%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO458^4 : 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 : n009.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 0.41s 0.62s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO458^4 : 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 : n009.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 00:11:14 EDT 2026 % 0.17/0.35 % CPUTime : % 0.34/0.52 %----Proving TH0 % 0.41/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.41/0.62 % SZS status Theorem % 0.41/0.62 % SZS output start Proof % 0.41/0.62 ( % 0.41/0.62 (declare-sort $$unsorted 0) % 0.41/0.62 (declare-sort tptp.mu 0) % 0.41/0.62 (declare-const tptp.rel_b (-> $$unsorted $$unsorted Bool)) % 0.41/0.62 (declare-const tptp.q (-> $$unsorted Bool)) % 0.41/0.62 (declare-const tptp.p (-> $$unsorted Bool)) % 0.41/0.62 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.41/0.62 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.41/0.62 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.41/0.62 (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)))))) % 0.41/0.62 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.41/0.62 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.41/0.62 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.41/0.62 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.41/0.62 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.41/0.62 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.41/0.62 (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))))))) % 0.41/0.62 (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))))))) % 0.41/0.62 (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)))))) % 0.41/0.62 (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)))))) % 0.41/0.62 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.41/0.62 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.41/0.62 (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)))))) % 0.41/0.62 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.41/0.62 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.41/0.62 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.41/0.62 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.41/0.62 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.41/0.62 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.41/0.62 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.41/0.62 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.41/0.62 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.41/0.62 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.41/0.62 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.41/0.62 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.41/0.62 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.41/0.62 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.41/0.62 (define tptp.mbox_b () (let ((_let_1 (@var "V" $$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_b _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.41/0.62 (define tptp.mdia_b () (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_b (_ tptp.mnot _let_2))) _let_1))))) % 0.41/0.62 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ (_ tptp.mand (_ tptp.mbox_b tptp.p)) (_ tptp.mbox_b tptp.q))) (_ tptp.mbox_b (_ (_ tptp.mequiv tptp.p) tptp.q)))))) % 0.41/0.62 (define @t2 () (@var "Y" tptp.mu)) % 0.41/0.62 (define @t3 () (@var "X" tptp.mu)) % 0.41/0.62 (define @t4 () (@var "W" $$unsorted)) % 0.41/0.62 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.41/0.62 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.41/0.62 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.41/0.62 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.41/0.62 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.41/0.62 (define @t10 () (_ @t9 @t4)) % 0.41/0.62 (define @t11 () (not @t10)) % 0.41/0.62 (define @t12 () (@list @t9 @t4)) % 0.41/0.62 (define @t13 () (lambda @t12 @t11)) % 0.41/0.62 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.41/0.62 (define @t15 () (_ @t14 @t4)) % 0.41/0.62 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.41/0.62 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.41/0.62 (define @t18 () (_ tptp.mnot @t14)) % 0.41/0.62 (define @t19 () (_ tptp.mnot @t9)) % 0.41/0.62 (define @t20 () (_ tptp.mor @t19)) % 0.41/0.62 (define @t21 () (@list @t9 @t14 @t17)) % 0.41/0.62 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.41/0.62 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.41/0.62 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.41/0.62 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.41/0.62 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.41/0.62 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.41/0.62 (define @t28 () (_ @t27 @t3)) % 0.41/0.62 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.41/0.62 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.41/0.62 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.41/0.62 (define @t32 () (_ @t31 @t30)) % 0.41/0.62 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.41/0.62 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.41/0.62 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.41/0.62 (define @t36 () (@list @t4)) % 0.41/0.62 (define @t37 () (lambda @t36 true)) % 0.41/0.62 (define @t38 () (@var "V" $$unsorted)) % 0.41/0.62 (define @t39 () (_ @t9 @t38)) % 0.41/0.62 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.41/0.62 (define @t41 () (@list @t38)) % 0.41/0.62 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.41/0.62 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.41/0.62 (define @t44 () (@var "S" $$unsorted)) % 0.41/0.62 (define @t45 () (_ @t40 @t44)) % 0.41/0.62 (define @t46 () (@list @t44)) % 0.41/0.62 (define @t47 () (@list @t40)) % 0.41/0.62 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.41/0.62 (define @t49 () (@var "T" $$unsorted)) % 0.41/0.62 (define @t50 () (_ @t40 @t49)) % 0.41/0.62 (define @t51 () (_ @t45 @t49)) % 0.41/0.62 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.41/0.62 (define @t53 () (@list @t49)) % 0.41/0.62 (define @t54 () (lambda @t47 (forall @t46 (exists @t53 @t51)))) % 0.41/0.62 (define @t55 () (@var "U" $$unsorted)) % 0.41/0.62 (define @t56 () (_ @t45 @t55)) % 0.41/0.62 (define @t57 () (_ @t50 @t55)) % 0.41/0.62 (define @t58 () (@list @t44 @t49 @t55)) % 0.41/0.62 (define @t59 () (lambda @t47 (forall @t58 (=> (and @t51 @t57) @t56)))) % 0.41/0.62 (define @t60 () (and @t51 @t56)) % 0.41/0.62 (define @t61 () (lambda @t47 (forall @t58 (=> @t60 @t57)))) % 0.41/0.62 (define @t62 () (= @t49 @t55)) % 0.41/0.62 (define @t63 () (lambda @t47 (forall @t58 (=> @t60 @t62)))) % 0.41/0.62 (define @t64 () (@list @t55)) % 0.41/0.62 (define @t65 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t64 (=> @t56 @t62))))))) % 0.41/0.62 (define @t66 () (_ @t40 @t55)) % 0.41/0.62 (define @t67 () (_ @t66 @t49)) % 0.41/0.62 (define @t68 () (lambda @t47 (forall @t58 (=> @t51 (exists @t64 (and @t56 @t67)))))) % 0.41/0.62 (define @t69 () (lambda @t47 (forall @t58 (=> @t60 (or @t57 @t62 @t67))))) % 0.41/0.62 (define @t70 () (lambda @t47 (forall @t58 (=> @t60 (exists @t41 (and (_ @t50 @t38) (_ @t66 @t38))))))) % 0.41/0.62 (define @t71 () (forall @t36 @t10)) % 0.41/0.62 (define @t72 () (@list @t9)) % 0.41/0.62 (define @t73 () (lambda @t72 @t71)) % 0.41/0.62 (define @t74 () (lambda @t72 (forall @t36 @t11))) % 0.41/0.62 (define @t75 () (lambda @t72 (exists @t36 @t10))) % 0.41/0.62 (define @t76 () (lambda @t72 (exists @t36 @t11))) % 0.41/0.62 (define @t77 () (_ (_ tptp.rel_b @t4) @t38)) % 0.41/0.62 (define @t78 () (not @t77)) % 0.41/0.62 (define @t79 () (or @t78 @t39)) % 0.41/0.62 (define @t80 () (forall @t41 @t79)) % 0.41/0.62 (define @t81 () (lambda @t12 @t80)) % 0.41/0.62 (define @t82 () (lambda (@list @t9 @t17) (_ (_ tptp.mnot (_ tptp.mbox_b @t19)) @t17))) % 0.41/0.62 (define @t83 () (@var "BOUND_VARIABLE_8525" $$unsorted)) % 0.41/0.62 (define @t84 () (tptp.p @t83)) % 0.41/0.62 (define @t85 () (tptp.q @t83)) % 0.41/0.62 (define @t86 () (and (or (not @t84) @t85) (or (not @t85) @t84))) % 0.41/0.62 (define @t87 () (not (tptp.rel_b @t4 @t83))) % 0.41/0.62 (define @t88 () (tptp.q @t38)) % 0.41/0.62 (define @t89 () (tptp.rel_b @t4 @t38)) % 0.41/0.62 (define @t90 () (not @t89)) % 0.41/0.62 (define @t91 () (forall @t41 (or @t90 @t88))) % 0.41/0.62 (define @t92 () (not @t91)) % 0.41/0.62 (define @t93 () (tptp.p @t38)) % 0.41/0.62 (define @t94 () (forall @t41 (or @t90 @t93))) % 0.41/0.62 (define @t95 () (not @t94)) % 0.41/0.62 (define @t96 () (or @t95 @t92 @t87 @t86)) % 0.41/0.62 (define @t97 () (or @t87 @t86)) % 0.41/0.62 (define @t98 () (or @t97 @t95 @t92)) % 0.41/0.62 (define @t99 () (@list @t4 @t83)) % 0.41/0.62 (define @t100 () (forall @t99 @t98)) % 0.41/0.62 (define @t101 () (@list @t83)) % 0.41/0.62 (define @t102 () (forall @t101 @t98)) % 0.41/0.62 (define @t103 () (forall @t101 @t97)) % 0.41/0.62 (define @t104 () (or @t103 @t95 @t92)) % 0.41/0.62 (define @t105 () (and (or (not @t93) @t88) (or (not @t88) @t93))) % 0.41/0.62 (define @t106 () (forall @t41 (or @t90 @t105))) % 0.41/0.62 (define @t107 () (or @t106 @t95 @t92)) % 0.41/0.62 (define @t108 () (not (tptp.rel_b @t17 @t38))) % 0.41/0.62 (define @t109 () (forall @t41 (or @t108 @t88))) % 0.41/0.62 (define @t110 () (not @t109)) % 0.41/0.62 (define @t111 () (forall @t41 (or @t108 @t93))) % 0.41/0.62 (define @t112 () (not @t111)) % 0.41/0.62 (define @t113 () (forall @t41 (or @t108 @t105))) % 0.41/0.62 (define @t114 () (@list @t17)) % 0.41/0.62 (define @t115 () (lambda @t114 (or @t113 @t112 @t110))) % 0.41/0.62 (define @t116 () (_ @t115 @t4)) % 0.41/0.62 (define @t117 () (forall @t36 @t116)) % 0.41/0.62 (define @t118 () (_ @t9 @t4)) % 0.41/0.62 (define @t119 () (lambda @t72 (forall @t36 @t118))) % 0.41/0.62 (define @t120 () (lambda @t36 @t106)) % 0.41/0.62 (define @t121 () (_ @t120 @t17)) % 0.41/0.62 (define @t122 () (or @t121 @t112 @t110)) % 0.41/0.62 (define @t123 () (lambda @t114 @t122)) % 0.41/0.62 (define @t124 () (_ @t14 @t17)) % 0.41/0.62 (define @t125 () (or @t124 @t112 @t110)) % 0.41/0.62 (define @t126 () (@list @t14 @t17)) % 0.41/0.62 (define @t127 () (_ tptp.p @t38)) % 0.41/0.62 (define @t128 () (_ tptp.q @t38)) % 0.41/0.62 (define @t129 () (not @t128)) % 0.41/0.62 (define @t130 () (or @t129 @t127)) % 0.41/0.62 (define @t131 () (not @t127)) % 0.41/0.62 (define @t132 () (or @t131 @t128)) % 0.41/0.62 (define @t133 () (and @t132 @t130)) % 0.41/0.62 (define @t134 () (or @t90 @t133)) % 0.41/0.62 (define @t135 () (not @t130)) % 0.41/0.62 (define @t136 () (not @t132)) % 0.41/0.62 (define @t137 () (not (or @t136 @t135))) % 0.41/0.62 (define @t138 () (or @t90 @t137)) % 0.41/0.62 (define @t139 () (_ tptp.p @t17)) % 0.41/0.62 (define @t140 () (_ tptp.q @t17)) % 0.41/0.62 (define @t141 () (not @t139)) % 0.41/0.62 (define @t142 () (lambda @t114 (not (or (not (or @t141 @t140)) (not (or (not @t140) @t139)))))) % 0.41/0.62 (define @t143 () (_ @t142 @t38)) % 0.41/0.62 (define @t144 () (or @t90 @t143)) % 0.41/0.62 (define @t145 () (forall @t41 @t144)) % 0.41/0.62 (define @t146 () (lambda @t36 @t145)) % 0.41/0.62 (define @t147 () (_ @t9 @t38)) % 0.41/0.62 (define @t148 () (lambda @t12 (forall @t41 (or @t90 @t147)))) % 0.41/0.62 (define @t149 () (not @t124)) % 0.41/0.62 (define @t150 () (lambda @t126 (not (or (not (or @t141 @t124)) (not (or @t149 @t139)))))) % 0.41/0.62 (define @t151 () (_ @t9 @t17)) % 0.41/0.62 (define @t152 () (or @t149 @t151)) % 0.41/0.62 (define @t153 () (not @t151)) % 0.41/0.62 (define @t154 () (or @t153 @t124)) % 0.41/0.62 (define @t155 () (not @t154)) % 0.41/0.62 (define @t156 () (not (or @t155 (not @t152)))) % 0.41/0.62 (define @t157 () (_ (lambda @t21 @t156) tptp.p)) % 0.41/0.62 (define @t158 () (or @t112 @t110)) % 0.41/0.62 (define @t159 () (not @t158)) % 0.41/0.62 (define @t160 () (lambda @t114 @t159)) % 0.41/0.62 (define @t161 () (_ @t160 @t17)) % 0.41/0.62 (define @t162 () (not @t161)) % 0.41/0.62 (define @t163 () (or @t162 @t124)) % 0.41/0.62 (define @t164 () (lambda @t126 @t163)) % 0.41/0.62 (define @t165 () (lambda @t21 @t154)) % 0.41/0.62 (define @t166 () (lambda @t36 @t91)) % 0.41/0.62 (define @t167 () (_ @t166 @t17)) % 0.41/0.62 (define @t168 () (not @t167)) % 0.41/0.62 (define @t169 () (or @t112 @t168)) % 0.41/0.62 (define @t170 () (not @t169)) % 0.41/0.62 (define @t171 () (lambda @t114 @t170)) % 0.41/0.62 (define @t172 () (_ @t148 tptp.q)) % 0.41/0.62 (define @t173 () (lambda @t36 @t94)) % 0.41/0.62 (define @t174 () (_ @t173 @t17)) % 0.41/0.62 (define @t175 () (not @t174)) % 0.41/0.62 (define @t176 () (or @t175 @t149)) % 0.41/0.62 (define @t177 () (not @t176)) % 0.41/0.62 (define @t178 () (lambda @t126 @t177)) % 0.41/0.62 (define @t179 () (not (or @t153 @t149))) % 0.41/0.62 (define @t180 () (lambda @t21 @t179)) % 0.41/0.62 (define @t181 () (_ @t148 tptp.p)) % 0.41/0.62 (define @t182 () (lambda @t114 @t152)) % 0.41/0.62 (define @t183 () (_ @t182 @t17)) % 0.41/0.62 (define @t184 () (not @t183)) % 0.41/0.62 (define @t185 () (or @t155 @t184)) % 0.41/0.62 (define @t186 () (not @t185)) % 0.41/0.62 (define @t187 () (lambda @t114 @t186)) % 0.41/0.62 (define @t188 () (@var "BOUND_VARIABLE_7581" (-> $$unsorted Bool))) % 0.41/0.62 (define @t189 () (not (_ @t188 @t17))) % 0.41/0.62 (define @t190 () (@list @t188 @t17)) % 0.41/0.62 (define @t191 () (@var "BOUND_VARIABLE_7601" (-> $$unsorted Bool))) % 0.41/0.62 (define @t192 () (_ @t191 @t17)) % 0.41/0.62 (define @t193 () (lambda (@list @t191 @t17) (or @t149 @t192))) % 0.41/0.62 (define @t194 () (@list @t14)) % 0.41/0.62 (define @t195 () (lambda @t114 @t154)) % 0.41/0.62 (define @t196 () (_ @t195 @t17)) % 0.41/0.62 (define @t197 () (not @t196)) % 0.41/0.62 (define @t198 () (or @t197 @t189)) % 0.41/0.62 (define @t199 () (not @t198)) % 0.41/0.62 (define @t200 () (lambda @t190 @t199)) % 0.41/0.62 (define @t201 () (lambda @t126 @t154)) % 0.41/0.62 (define @t202 () (or @t11 @t15)) % 0.41/0.62 (define @t203 () (lambda @t36 @t202)) % 0.41/0.62 (define @t204 () (@list @t14 @t4)) % 0.41/0.62 (define @t205 () (lambda @t204 @t202)) % 0.41/0.62 (define @t206 () (lambda @t36 @t11)) % 0.41/0.62 (define @t207 () (_ @t206 @t4)) % 0.41/0.62 (define @t208 () (or @t207 @t15)) % 0.41/0.62 (define @t209 () (lambda @t204 @t208)) % 0.41/0.62 (define @t210 () (not @t15)) % 0.41/0.62 (define @t211 () (or @t11 @t210)) % 0.41/0.62 (define @t212 () (lambda @t36 @t211)) % 0.41/0.62 (define @t213 () (_ @t212 @t4)) % 0.41/0.62 (define @t214 () (not @t213)) % 0.41/0.62 (define @t215 () (lambda @t36 @t214)) % 0.41/0.62 (define @t216 () (lambda @t36 @t210)) % 0.41/0.62 (define @t217 () (_ @t216 @t4)) % 0.41/0.62 (define @t218 () (or @t11 @t217)) % 0.41/0.62 (define @t219 () (lambda @t36 @t218)) % 0.41/0.62 (define @t220 () (forall @t99 @t96)) % 0.41/0.62 (define @t221 () (@quantifiers_skolemize @t220 0)) % 0.41/0.62 (define @t222 () (not (tptp.rel_b @t221 @t38))) % 0.41/0.62 (define @t223 () (forall @t41 (or @t222 @t93))) % 0.41/0.62 (define @t224 () (@quantifiers_skolemize @t220 1)) % 0.41/0.62 (define @t225 () (tptp.p @t224)) % 0.41/0.62 (define @t226 () (tptp.q @t224)) % 0.41/0.62 (define @t227 () (or (not @t226) @t225)) % 0.41/0.62 (define @t228 () (not @t225)) % 0.41/0.62 (define @t229 () (or @t228 @t226)) % 0.41/0.62 (define @t230 () (and @t229 @t227)) % 0.41/0.62 (define @t231 () (tptp.rel_b @t221 @t224)) % 0.41/0.62 (define @t232 () (not @t231)) % 0.41/0.62 (define @t233 () (forall @t41 (or @t222 @t88))) % 0.41/0.62 (define @t234 () (not @t233)) % 0.41/0.62 (define @t235 () (not @t223)) % 0.41/0.62 (define @t236 () (or @t235 @t234 @t232 @t230)) % 0.41/0.62 (define @t237 () (@list true)) % 0.41/0.62 (define @t238 () (@list @t236)) % 0.41/0.62 (define @t239 () (@list @t224)) % 0.41/0.62 (define @t240 () (or @t232 @t226)) % 0.41/0.62 (define @t241 () (@list true false)) % 0.41/0.62 (define @t242 () (or @t232 @t225)) % 0.41/0.62 (define @t243 () (not @t242)) % 0.41/0.62 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.41/0.62 (assume @p2 (_ tptp.mreflexive tptp.rel_b)) % 0.41/0.62 (assume @p3 (_ tptp.msymmetric tptp.rel_b)) % 0.41/0.62 (assume @p4 @t1) % 0.41/0.62 (assume @p5 true) % 0.41/0.62 (step @p6 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.41/0.62 (step @p7 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.41/0.62 (step @p8 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.41/0.62 (step @p9 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.41/0.62 (step @p10 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.41/0.62 (step @p11 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.41/0.62 (step @p12 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.41/0.62 (step @p13 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.41/0.62 (step @p14 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.41/0.62 (step @p15 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.41/0.62 (step @p16 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.41/0.62 (step @p17 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.41/0.62 (step @p18 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.41/0.62 (step @p19 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.41/0.62 (step @p20 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.41/0.62 (step @p21 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.41/0.62 (step @p22 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.41/0.62 (step @p23 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.41/0.62 (step @p24 (= tptp.mserial @t54) :rule refl :args (@t54)) % 0.41/0.62 (step @p25 (= tptp.mtransitive @t59) :rule refl :args (@t59)) % 0.41/0.62 (step @p26 (= tptp.meuclidean @t61) :rule refl :args (@t61)) % 0.41/0.62 (step @p27 (= tptp.mpartially_functional @t63) :rule refl :args (@t63)) % 0.41/0.62 (step @p28 (= tptp.mfunctional @t65) :rule refl :args (@t65)) % 0.41/0.62 (step @p29 (= tptp.mweakly_dense @t68) :rule refl :args (@t68)) % 0.41/0.62 (step @p30 (= tptp.mweakly_connected @t69) :rule refl :args (@t69)) % 0.41/0.62 (step @p31 (= tptp.mweakly_directed @t70) :rule refl :args (@t70)) % 0.41/0.62 (step @p32 (= tptp.mvalid @t73) :rule refl :args (@t73)) % 0.41/0.62 (step @p33 (= tptp.minvalid @t74) :rule refl :args (@t74)) % 0.41/0.62 (step @p34 (= tptp.msatisfiable @t75) :rule refl :args (@t75)) % 0.41/0.62 (step @p35 (= tptp.mcountersatisfiable @t76) :rule refl :args (@t76)) % 0.41/0.62 (step @p36 (= tptp.mbox_b @t81) :rule refl :args (@t81)) % 0.41/0.62 (step @p37 (= tptp.mdia_b @t82) :rule refl :args (@t82)) % 0.41/0.62 (step @p38 :rule aci_norm :args ((= @t98 @t96))) % 0.41/0.62 (step @p39 :rule cong :premises (@p38) :args (@t100)) % 0.41/0.62 (step @p40 :rule quant-merge-prenex :args ((= (forall @t36 @t102) @t100))) % 0.41/0.62 (step @p41 :rule refl :args (@t92)) % 0.41/0.62 (step @p42 :rule refl :args (@t95)) % 0.41/0.62 (step @p43 :rule alpha_equiv :args (@t103 (@list @t83) (@list @t38))) % 0.41/0.62 (step @p44 :rule nary_cong :premises (@p43 @p42 @p41) :args (@t104)) % 0.41/0.62 (step @p45 :rule quant-miniscope-or :args ((= @t102 @t104))) % 0.41/0.62 (step @p46 :rule trans :premises (@p45 @p44)) % 0.41/0.62 (step @p47 :rule symm :premises (@p46)) % 0.41/0.62 (step @p48 :rule cong :premises (@p47) :args ((forall @t36 @t107))) % 0.41/0.62 (step @p49 :rule trans :premises (@p48 @p40)) % 0.41/0.62 (step @p50 :rule trans :premises (@p49 @p39)) % 0.41/0.62 (step @p51 :rule beta-reduce :args ((= @t116 @t107))) % 0.41/0.62 (step @p52 :rule cong :premises (@p51) :args (@t117)) % 0.41/0.62 (step @p53 :rule trans :premises (@p52 @p50)) % 0.41/0.62 (step @p54 :rule beta-reduce :args ((= (_ @t119 @t115) @t117))) % 0.41/0.62 (step @p55 :rule trans :premises (@p54 @p53)) % 0.41/0.62 (step @p56 :rule refl :args (@t110)) % 0.41/0.62 (step @p57 :rule refl :args (@t112)) % 0.41/0.62 (step @p58 :rule beta-reduce :args ((= @t121 @t113))) % 0.41/0.62 (step @p59 :rule nary_cong :premises (@p58 @p57 @p56) :args (@t122)) % 0.41/0.62 (step @p60 :rule cong :premises (@p59) :args (@t123)) % 0.41/0.62 (step @p61 :rule beta-reduce :args ((= (_ (lambda @t126 @t125) @t120) @t123))) % 0.41/0.62 (step @p62 :rule trans :premises (@p61 @p60)) % 0.41/0.62 (step @p63 :rule refl :args (@t93)) % 0.41/0.62 (step @p64 :rule refl :args (@t127)) % 0.41/0.62 (step @p65 :rule cong :premises (@p64 @p63) :args ((= @t127 @t93))) % 0.41/0.62 (step @p66 :rule symm :premises (@p65)) % 0.41/0.62 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.41/0.62 (step @p68 :rule refl :args (@t88)) % 0.41/0.62 (step @p69 :rule refl :args (@t128)) % 0.41/0.62 (step @p70 :rule cong :premises (@p69 @p68) :args ((= @t128 @t88))) % 0.41/0.62 (step @p71 :rule symm :premises (@p70)) % 0.41/0.62 (step @p72 :rule eq_resolve :premises (@p69 @p71)) % 0.41/0.62 (step @p73 :rule cong :premises (@p72) :args (@t129)) % 0.41/0.62 (step @p74 :rule nary_cong :premises (@p73 @p67) :args (@t130)) % 0.41/0.62 (step @p75 :rule cong :premises (@p67) :args (@t131)) % 0.41/0.62 (step @p76 :rule nary_cong :premises (@p75 @p72) :args (@t132)) % 0.41/0.62 (step @p77 :rule nary_cong :premises (@p76 @p74) :args (@t133)) % 0.41/0.62 (step @p78 :rule refl :args (@t90)) % 0.41/0.62 (step @p79 :rule nary_cong :premises (@p78 @p77) :args (@t134)) % 0.41/0.62 (step @p80 :rule cong :premises (@p79) :args ((forall @t41 @t134))) % 0.41/0.62 (step @p81 :rule bool-double-not-elim :args (@t130)) % 0.41/0.62 (step @p82 :rule bool-double-not-elim :args (@t132)) % 0.41/0.62 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((and (not @t136) (not @t135)))) % 0.41/0.62 (step @p84 :rule bool-or-de-morgan :args (@t136 @t135 false)) % 0.41/0.62 (step @p85 :rule trans :premises (@p84 @p83)) % 0.41/0.62 (step @p86 :rule nary_cong :premises (@p78 @p85) :args (@t138)) % 0.41/0.62 (step @p87 :rule cong :premises (@p86) :args ((forall @t41 @t138))) % 0.41/0.62 (step @p88 :rule trans :premises (@p87 @p80)) % 0.41/0.62 (step @p89 :rule beta-reduce :args ((= @t143 @t137))) % 0.41/0.62 (step @p90 :rule refl :args (@t90)) % 0.41/0.62 (step @p91 :rule nary_cong :premises (@p90 @p89) :args (@t144)) % 0.41/0.62 (step @p92 :rule cong :premises (@p91) :args (@t145)) % 0.41/0.62 (step @p93 :rule trans :premises (@p92 @p88)) % 0.41/0.62 (step @p94 :rule cong :premises (@p93) :args (@t146)) % 0.41/0.62 (step @p95 :rule beta-reduce :args ((= (_ @t148 @t142) @t146))) % 0.41/0.62 (step @p96 :rule trans :premises (@p95 @p94)) % 0.41/0.62 (step @p97 :rule beta-reduce :args ((= (_ @t150 tptp.q) @t142))) % 0.41/0.62 (step @p98 :rule refl :args (tptp.q)) % 0.41/0.62 (step @p99 :rule beta-reduce :args ((= @t157 @t150))) % 0.41/0.62 (step @p100 :rule ho_cong :premises (@p99 @p98)) % 0.41/0.62 (step @p101 :rule trans :premises (@p100 @p97)) % 0.41/0.62 (step @p102 :rule refl :args (@t148)) % 0.41/0.62 (step @p103 :rule ho_cong :premises (@p102 @p101)) % 0.41/0.62 (step @p104 :rule trans :premises (@p103 @p96)) % 0.41/0.62 (step @p105 :rule aci_norm :args ((= (or @t158 @t124) @t125))) % 0.41/0.62 (step @p106 :rule refl :args (@t124)) % 0.41/0.62 (step @p107 :rule bool-double-not-elim :args (@t158)) % 0.41/0.62 (step @p108 :rule beta-reduce :args ((= @t161 @t159))) % 0.41/0.62 (step @p109 :rule cong :premises (@p108) :args (@t162)) % 0.41/0.62 (step @p110 :rule trans :premises (@p109 @p107)) % 0.41/0.62 (step @p111 :rule nary_cong :premises (@p110 @p106) :args (@t163)) % 0.41/0.62 (step @p112 :rule trans :premises (@p111 @p105)) % 0.41/0.62 (step @p113 :rule cong :premises (@p112) :args (@t164)) % 0.41/0.62 (step @p114 :rule beta-reduce :args ((= (_ @t165 @t160) @t164))) % 0.41/0.62 (step @p115 :rule trans :premises (@p114 @p113)) % 0.41/0.62 (step @p116 :rule beta-reduce :args ((= @t167 @t109))) % 0.41/0.62 (step @p117 :rule cong :premises (@p116) :args (@t168)) % 0.41/0.62 (step @p118 :rule nary_cong :premises (@p57 @p117) :args (@t169)) % 0.41/0.62 (step @p119 :rule cong :premises (@p118) :args (@t170)) % 0.41/0.62 (step @p120 :rule cong :premises (@p119) :args (@t171)) % 0.41/0.62 (step @p121 :rule beta-reduce 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:rule cong :premises (@p150) :args (@t184)) % 0.41/0.62 (step @p152 :rule refl :args (@t155)) % 0.41/0.62 (step @p153 :rule nary_cong :premises (@p152 @p151) :args (@t185)) % 0.41/0.62 (step @p154 :rule cong :premises (@p153) :args (@t186)) % 0.41/0.62 (step @p155 :rule cong :premises (@p154) :args (@t187)) % 0.41/0.62 (step @p156 :rule beta-reduce :args ((= (_ (lambda @t190 (not (or @t155 @t189))) @t182) @t187))) % 0.41/0.62 (step @p157 :rule trans :premises (@p156 @p155)) % 0.41/0.62 (step @p158 :rule beta-reduce :args ((= (_ @t193 @t9) @t182))) % 0.41/0.62 (step @p159 :rule refl :args (@t9)) % 0.41/0.62 (step @p160 :rule beta-reduce :args ((= (_ (lambda (@list @t9 @t191 @t17) (or @t153 @t192)) @t14) @t193))) % 0.41/0.62 (step @p161 :rule refl :args (@t14)) % 0.41/0.62 (step @p162 :rule alpha_equiv :args (@t165 @t194 (@list @t191))) % 0.41/0.62 (step @p163 :rule ho_cong :premises (@p162 @p161)) % 0.41/0.62 (step @p164 :rule trans :premises (@p163 @p160)) % 0.41/0.62 (step @p165 :rule 