58)) % 0.39/0.60 (define @t60 () (_ @t50 @t58)) % 0.39/0.60 (define @t61 () (and @t52 @t60)) % 0.39/0.60 (define @t62 () (@list @t44 @t49 @t58)) % 0.39/0.60 (define @t63 () (forall @t62 (=> @t61 @t59))) % 0.39/0.60 (define @t64 () (lambda @t47 @t63)) % 0.39/0.60 (define @t65 () (and @t52 @t59)) % 0.39/0.60 (define @t66 () (lambda @t47 (forall @t62 (=> @t65 @t60)))) % 0.39/0.60 (define @t67 () (= @t49 @t58)) % 0.39/0.60 (define @t68 () (lambda @t47 (forall @t62 (=> @t65 @t67)))) % 0.39/0.60 (define @t69 () (@list @t58)) % 0.39/0.60 (define @t70 () (lambda @t47 (forall @t46 (exists @t56 (and @t52 (forall @t69 (=> @t59 @t67))))))) % 0.39/0.60 (define @t71 () (_ @t40 @t58)) % 0.39/0.60 (define @t72 () (_ @t71 @t49)) % 0.39/0.60 (define @t73 () (lambda @t47 (forall @t62 (=> @t52 (exists @t69 (and @t59 @t72)))))) % 0.39/0.60 (define @t74 () (lambda @t47 (forall @t62 (=> @t65 (or @t60 @t67 @t72))))) % 0.39/0.60 (define @t75 () (lambda @t47 (forall @t62 (=> @t65 (exists @t41 (and (_ @t50 @t38) (_ @t71 @t38))))))) % 0.39/0.60 (define @t76 () (forall @t36 @t10)) % 0.39/0.60 (define @t77 () (@list @t9)) % 0.39/0.60 (define @t78 () (lambda @t77 @t76)) % 0.39/0.60 (define @t79 () (lambda @t77 (forall @t36 @t11))) % 0.39/0.60 (define @t80 () (lambda @t77 (exists @t36 @t10))) % 0.39/0.60 (define @t81 () (lambda @t77 (exists @t36 @t11))) % 0.39/0.60 (define @t82 () (_ (_ tptp.rel_s5 @t4) @t38)) % 0.39/0.60 (define @t83 () (not @t82)) % 0.39/0.60 (define @t84 () (or @t83 @t39)) % 0.39/0.60 (define @t85 () (forall @t41 @t84)) % 0.39/0.60 (define @t86 () (lambda @t12 @t85)) % 0.39/0.60 (define @t87 () (@list @t9 @t17)) % 0.39/0.60 (define @t88 () (lambda @t87 (_ (_ tptp.mnot (_ tptp.mbox_s5 @t19)) @t17))) % 0.39/0.60 (define @t89 () (@var "BOUND_VARIABLE_8435" $$unsorted)) % 0.39/0.60 (define @t90 () (tptp.p @t89)) % 0.39/0.60 (define @t91 () (@var "BOUND_VARIABLE_8513" $$unsorted)) % 0.39/0.60 (define @t92 () (@list @t89)) % 0.39/0.60 (define @t93 () (not (forall @t92 (or (not (tptp.rel_s5 @t91 @t89)) @t90)))) % 0.39/0.60 (define @t94 () (not (tptp.rel_s5 @t4 @t91))) % 0.39/0.60 (define @t95 () (tptp.p @t38)) % 0.39/0.60 (define @t96 () (tptp.q @t38)) % 0.39/0.60 (define @t97 () (and @t96 (not @t95))) % 0.39/0.60 (define @t98 () (tptp.rel_s5 @t4 @t38)) % 0.39/0.60 (define @t99 () (not @t98)) % 0.39/0.60 (define @t100 () (not (forall @t41 (or @t99 @t97)))) % 0.39/0.60 (define @t101 () (or @t100 @t94 @t93)) % 0.39/0.60 (define @t102 () (or @t94 @t93)) % 0.39/0.60 (define @t103 () (or @t102 @t100)) % 0.39/0.60 (define @t104 () (@list @t4 @t91)) % 0.39/0.60 (define @t105 () (forall @t104 @t103)) % 0.39/0.60 (define @t106 () (@list @t91)) % 0.39/0.60 (define @t107 () (forall @t106 @t103)) % 0.39/0.60 (define @t108 () (forall @t106 @t102)) % 0.39/0.60 (define @t109 () (@list @t38)) % 0.39/0.60 (define @t110 () (or @t108 @t100)) % 0.39/0.60 (define @t111 () (forall @t92 (or (not (tptp.rel_s5 @t38 @t89)) @t90))) % 0.39/0.60 (define @t112 () (not @t111)) % 0.39/0.60 (define @t113 () (or (forall @t41 (or @t99 @t112)) @t100)) % 0.39/0.60 (define @t114 () (not (tptp.rel_s5 @t17 @t38))) % 0.39/0.60 (define @t115 () (not (forall @t41 (or @t114 @t97)))) % 0.39/0.60 (define @t116 () (forall @t41 (or @t114 @t112))) % 0.39/0.60 (define @t117 () (@list @t17)) % 0.39/0.60 (define @t118 () (lambda @t117 (or @t116 @t115))) % 0.39/0.60 (define @t119 () (_ @t118 @t4)) % 0.39/0.60 (define @t120 () (forall @t36 @t119)) % 0.39/0.60 (define @t121 () (_ @t9 @t4)) % 0.39/0.60 (define @t122 () (lambda @t77 (forall @t36 @t121))) % 0.39/0.60 (define @t123 () (lambda @t117 @t115)) % 0.39/0.60 (define @t124 () (_ @t123 @t17)) % 0.39/0.60 (define @t125 () (or @t116 @t124)) % 0.39/0.60 (define @t126 () (lambda @t117 @t125)) % 0.39/0.60 (define @t127 () (_ @t14 @t17)) % 0.39/0.60 (define @t128 () (@list @t14 @t17)) % 0.39/0.60 (define @t129 () (_ tptp.p @t38)) % 0.39/0.60 (define @t130 () (not @t129)) % 0.39/0.60 (define @t131 () (_ tptp.q @t38)) % 0.39/0.60 (define @t132 () (and @t131 @t130)) % 0.39/0.60 (define @t133 () (or @t114 @t132)) % 0.39/0.60 (define @t134 () (not @t131)) % 0.39/0.60 (define @t135 () (or @t134 @t129)) % 0.39/0.60 (define @t136 () (or @t114 (not @t135))) % 0.39/0.60 (define @t137 () (not (_ tptp.q @t17))) % 0.39/0.60 (define @t138 () (lambda @t117 (or @t137 (_ tptp.p @t17)))) % 0.39/0.60 (define @t139 () (_ @t138 @t38)) % 0.39/0.60 (define @t140 () (not @t139)) % 0.39/0.60 (define @t141 () (or @t114 @t140)) % 0.39/0.60 (define @t142 () (forall @t41 @t141)) % 0.39/0.60 (define @t143 () (not @t142)) % 0.39/0.60 (define @t144 () (lambda @t117 @t143)) % 0.39/0.60 (define @t145 () (_ @t9 @t38)) % 0.39/0.60 (define @t146 () (not @t145)) % 0.39/0.60 (define @t147 () (not (forall @t41 (or @t114 @t146)))) % 0.39/0.60 (define @t148 () (lambda @t87 @t147)) % 0.39/0.60 (define @t149 () (lambda @t128 (or @t137 @t127))) % 0.39/0.60 (define @t150 () (or (not (_ @t9 @t17)) @t127)) % 0.39/0.60 (define @t151 () (lambda @t21 @t150)) % 0.39/0.60 (define @t152 () (_ @t151 tptp.q)) % 0.39/0.60 (define @t153 () (not @t116)) % 0.39/0.60 (define @t154 () (lambda @t117 @t153)) % 0.39/0.60 (define @t155 () (_ @t154 @t17)) % 0.39/0.60 (define @t156 () (not @t155)) % 0.39/0.60 (define @t157 () (or @t156 @t127)) % 0.39/0.60 (define @t158 () (lambda @t128 @t157)) % 0.39/0.60 (define @t159 () (forall @t41 (or @t99 @t95))) % 0.39/0.60 (define @t160 () (lambda @t36 @t159)) % 0.39/0.60 (define @t161 () (not (_ @t160 @t38))) % 0.39/0.60 (define @t162 () (or @t114 @t161)) % 0.39/0.60 (define @t163 () (forall @t41 @t162)) % 0.39/0.60 (define @t164 () (not @t163)) % 0.39/0.60 (define @t165 () (lambda @t117 @t164)) % 0.39/0.60 (define @t166 () (lambda @t12 (forall @t41 (or @t99 @t145)))) % 0.39/0.60 (define @t167 () (_ @t166 tptp.p)) % 0.39/0.60 (define @t168 () (or @t11 @t15)) % 0.39/0.60 (define @t169 () (lambda @t36 @t168)) % 0.39/0.60 (define @t170 () (@list @t14 @t4)) % 0.39/0.60 (define @t171 () (lambda @t36 @t11)) % 0.39/0.60 (define @t172 () (_ @t171 @t4)) % 0.39/0.60 (define @t173 () (or @t172 @t15)) % 0.39/0.60 (define @t174 () (lambda @t170 @t173)) % 0.39/0.60 (define @t175 () (forall @t41 (or @t99 @t146))) % 0.39/0.60 (define @t176 () (lambda @t36 @t175)) % 0.39/0.60 (define @t177 () (_ @t176 @t4)) % 0.39/0.60 (define @t178 () (not @t177)) % 0.39/0.60 (define @t179 () (lambda @t36 @t178)) % 0.39/0.60 (define @t180 () (not @t39)) % 0.39/0.60 (define @t181 () (or @t99 @t180)) % 0.39/0.60 (define @t182 () (_ @t171 @t38)) % 0.39/0.60 (define @t183 () (or @t99 @t182)) % 0.39/0.60 (define @t184 () (forall @t41 @t183)) % 0.39/0.60 (define @t185 () (lambda @t36 @t184)) % 0.39/0.60 (define @t186 () (forall @t104 @t101)) % 0.39/0.60 (define @t187 () (@quantifiers_skolemize @t186 0)) % 0.39/0.60 (define @t188 () (forall @t41 (or (not (tptp.rel_s5 @t187 @t38)) @t97))) % 0.39/0.60 (define @t189 () (@quantifiers_skolemize @t186 1)) % 0.39/0.60 (define @t190 () (forall @t92 (or (not (tptp.rel_s5 @t189 @t89)) @t90))) % 0.39/0.60 (define @t191 () (not @t190)) % 0.39/0.60 (define @t192 () (tptp.rel_s5 @t187 @t189)) % 0.39/0.60 (define @t193 () (not @t192)) % 0.39/0.60 (define @t194 () (not @t188)) % 0.39/0.60 (define @t195 () (or @t194 @t193 @t191)) % 0.39/0.60 (define @t196 () (@list true)) % 0.39/0.60 (define @t197 () (@list @t195)) % 0.39/0.60 (define @t198 () (@list @t189)) % 0.39/0.60 (define @t199 () (tptp.p @t189)) % 0.39/0.60 (define @t200 () (not @t199)) % 0.39/0.60 (define @t201 () (and (tptp.q @t189) @t200)) % 0.39/0.60 (define @t202 () (or @t193 @t201)) % 0.39/0.60 (define @t203 () (@list false false)) % 0.39/0.60 (define @t204 () (not (tptp.rel_s5 @t44 @t49))) % 0.39/0.60 (define @t205 () (_ @t40 @t44 @t58)) % 0.39/0.60 (define @t206 () (_ @t40 @t49 @t58)) % 0.39/0.60 (define @t207 () (_ @t40 @t44 @t49)) % 0.39/0.60 (define @t208 () (not @t207)) % 0.39/0.60 (define @t209 () (not @t60)) % 0.39/0.60 (define @t210 () (not @t52)) % 0.39/0.60 (define @t211 () (or @t210 @t209 @t59)) % 0.39/0.60 (define @t212 () (_ @t40 @t49 @t44)) % 0.39/0.60 (define @t213 () (or @t210 @t51)) % 0.39/0.60 (define @t214 () (tptp.rel_s5 @t189 @t187)) % 0.39/0.60 (define @t215 () (or @t193 @t214)) % 0.39/0.60 (define @t216 () (tptp.rel_s5 @t189 @t189)) % 0.39/0.60 (define @t217 () (not @t214)) % 0.39/0.60 (define @t218 () (or @t217 @t193 @t216)) % 0.39/0.60 (define @t219 () (not @t216)) % 0.39/0.60 (define @t220 () (or @t219 @t199)) % 0.39/0.60 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.39/0.60 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.39/0.60 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.39/0.60 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.39/0.60 (assume @p5 @t1) % 0.39/0.60 (assume @p6 true) % 0.39/0.60 (step @p7 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.39/0.60 (step @p8 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.39/0.60 (step @p9 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.39/0.60 (step @p10 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.39/0.60 (step @p11 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.39/0.60 (step @p12 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.39/0.60 (step @p13 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.39/0.60 (step @p14 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.39/0.60 (step @p15 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.39/0.60 (step @p16 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.39/0.60 (step @p17 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.39/0.60 (step @p18 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.39/0.60 (step @p19 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.39/0.60 (step @p20 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.39/0.60 (step @p21 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.39/0.60 (step @p22 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.39/0.60 (step @p23 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.39/0.60 (step @p24 (= tptp.msymmetric @t55) :rule refl :args (@t55)) % 0.39/0.60 (step @p25 (= tptp.mserial @t57) :rule refl :args (@t57)) % 0.39/0.60 (step @p26 (= tptp.mtransitive @t64) :rule refl :args (@t64)) % 0.39/0.60 (step @p27 (= tptp.meuclidean @t66) :rule refl :args (@t66)) % 0.39/0.60 (step @p28 (= tptp.mpartially_functional @t68) :rule refl :args (@t68)) % 0.39/0.60 (step @p29 (= tptp.mfunctional @t70) :rule refl :args (@t70)) % 0.39/0.60 (step @p30 (= tptp.mweakly_dense @t73) :rule refl :args (@t73)) % 0.39/0.60 (step @p31 (= tptp.mweakly_connected @t74) :rule refl :args (@t74)) % 0.39/0.60 (step @p32 (= tptp.mweakly_directed @t75) :rule refl :args (@t75)) % 0.39/0.60 (step @p33 (= tptp.mvalid @t78) :rule refl :args (@t78)) % 0.39/0.60 (step @p34 (= tptp.minvalid @t79) :rule refl :args (@t79)) % 0.39/0.60 (step @p35 (= tptp.msatisfiable @t80) :rule refl :args (@t80)) % 0.39/0.60 (step @p36 (= tptp.mcountersatisfiable @t81) :rule refl :args (@t81)) % 0.39/0.60 (step @p37 (= tptp.mbox_s5 @t86) :rule refl :args (@t86)) % 0.39/0.60 (step @p38 (= tptp.mdia_s5 @t88) :rule refl :args (@t88)) % 0.39/0.60 (step @p39 :rule aci_norm :args ((= @t103 @t101))) % 0.39/0.60 (step @p40 :rule cong :premises (@p39) :args (@t105)) % 0.39/0.60 (step @p41 :rule quant-merge-prenex :args ((= (forall @t36 @t107) @t105))) % 0.39/0.60 (step @p42 :rule refl :args (@t100)) % 0.39/0.60 (step @p43 :rule alpha_equiv :args (@t108 (@list @t91) @t109)) % 0.39/0.60 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t110)) % 0.39/0.60 (step @p45 :rule quant-miniscope-or :args ((= @t107 @t110))) % 0.39/0.60 (step @p46 :rule trans :premises (@p45 @p44)) % 0.39/0.60 (step @p47 :rule symm :premises (@p46)) % 0.39/0.60 (step @p48 :rule cong :premises (@p47) :args ((forall @t36 @t113))) % 0.39/0.60 (step @p49 :rule trans :premises (@p48 @p41)) % 0.39/0.60 (step @p50 :rule trans :premises (@p49 @p40)) % 0.39/0.60 (step @p51 :rule beta-reduce :args ((= @t119 @t113))) % 0.39/0.60 (step @p52 :rule cong :premises (@p51) :args (@t120)) % 0.39/0.60 (step @p53 :rule trans :premises (@p52 @p50)) % 0.39/0.60 (step @p54 :rule beta-reduce :args ((= (_ @t122 @t118) @t120))) % 0.39/0.60 (step @p55 :rule trans :premises (@p54 @p53)) % 0.39/0.60 (step @p56 :rule beta-reduce :args ((= @t124 @t115))) % 0.39/0.60 (step @p57 :rule refl :args (@t116)) % 0.39/0.60 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t125)) % 0.39/0.60 (step @p59 :rule cong :premises (@p58) :args (@t126)) % 0.39/0.60 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t128 (or @t116 @t127)) @t123) @t126))) % 0.39/0.60 (step @p61 :rule trans :premises (@p60 @p59)) % 0.39/0.60 (step @p62 :rule refl :args (@t95)) % 0.39/0.60 (step @p63 :rule refl :args (@t129)) % 0.39/0.60 (step @p64 :rule cong :premises (@p63 @p62) :args ((= @t129 @t95))) % 0.39/0.60 (step @p65 :rule symm :premises (@p64)) % 0.39/0.60 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 0.39/0.60 (step @p67 :rule cong :premises (@p66) :args (@t130)) % 0.39/0.60 (step @p68 :rule refl :args (@t96)) % 0.39/0.60 (step @p69 :rule refl :args (@t131)) % 0.39/0.60 (step @p70 :rule cong :premises (@p69 @p68) :args ((= @t131 @t96))) % 0.39/0.60 (step @p71 :rule symm :premises (@p70)) % 0.39/0.60 (step @p72 :rule eq_resolve :premises (@p69 @p71)) % 0.39/0.60 (step @p73 :rule nary_cong :premises (@p72 @p67) :args (@t132)) % 0.39/0.60 (step @p74 :rule refl :args (@t114)) % 0.39/0.60 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t133)) % 0.39/0.60 (step @p76 :rule cong :premises (@p75) :args ((forall @t41 @t133))) % 0.39/0.60 (step @p77 :rule refl :args (@t130)) % 0.39/0.60 (step @p78 :rule bool-double-not-elim :args (@t131)) % 0.39/0.60 (step @p79 :rule nary_cong :premises (@p78 @p77) :args ((and (not @t134) @t130))) % 0.39/0.60 (step @p80 :rule bool-or-de-morgan :args (@t134 @t129 false)) % 0.39/0.60 (step @p81 :rule trans :premises (@p80 @p79)) % 0.39/0.60 (step @p82 :rule nary_cong :premises (@p74 @p81) :args (@t136)) % 0.39/0.60 (step @p83 :rule cong :premises (@p82) :args ((forall @t41 @t136))) % 0.39/0.60 (step @p84 :rule trans :premises (@p83 @p76)) % 0.39/0.60 (step @p85 :rule beta-reduce :args ((= @t139 @t135))) % 0.39/0.60 (step @p86 :rule cong :premises (@p85) :args (@t140)) % 0.39/0.60 (step @p87 :rule refl :args (@t114)) % 0.39/0.60 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t141)) % 0.39/0.60 (step @p89 :rule cong :premises (@p88) :args (@t142)) % 0.39/0.60 (step @p90 :rule trans :premises (@p89 @p84)) % 0.39/0.60 (step @p91 :rule cong :premises (@p90) :args (@t143)) % 0.39/0.60 (step @p92 :rule cong :premises (@p91) :args (@t144)) % 0.39/0.60 (step @p93 :rule beta-reduce :args ((= (_ @t148 @t138) @t144))) % 0.39/0.60 (step @p94 :rule trans :premises (@p93 @p92)) % 0.39/0.60 (step @p95 :rule beta-reduce :args ((= (_ @t149 tptp.p) @t138))) % 0.39/0.60 (step @p96 :rule refl :args (tptp.p)) % 0.39/0.60 (step @p97 :rule beta-reduce :args ((= @t152 @t149))) % 0.39/0.60 (step @p98 :rule ho_cong :premises (@p97 @p96)) % 0.39/0.60 (step @p99 :rule trans :premises (@p98 @p95)) % 0.39/0.60 (step @p100 :rule refl :args (@t148)) % 0.39/0.60 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 0.39/0.60 (step @p102 :rule trans :premises (@p101 @p94)) % 0.39/0.60 (step @p103 :rule refl :args (@t127)) % 0.39/0.60 (step @p104 :rule bool-double-not-elim :args (@t116)) % 0.39/0.60 (step @p105 :rule beta-reduce :args ((= @t155 @t153))) % 0.39/0.60 (step @p106 :rule cong :premises (@p105) :args (@t156)) % 0.39/0.60 (step @p107 :rule trans :premises (@p106 @p104)) % 0.39/0.60 (step @p108 :rule nary_cong :premises (@p107 @p103) :args (@t157)) % 0.39/0.60 (step @p109 :rule cong :premises (@p108) :args (@t158)) % 0.39/0.60 (step @p110 :rule beta-reduce :args ((= (_ @t151 @t154) @t158))) % 0.39/0.60 (step @p111 :rule trans :premises (@p110 @p109)) % 0.39/0.60 (step @p112 :rule beta-reduce :args ((= (_ (lambda @t36 (forall @t92 (or (not (tptp.rel_s5 @t4 @t89)) @t90))) @t38) @t111))) % 0.39/0.60 (step @p113 :rule refl :args (@t38)) % 0.39/0.60 (step @p114 :rule alpha_equiv :args (@t159 @t109 (@list @t89))) % 0.39/0.60 (step @p115 :rule cong :premises (@p114) :args (@t160)) % 0.39/0.60 (step @p116 :rule ho_cong :premises (@p115 @p113)) % 0.39/0.60 (step @p117 :rule trans :premises (@p116 @p112)) % 0.39/0.60 (step @p118 :rule cong :premises (@p117) :args (@t161)) % 0.39/0.60 (step @p119 :rule nary_cong :premises (@p87 @p118) :args (@t162)) % 0.39/0.60 (step @p120 :rule cong :premises (@p119) :args (@t163)) % 0.39/0.60 (step @p121 :rule cong :premises (@p120) :args (@t164)) % 0.39/0.60 (step @p122 :rule cong :premises (@p121) :args (@t165)) % 0.39/0.60 (step @p123 :rule beta-reduce :args ((= (_ @t148 @t160) @t165))) % 0.39/0.60 (step @p124 :rule trans :premises (@p123 @p122)) % 0.39/0.60 (step @p125 :rule beta-reduce :args ((= @t167 @t160))) % 0.39/0.60 (step @p126 :rule ho_cong :premises (@p100 @p125)) % 0.39/0.60 (step @p127 :rule trans :premises (@p126 @p124)) % 0.39/0.60 (step @p128 :rule refl :args (@t151)) % 0.39/0.60 (step @p129 :rule ho_cong :premises (@p128 @p127)) % 0.39/0.60 (step @p130 :rule trans :premises (@p129 @p111)) % 0.39/0.60 (step @p131 :rule ho_cong :premises (@p130 @p102)) % 0.39/0.60 (step @p132 :rule trans :premises (@p131 @p61)) % 0.39/0.60 (step @p133 :rule refl :args (@t122)) % 0.39/0.60 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.39/0.60 (step @p135 :rule trans :premises (@p134 @p55)) % 0.39/0.60 (step @p136 :rule cong :premises (@p135) :args ((not (_ @t122 (_ (_ @t151 (_ @t148 @t167)) (_ @t148 (_ @t152 tptp.p))))))) % 0.39/0.60 (step @p137 :rule refl :args (tptp.q)) % 0.39/0.60 (step @p138 :rule beta-reduce :args ((= (_ @t169 @t17) @t150))) % 0.39/0.60 (step @p139 :rule refl :args (@t17)) % 0.39/0.60 (step @p140 :rule beta-reduce :args ((= (_ (lambda @t170 @t168) @t14) @t169))) % 0.39/0.60 (step @p141 :rule refl :args (@t14)) % 0.39/0.60 (step @p142 :rule refl :args (@t15)) % 0.39/0.60 (step @p143 :rule beta-reduce :args ((= @t172 @t11))) % 0.39/0.60 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t173)) % 0.39/0.60 (step @p145 :rule cong :premises (@p144) :args (@t174)) % 0.39/0.60 (step @p146 :rule beta-reduce :args ((= (_ @t16 @t171) @t174))) % 0.39/0.60 (step @p147 :rule trans :premises (@p146 @p145)) % 0.39/0.60 (step @p148 :rule beta-reduce :args ((= (_ @t13 @t9) @t171))) % 0.39/0.60 (step @p149 :rule refl :args (@t16)) % 0.39/0.60 (step @p150 :rule ho_cong :premises (@p149 @p148)) % 0.39/0.60 (step @p151 :rule trans :premises (@p150 @p147)) % 0.39/0.60 (step @p152 :rule ho_cong :premises (@p151 @p141)) % 0.39/0.60 (step @p153 :rule trans :premises (@p152 @p140)) % 0.39/0.60 (step @p154 :rule ho_cong :premises (@p153 @p139)) % 0.39/0.60 (step @p155 :rule trans :premises (@p154 @p138)) % 0.39/0.60 (step @p156 :rule refl :args (@t9)) % 0.39/0.60 (step @p157 :rule ho_cong :premises (@p9 @p156)) % 0.39/0.60 (step @p158 :rule ho_cong :premises (@p10 @p157)) % 0.39/0.60 (step @p159 :rule ho_cong :premises (@p158 @p141)) % 0.39/0.60 (step @p160 :rule ho_cong :premises (@p159 @p139)) % 0.39/0.60 (step @p161 :rule trans :premises (@p160 @p155)) % 0.39/0.60 (step @p162 :rule cong :premises (@p161) :args (@t23)) % 0.39/0.60 (step @p163 :rule trans :premises (@p12 @p162)) % 0.39/0.60 (step @p164 :rule ho_cong :premises (@p163 @p137)) % 0.39/0.60 (step @p165 :rule ho_cong :premises (@p164 @p96)) % 0.39/0.60 (step @p166 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t175)) @t17) @t147))) % 0.39/0.60 (step @p167 :rule beta-reduce :args ((= @t177 @t175))) % 0.39/0.60 (step @p168 :rule cong :premises (@p167) :args (@t178)) % 0.39/0.60 (step @p169 :rule cong :premises (@p168) :args (@t179)) % 0.39/0.60 (step @p170 :rule beta-reduce :args ((= (_ @t13 @t176) @t179))) % 0.39/0.60 (step @p171 :rule trans :premises (@p170 @p169)) % 0.39/0.60 (step @p172 :rule refl :args (@t145)) % 0.39/0.60 (step @p173 :rule refl :args (@t39)) % 0.39/0.60 (step @p174 :rule cong :premises (@p173 @p172) :args ((= @t39 @t145))) % 0.39/0.60 (step @p175 :rule symm :premises (@p174)) % 0.39/0.60 (step @p176 :rule eq_resolve :premises (@p173 @p175)) % 0.39/0.60 (step @p177 :rule cong :premises (@p176) :args (@t180)) % 0.39/0.60 (step @p178 :rule refl :args (@t99)) % 0.39/0.60 (step @p179 :rule nary_cong :premises (@p178 @p177) :args (@t181)) % 0.39/0.61 (step @p180 :rule cong :premises (@p179) :args ((forall @t41 @t181))) % 0.39/0.61 (step @p181 :rule beta-reduce :args ((= @t182 @t180))) % 0.39/0.61 (step @p182 :rule refl :args (@t99)) % 0.39/0.61 (step @p183 :rule nary_cong :premises (@p182 @p181) :args (@t183)) % 0.39/0.61 (step @p184 :rule cong :premises (@p183) :args (@t184)) % 0.39/0.61 (step @p185 :rule trans :premises (@p184 @p180)) % 0.39/0.61 (step @p186 :rule cong :premises (@p185) :args (@t185)) % 0.39/0.61 (step @p187 :rule beta-reduce :args ((= (_ @t166 @t171) @t185))) % 0.39/0.61 (step @p188 :rule trans :premises (@p187 @p186)) % 0.39/0.61 (step @p189 :rule refl :args (@t166)) % 0.39/0.61 (step @p190 :rule ho_cong :premises (@p189 @p148)) % 0.39/0.61 (step @p191 :rule trans :premises (@p190 @p188)) % 0.39/0.61 (step @p192 :rule refl :args (@t13)) % 0.39/0.61 (step @p193 :rule ho_cong :premises (@p192 @p191)) % 0.39/0.61 (step @p194 :rule trans :premises (@p193 @p171)) % 0.39/0.61 (step @p195 :rule ho_cong :premises (@p194 @p139)) % 0.39/0.61 (step @p196 :rule trans :premises (@p195 @p166)) % 0.39/0.61 (step @p197 :rule refl :args (@t98)) % 0.39/0.61 (step @p198 :rule refl :args (@t82)) % 0.39/0.61 (step @p199 :rule cong :premises (@p198 @p197) :args ((= @t82 @t98))) % 0.39/0.61 (step @p200 :rule symm :premises (@p199)) % 0.39/0.61 (step @p201 :rule eq_resolve :premises (@p198 @p200)) % 0.39/0.61 (step @p202 :rule cong :premises (@p201) :args (@t83)) % 0.39/0.61 (step @p203 :rule nary_cong :premises (@p202 @p176) :args (@t84)) % 0.39/0.61 (step @p204 :rule cong :premises (@p203) :args (@t85)) % 0.39/0.61 (step @p205 :rule cong :premises (@p204) :args (@t86)) % 0.39/0.61 (step @p206 :rule trans :premises (@p37 @p205)) % 0.39/0.61 (step @p207 :rule ho_cong :premises (@p206 @p157)) % 0.39/0.61 (step @p208 :rule ho_cong :premises (@p9 @p207)) % 0.39/0.61 (step @p209 :rule ho_cong :premises (@p208 @p139)) % 0.39/0.61 (step @p210 :rule trans :premises (@p209 @p196)) % 0.39/0.61 (step @p211 :rule cong :premises (@p210) :args (@t88)) % 0.39/0.61 (step @p212 :rule trans :premises (@p38 @p211)) % 0.39/0.61 (step @p213 :rule ho_cong :premises (@p212 @p165)) % 0.39/0.61 (step @p214 :rule ho_cong :premises (@p206 @p96)) % 0.39/0.61 (step @p215 :rule ho_cong :premises (@p212 @p214)) % 0.39/0.61 (step @p216 :rule ho_cong :premises (@p163 @p215)) % 0.39/0.61 (step @p217 :rule ho_cong :premises (@p216 @p213)) % 0.39/0.61 (step @p218 :rule refl :args (@t121)) % 0.39/0.61 (step @p219 :rule