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(step @p211 :rule cong :premises (@p210) :args (@t23)) % 0.41/0.62 (step @p212 :rule trans :premises (@p11 @p211)) % 0.41/0.62 (step @p213 :rule ho_cong :premises (@p212 @p180)) % 0.41/0.62 (step @p214 :rule ho_cong :premises (@p213 @p159)) % 0.41/0.62 (step @p215 :rule ho_cong :premises (@p212 @p159)) % 0.41/0.62 (step @p216 :rule ho_cong :premises (@p215 @p180)) % 0.41/0.62 (step @p217 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t211)) @t17) @t179))) % 0.41/0.62 (step @p218 :rule beta-reduce :args ((= @t213 @t211))) % 0.41/0.62 (step @p219 :rule cong :premises (@p218) :args (@t214)) % 0.41/0.62 (step @p220 :rule cong :premises (@p219) :args (@t215)) % 0.41/0.62 (step @p221 :rule beta-reduce :args ((= (_ @t13 @t212) @t215))) % 0.41/0.62 (step @p222 :rule trans :premises (@p221 @p220)) % 0.41/0.62 (step @p223 :rule beta-reduce :args ((= @t217 @t210))) % 0.41/0.62 (step @p224 :rule refl :args (@t11)) % 0.41/0.62 (step @p225 :rule nary_cong :premises (@p224 @p223) :args (@t218)) % 0.41/0.62 (step @p226 :rule cong :premises (@p225) :args (@t219)) % 0.41/0.62 (step @p227 :rule beta-reduce :args ((= (_ @t205 @t216) @t219))) % 0.41/0.62 (step @p228 :rule trans :premises (@p227 @p226)) % 0.41/0.62 (step @p229 :rule beta-reduce :args ((= (_ @t13 @t14) @t216))) % 0.41/0.62 (step @p230 :rule ho_cong :premises (@p201 @p229)) % 0.41/0.62 (step @p231 :rule trans :premises (@p230 @p228)) % 0.41/0.62 (step @p232 :rule refl :args (@t13)) % 0.41/0.62 (step @p233 :rule ho_cong :premises (@p232 @p231)) % 0.41/0.62 (step @p234 :rule trans :premises (@p233 @p222)) % 0.41/0.62 (step @p235 :rule ho_cong :premises (@p234 @p149)) % 0.41/0.62 (step @p236 :rule trans :premises (@p235 @p217)) % 0.41/0.62 (step @p237 :rule ho_cong :premises (@p8 @p180)) % 0.41/0.62 (step @p238 :rule ho_cong :premises (@p207 @p237)) % 0.41/0.62 (step @p239 :rule ho_cong :premises (@p8 @p238)) % 0.41/0.62 (step @p240 :rule ho_cong :premises (@p239 @p149)) % 0.41/0.62 (step @p241 :rule trans :premises (@p240 @p236)) % 0.41/0.62 (step @p242 :rule cong :premises (@p241) :args (@t22)) % 0.41/0.62 (step @p243 :rule trans :premises (@p10 @p242)) % 0.41/0.62 (step @p244 :rule ho_cong :premises (@p243 @p216)) % 0.41/0.62 (step @p245 :rule ho_cong :premises (@p244 @p214)) % 0.41/0.62 (step @p246 :rule ho_cong :premises (@p245 @p149)) % 0.41/0.62 (step @p247 :rule trans :premises (@p246 @p189)) % 0.41/0.62 (step @p248 :rule cong :premises (@p247) :args (@t25)) % 0.41/0.62 (step @p249 :rule trans :premises (@p13 @p248)) % 0.41/0.62 (step @p250 :rule ho_cong :premises (@p249 @p147)) % 0.41/0.62 (step @p251 :rule ho_cong :premises (@p250 @p98)) % 0.41/0.62 (step @p252 :rule refl :args (@t147)) % 0.41/0.62 (step @p253 :rule refl :args (@t39)) % 0.41/0.62 (step @p254 :rule cong :premises (@p253 @p252) :args ((= @t39 @t147))) % 0.41/0.62 (step @p255 :rule symm :premises (@p254)) % 0.41/0.62 (step @p256 :rule eq_resolve :premises (@p253 @p255)) % 0.41/0.62 (step @p257 :rule refl :args (@t89)) % 0.41/0.62 (step @p258 :rule refl :args (@t77)) % 0.41/0.62 (step @p259 :rule cong :premises (@p258 @p257) :args ((= @t77 @t89))) % 0.41/0.62 (step @p260 :rule symm :premises (@p259)) % 0.41/0.62 (step @p261 :rule eq_resolve :premises (@p258 @p260)) % 0.41/0.62 (step @p262 :rule cong :premises (@p261) :args (@t78)) % 0.41/0.62 (step @p263 :rule nary_cong :premises (@p262 @p256) :args (@t79)) % 0.41/0.62 (step @p264 :rule cong :premises (@p263) :args (@t80)) % 0.41/0.62 (step @p265 :rule cong :premises (@p264) :args (@t81)) % 0.41/0.62 (step @p266 :rule trans :premises (@p36 @p265)) % 0.41/0.62 (step @p267 :rule ho_cong :premises (@p266 @p251)) % 0.41/0.62 (step @p268 :rule ho_cong :premises (@p266 @p98)) % 0.41/0.62 (step @p269 :rule ho_cong :premises (@p266 @p147)) % 0.41/0.62 (step @p270 :rule ho_cong :premises (@p243 @p269)) % 0.41/0.62 (step @p271 :rule ho_cong :premises (@p270 @p268)) % 0.41/0.62 (step @p272 :rule ho_cong :premises (@p212 @p271)) % 0.41/0.62 (step @p273 :rule ho_cong :premises (@p272 @p267)) % 0.41/0.62 (step @p274 :rule refl :args (@t118)) % 0.41/0.62 (step @p275 :rule refl :args (@t10)) % 0.41/0.62 (step @p276 :rule cong :premises (@p275 @p274) :args ((= @t10 @t118))) % 0.41/0.62 (step @p277 :rule symm :premises (@p276)) % 0.41/0.62 (step @p278 :rule eq_resolve :premises (@p275 @p277)) % 0.41/0.62 (step @p279 :rule cong :premises (@p278) :args (@t71)) % 0.41/0.62 (step @p280 :rule cong :premises (@p279) :args (@t73)) % 0.41/0.62 (step @p281 :rule trans :premises (@p32 @p280)) % 0.41/0.62 (step @p282 :rule ho_cong :premises (@p281 @p273)) % 0.41/0.62 (step @p283 :rule cong :premises (@p282) :args (@t1)) % 0.41/0.62 (step @p284 :rule trans :premises (@p283 @p146)) % 0.41/0.62 (step @p285 :rule eq_resolve :premises (@p4 @p284)) % 0.41/0.62 (step @p286 :rule skolemize :premises (@p285)) % 0.41/0.62 (step @p287 :rule bool-double-not-elim :args (@t223)) % 0.41/0.62 (step @p288 :rule refl :args (@t236)) % 0.41/0.62 (step @p289 :rule nary_cong :premises (@p288 @p287) :args ((or @t236 (not @t235)))) % 0.41/0.62 (step @p290 :rule cnf_or_neg :args (@t236 0)) % 0.41/0.62 (step @p291 :rule eq_resolve :premises (@p290 @p289)) % 0.41/0.62 (step @p292 :rule reordering :premises (@p291) :args ((or @t223 @t236))) % 0.41/0.62 (step @p293 :rule chain_m_resolution :premises (@p292 @p286) :args (@t223 @t237 @t238)) % 0.41/0.62 (step @p294 :rule bool-double-not-elim :args (@t233)) % 0.41/0.62 (step @p295 :rule nary_cong :premises (@p288 @p294) :args ((or @t236 (not @t234)))) % 0.41/0.62 (step @p296 :rule cnf_or_neg :args (@t236 1)) % 0.41/0.62 (step @p297 :rule eq_resolve :premises (@p296 @p295)) % 0.41/0.62 (step @p298 :rule reordering :premises (@p297) :args ((or @t233 @t236))) % 0.41/0.62 (step @p299 :rule chain_m_resolution :premises (@p298 @p286) :args (@t233 @t237 @t238)) % 0.41/0.62 (step @p300 :rule instantiate :premises (@p299) :args (@t239)) % 0.41/0.62 (step @p301 :rule bool-double-not-elim :args (@t231)) % 0.41/0.62 (step @p302 :rule nary_cong :premises (@p288 @p301) :args ((or @t236 (not @t232)))) % 0.41/0.62 (step @p303 :rule cnf_or_neg :args (@t236 2)) % 0.41/0.62 (step @p304 :rule eq_resolve :premises (@p303 @p302)) % 0.41/0.62 (step @p305 :rule reordering :premises (@p304) :args ((or @t231 @t236))) % 0.41/0.62 (step @p306 :rule chain_m_resolution :premises (@p305 @p286) :args (@t231 @t237 @t238)) % 0.41/0.62 (step @p307 :rule cnf_or_pos :args (@t240)) % 0.41/0.62 (step @p308 :rule reordering :premises (@p307) :args ((or @t232 @t226 (not @t240)))) % 0.41/0.62 (step @p309 :rule chain_m_resolution :premises (@p308 @p306 @p300) :args (@t226 (@list false false) (@list @t231 @t240))) % 0.41/0.62 (step @p310 :rule cnf_or_neg :args (@t229 1)) % 0.41/0.62 (step @p311 :rule chain_m_resolution :premises (@p310 @p309) :args (@t229 (@list false) (@list @t226))) % 0.41/0.62 (step @p312 :rule cnf_or_neg :args (@t236 3)) % 0.41/0.62 (step @p313 :rule chain_m_resolution :premises (@p312 @p286) :args ((not @t230) @t237 @t238)) % 0.41/0.62 (step @p314 :rule cnf_and_neg :args (@t230)) % 0.41/0.62 (step @p315 :rule chain_m_resolution :premises (@p314 @p313 @p311) :args ((not @t227) @t241 (@list @t230 @t229))) % 0.41/0.62 (step @p316 :rule cnf_or_neg :args (@t227 1)) % 0.41/0.62 (step @p317 :rule reordering :premises (@p316) :args ((or @t228 @t227))) % 0.41/0.62 (step @p318 :rule chain_m_resolution :premises (@p317 @p315) :args (@t228 @t237 (@list @t227))) % 0.41/0.62 (step @p319 :rule cnf_or_pos :args (@t242)) % 0.41/0.62 (step @p320 :rule reordering :premises (@p319) :args ((or @t232 @t225 @t243))) % 0.41/0.62 (step @p321 :rule chain_m_resolution :premises (@p320 @p306 @p318) :args (@t243 (@list false true) (@list @t231 @t225))) % 0.41/0.62 (assume-push @p328 @t223) % 0.41/0.62 (step @p323 :rule instantiate :premises (@p293) :args (@t239)) % 0.41/0.62 (step-pop @p329 :rule scope :premises (@p323)) % 0.41/0.62 (step @p324 :rule process_scope :premises (@p329) :args (@t242)) % 0.41/0.62 (step @p326 :rule implies_elim :premises (@p324)) % 0.41/0.62 (step @p327 false :rule chain_m_resolution :premises (@p326 @p321 @p293) :args (false @t241 (@list @t242 @t223))) % 0.41/0.62 ) % 0.41/0.62 % SZS output end Proof % 0.41/0.63 % cvc5 exiting %------------------------------------------------------------------------------