refl :args (@t10)) % 0.39/0.61 (step @p220 :rule cong :premises (@p219 @p218) :args ((= @t10 @t121))) % 0.39/0.61 (step @p221 :rule symm :premises (@p220)) % 0.39/0.61 (step @p222 :rule eq_resolve :premises (@p219 @p221)) % 0.39/0.61 (step @p223 :rule cong :premises (@p222) :args (@t76)) % 0.39/0.61 (step @p224 :rule cong :premises (@p223) :args (@t78)) % 0.39/0.61 (step @p225 :rule trans :premises (@p33 @p224)) % 0.39/0.61 (step @p226 :rule ho_cong :premises (@p225 @p217)) % 0.39/0.61 (step @p227 :rule cong :premises (@p226) :args (@t1)) % 0.39/0.61 (step @p228 :rule trans :premises (@p227 @p136)) % 0.39/0.61 (step @p229 :rule eq_resolve :premises (@p5 @p228)) % 0.39/0.61 (step @p230 :rule skolemize :premises (@p229)) % 0.39/0.61 (step @p231 :rule bool-double-not-elim :args (@t188)) % 0.39/0.61 (step @p232 :rule refl :args (@t195)) % 0.39/0.61 (step @p233 :rule nary_cong :premises (@p232 @p231) :args ((or @t195 (not @t194)))) % 0.39/0.61 (step @p234 :rule cnf_or_neg :args (@t195 0)) % 0.39/0.61 (step @p235 :rule eq_resolve :premises (@p234 @p233)) % 0.39/0.61 (step @p236 :rule reordering :premises (@p235) :args ((or @t188 @t195))) % 0.39/0.61 (step @p237 :rule chain_m_resolution :premises (@p236 @p230) :args (@t188 @t196 @t197)) % 0.39/0.61 (step @p238 :rule instantiate :premises (@p237) :args (@t198)) % 0.39/0.61 (step @p239 :rule bool-double-not-elim :args (@t192)) % 0.39/0.61 (step @p240 :rule nary_cong :premises (@p232 @p239) :args ((or @t195 (not @t193)))) % 0.39/0.61 (step @p241 :rule cnf_or_neg :args (@t195 1)) % 0.39/0.61 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.39/0.61 (step @p243 :rule reordering :premises (@p242) :args ((or @t192 @t195))) % 0.39/0.61 (step @p244 :rule chain_m_resolution :premises (@p243 @p230) :args (@t192 @t196 @t197)) % 0.39/0.61 (step @p245 :rule cnf_or_pos :args (@t202)) % 0.39/0.61 (step @p246 :rule reordering :premises (@p245) :args ((or @t193 @t201 (not @t202)))) % 0.39/0.61 (step @p247 :rule chain_m_resolution :premises (@p246 @p244 @p238) :args (@t201 @t203 (@list @t192 @t202))) % 0.39/0.61 (step @p248 :rule cnf_and_pos :args (@t201 1)) % 0.39/0.61 (step @p249 :rule reordering :premises (@p248) :args ((or @t200 (not @t201)))) % 0.39/0.61 (step @p250 :rule chain_m_resolution :premises (@p249 @p247) :args (@t200 (@list false) (@list @t201))) % 0.39/0.61 (step @p251 :rule bool-double-not-elim :args (@t190)) % 0.39/0.61 (step @p252 :rule nary_cong :premises (@p232 @p251) :args ((or @t195 (not @t191)))) % 0.39/0.61 (step @p253 :rule cnf_or_neg :args (@t195 2)) % 0.39/0.61 (step @p254 :rule eq_resolve :premises (@p253 @p252)) % 0.39/0.61 (step @p255 :rule reordering :premises (@p254) :args ((or @t190 @t195))) % 0.39/0.61 (step @p256 :rule chain_m_resolution :premises (@p255 @p230) :args (@t190 @t196 @t197)) % 0.39/0.61 (step @p257 :rule instantiate :premises (@p256) :args (@t198)) % 0.39/0.61 (step @p258 :rule beta-reduce :args ((= (_ (lambda @t47 (forall @t62 (or @t208 (not @t206) @t205))) tptp.rel_s5) (forall @t62 (or @t204 (not (tptp.rel_s5 @t49 @t58)) (tptp.rel_s5 @t44 @t58)))))) % 0.39/0.61 (step @p259 :rule refl :args (tptp.rel_s5)) % 0.39/0.61 (step @p260 :rule refl :args (@t205)) % 0.39/0.61 (step @p261 :rule refl :args (@t59)) % 0.39/0.61 (step @p262 :rule cong :premises (@p261 @p260) :args ((= @t59 @t205))) % 0.39/0.61 (step @p263 :rule symm :premises (@p262)) % 0.39/0.61 (step @p264 :rule eq_resolve :premises (@p261 @p263)) % 0.39/0.61 (step @p265 :rule refl :args (@t206)) % 0.39/0.61 (step @p266 :rule refl :args (@t60)) % 0.39/0.61 (step @p267 :rule cong :premises (@p266 @p265) :args ((= @t60 @t206))) % 0.39/0.61 (step @p268 :rule symm :premises (@p267)) % 0.39/0.61 (step @p269 :rule eq_resolve :premises (@p266 @p268)) % 0.39/0.61 (step @p270 :rule cong :premises (@p269) :args (@t209)) % 0.39/0.61 (step @p271 :rule refl :args (@t207)) % 0.39/0.61 (step @p272 :rule refl :args (@t52)) % 0.39/0.61 (step @p273 :rule cong :premises (@p272 @p271) :args ((= @t52 @t207))) % 0.39/0.61 (step @p274 :rule symm :premises (@p273)) % 0.39/0.61 (step @p275 :rule eq_resolve :premises (@p272 @p274)) % 0.39/0.61 (step @p276 :rule cong :premises (@p275) :args (@t210)) % 0.39/0.61 (step @p277 :rule nary_cong :premises (@p276 @p270 @p264) :args (@t211)) % 0.39/0.61 (step @p278 :rule cong :premises (@p277) :args ((forall @t62 @t211))) % 0.39/0.61 (step @p279 :rule aci_norm :args ((= (or (or @t210 @t209) @t59) @t211))) % 0.39/0.61 (step @p280 :rule bool-and-de-morgan :args (@t52 @t60 true)) % 0.39/0.61 (step @p281 :rule nary_cong :premises (@p280 @p261) :args ((or (not @t61) @t59))) % 0.39/0.61 (step @p282 :rule trans :premises (@p281 @p279)) % 0.39/0.61 (step @p283 :rule bool-impl-elim :args (@t61 @t59)) % 0.39/0.61 (step @p284 :rule trans :premises (@p283 @p282)) % 0.39/0.61 (step @p285 :rule cong :premises (@p284) :args (@t63)) % 0.39/0.61 (step @p286 :rule trans :premises (@p285 @p278)) % 0.39/0.61 (step @p287 :rule cong :premises (@p286) :args (@t64)) % 0.39/0.61 (step @p288 :rule trans :premises (@p26 @p287)) % 0.39/0.61 (step @p289 :rule ho_cong :premises (@p288 @p259)) % 0.39/0.61 (step @p290 :rule trans :premises (@p289 @p258)) % 0.39/0.61 (step @p291 :rule eq_resolve :premises (@p3 @p290)) % 0.39/0.61 (step @p292 :rule instantiate :premises (@p291) :args ((@list @t189 @t187 @t189))) % 0.39/0.61 (step @p293 :rule beta-reduce :args ((= (_ (lambda @t47 (forall @t53 (or @t208 @t212))) tptp.rel_s5) (forall @t53 (or @t204 (tptp.rel_s5 @t49 @t44)))))) % 0.39/0.61 (step @p294 :rule refl :args (@t212)) % 0.39/0.61 (step @p295 :rule refl :args (@t51)) % 0.39/0.61 (step @p296 :rule cong :premises (@p295 @p294) :args ((= @t51 @t212))) % 0.39/0.61 (step @p297 :rule symm :premises (@p296)) % 0.39/0.61 (step @p298 :rule eq_resolve :premises (@p295 @p297)) % 0.39/0.61 (step @p299 :rule nary_cong :premises (@p276 @p298) :args (@t213)) % 0.39/0.61 (step @p300 :rule cong :premises (@p299) :args ((forall @t53 @t213))) % 0.39/0.61 (step @p301 :rule bool-impl-elim :args (@t52 @t51)) % 0.39/0.61 (step @p302 :rule cong :premises (@p301) :args (@t54)) % 0.39/0.61 (step @p303 :rule trans :premises (@p302 @p300)) % 0.39/0.61 (step @p304 :rule cong :premises (@p303) :args (@t55)) % 0.39/0.61 (step @p305 :rule trans :premises (@p24 @p304)) % 0.39/0.61 (step @p306 :rule ho_cong :premises (@p305 @p259)) % 0.39/0.61 (step @p307 :rule trans :premises (@p306 @p293)) % 0.39/0.61 (step @p308 :rule eq_resolve :premises (@p4 @p307)) % 0.39/0.61 (step @p309 :rule instantiate :premises (@p308) :args ((@list @t187 @t189))) % 0.39/0.61 (step @p310 :rule cnf_or_pos :args (@t215)) % 0.39/0.61 (step @p311 :rule reordering :premises (@p310) :args ((or @t193 @t214 (not @t215)))) % 0.39/0.61 (step @p312 :rule chain_m_resolution :premises (@p311 @p244 @p309) :args (@t214 @t203 (@list @t192 @t215))) % 0.39/0.61 (step @p313 :rule cnf_or_pos :args (@t218)) % 0.39/0.61 (step @p314 :rule reordering :premises (@p313) :args ((or @t193 @t217 @t216 (not @t218)))) % 0.39/0.61 (step @p315 :rule chain_m_resolution :premises (@p314 @p244 @p312 @p292) :args (@t216 (@list false false false) (@list @t192 @t214 @t218))) % 0.39/0.61 (step @p316 :rule cnf_or_pos :args (@t220)) % 0.39/0.61 (step @p317 :rule reordering :premises (@p316) :args ((or @t199 @t219 (not @t220)))) % 0.39/0.61 (step @p318 false :rule chain_m_resolution :premises (@p317 @p315 @p257 @p250) :args (false (@list false false true) (@list @t216 @t220 @t199))) % 0.39/0.61 ) % 0.39/0.61 % SZS output end Proof % 0.39/0.61 % cvc5 exiting %------------------------------------------------------------------------------