%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL700^1 : TPTP v9.3.1. Bugfixed v5.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n010.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:39 AM UTC 2026 % Result : Theorem 0.18s 0.52s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL700^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.09/0.34 % Computer : n010.cluster.edu % 0.09/0.34 % Model : x86_64 x86_64 % 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.34 % Memory : 8046.5625MB % 0.09/0.34 % OS : Linux 6.8.0-71-generic % 0.09/0.34 % CPULimit : 300 % 0.09/0.34 % WCLimit : 300 % 0.09/0.34 % DateTime : Fri Sep 4 23:34:08 UTC 2026 % 0.09/0.34 % CPUTime : % 0.13/0.41 %----Proving TH0 % 0.18/0.52 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.18/0.52 % SZS status Theorem % 0.18/0.52 % SZS output start Proof % 0.18/0.52 ( % 0.18/0.52 (declare-sort $$unsorted 0) % 0.18/0.52 (declare-sort tptp.mu 0) % 0.18/0.52 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.18/0.52 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.18/0.52 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.18/0.52 (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)))))) % 0.18/0.52 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.18/0.52 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.18/0.52 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.18/0.52 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.18/0.52 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.18/0.52 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.18/0.52 (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))))))) % 0.18/0.52 (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))))))) % 0.18/0.52 (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)))))) % 0.18/0.52 (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)))))) % 0.18/0.52 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.18/0.52 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.18/0.52 (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)))))) % 0.18/0.52 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.18/0.52 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.18/0.52 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.18/0.52 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.18/0.52 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.18/0.52 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.18/0.52 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.18/0.52 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.18/0.52 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.18/0.52 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.18/0.52 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.52 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.52 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.52 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.52 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.18/0.52 (define @t2 () (@var "A" (-> $$unsorted Bool))) % 0.18/0.52 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.18/0.52 (define @t4 () (_ tptp.mbox @t3)) % 0.18/0.52 (define @t5 () (@list @t2 @t1)) % 0.18/0.52 (define @t6 () (lambda @t5 (_ (_ (_ tptp.mimplies @t2) (_ @t4 (_ (_ tptp.mdia @t3) @t2))) @t1))) % 0.18/0.52 (define @t7 () (=> (_ tptp.msymmetric @t3) (_ tptp.mvalid (_ tptp.mforall_prop @t6)))) % 0.18/0.52 (define @t8 () (@list @t3)) % 0.18/0.52 (define @t9 () (forall @t8 @t7)) % 0.18/0.52 (define @t10 () (not @t9)) % 0.18/0.52 (define @t11 () (@var "Y" tptp.mu)) % 0.18/0.52 (define @t12 () (@var "X" tptp.mu)) % 0.18/0.52 (define @t13 () (@var "W" $$unsorted)) % 0.18/0.52 (define @t14 () (lambda (@list @t12 @t11 @t13) (= @t12 @t11))) % 0.18/0.52 (define @t15 () (@var "Y" (-> $$unsorted Bool))) % 0.18/0.52 (define @t16 () (@var "X" (-> $$unsorted Bool))) % 0.18/0.52 (define @t17 () (lambda (@list @t16 @t15 @t13) (= (_ @t16 @t13) (_ @t15 @t13)))) % 0.18/0.52 (define @t18 () (@var "Phi" (-> $$unsorted Bool))) % 0.18/0.52 (define @t19 () (_ @t18 @t13)) % 0.18/0.52 (define @t20 () (not @t19)) % 0.18/0.52 (define @t21 () (@list @t18 @t13)) % 0.18/0.52 (define @t22 () (lambda @t21 @t20)) % 0.18/0.52 (define @t23 () (@var "Psi" (-> $$unsorted Bool))) % 0.18/0.52 (define @t24 () (_ @t23 @t13)) % 0.18/0.52 (define @t25 () (lambda (@list @t18 @t23 @t13) (or @t19 @t24))) % 0.18/0.52 (define @t26 () (_ tptp.mnot @t23)) % 0.18/0.52 (define @t27 () (_ tptp.mnot @t18)) % 0.18/0.52 (define @t28 () (_ tptp.mor @t27)) % 0.18/0.52 (define @t29 () (@list @t18 @t23 @t1)) % 0.18/0.52 (define @t30 () (lambda @t29 (_ (_ tptp.mnot (_ @t28 @t26)) @t1))) % 0.18/0.52 (define @t31 () (lambda @t29 (_ (_ @t28 @t23) @t1))) % 0.18/0.52 (define @t32 () (lambda @t29 (_ (_ (_ tptp.mor @t26) @t18) @t1))) % 0.18/0.52 (define @t33 () (lambda @t29 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t18) @t23)) (_ (_ tptp.mimplies @t23) @t18)) @t1))) % 0.18/0.52 (define @t34 () (lambda @t29 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t18) @t23)) @t1))) % 0.18/0.52 (define @t35 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.18/0.52 (define @t36 () (_ @t35 @t12)) % 0.18/0.52 (define @t37 () (lambda (@list @t35 @t13) (forall (@list @t12) (_ @t36 @t13)))) % 0.18/0.52 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 0.18/0.52 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.18/0.52 (define @t40 () (_ @t39 @t38)) % 0.18/0.52 (define @t41 () (_ @t40 @t13)) % 0.18/0.52 (define @t42 () (@list @t38)) % 0.18/0.52 (define @t43 () (forall @t42 @t41)) % 0.18/0.52 (define @t44 () (@list @t39 @t13)) % 0.18/0.52 (define @t45 () (lambda @t44 @t43)) % 0.18/0.52 (define @t46 () (lambda (@list @t35 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t12 @t1) (_ (_ tptp.mnot @t36) @t1)))) @t1))) % 0.18/0.52 (define @t47 () (lambda (@list @t39 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t1) (_ (_ tptp.mnot @t40) @t1)))) @t1))) % 0.18/0.52 (define @t48 () (@list @t13)) % 0.18/0.52 (define @t49 () (lambda @t48 true)) % 0.18/0.52 (define @t50 () (@var "V" $$unsorted)) % 0.18/0.52 (define @t51 () (_ @t18 @t50)) % 0.18/0.52 (define @t52 () (_ (_ @t3 @t13) @t50)) % 0.18/0.52 (define @t53 () (not @t52)) % 0.18/0.52 (define @t54 () (or @t53 @t51)) % 0.18/0.52 (define @t55 () (@list @t50)) % 0.18/0.52 (define @t56 () (forall @t55 @t54)) % 0.18/0.52 (define @t57 () (@list @t3 @t18 @t13)) % 0.18/0.52 (define @t58 () (lambda @t57 @t56)) % 0.18/0.52 (define @t59 () (@list @t3 @t18 @t1)) % 0.18/0.52 (define @t60 () (lambda @t59 (_ (_ tptp.mnot (_ @t4 @t27)) @t1))) % 0.18/0.52 (define @t61 () (@var "S" $$unsorted)) % 0.18/0.52 (define @t62 () (_ @t3 @t61)) % 0.18/0.52 (define @t63 () (@list @t61)) % 0.18/0.52 (define @t64 () (lambda @t8 (forall @t63 (_ @t62 @t61)))) % 0.18/0.52 (define @t65 () (@var "T" $$unsorted)) % 0.18/0.52 (define @t66 () (_ @t3 @t65)) % 0.18/0.52 (define @t67 () (_ @t66 @t61)) % 0.18/0.52 (define @t68 () (_ @t62 @t65)) % 0.18/0.52 (define @t69 () (@list @t61 @t65)) % 0.18/0.52 (define @t70 () (forall @t69 (=> @t68 @t67))) % 0.18/0.52 (define @t71 () (lambda @t8 @t70)) % 0.18/0.52 (define @t72 () (@list @t65)) % 0.18/0.52 (define @t73 () (lambda @t8 (forall @t63 (exists @t72 @t68)))) % 0.18/0.52 (define @t74 () (@var "U" $$unsorted)) % 0.18/0.52 (define @t75 () (_ @t62 @t74)) % 0.18/0.52 (define @t76 () (_ @t66 @t74)) % 0.18/0.52 (define @t77 () (@list @t61 @t65 @t74)) % 0.18/0.52 (define @t78 () (lambda @t8 (forall @t77 (=> (and @t68 @t76) @t75)))) % 0.18/0.52 (define @t79 () (and @t68 @t75)) % 0.18/0.52 (define @t80 () (lambda @t8 (forall @t77 (=> @t79 @t76)))) % 0.18/0.52 (define @t81 () (= @t65 @t74)) % 0.18/0.52 (define @t82 () (lambda @t8 (forall @t77 (=> @t79 @t81)))) % 0.18/0.52 (define @t83 () (@list @t74)) % 0.18/0.52 (define @t84 () (lambda @t8 (forall @t63 (exists @t72 (and @t68 (forall @t83 (=> @t75 @t81))))))) % 0.18/0.52 (define @t85 () (_ @t3 @t74)) % 0.18/0.52 (define @t86 () (_ @t85 @t65)) % 0.18/0.52 (define @t87 () (lambda @t8 (forall @t77 (=> @t68 (exists @t83 (and @t75 @t86)))))) % 0.18/0.52 (define @t88 () (lambda @t8 (forall @t77 (=> @t79 (or @t76 @t81 @t86))))) % 0.18/0.52 (define @t89 () (lambda @t8 (forall @t77 (=> @t79 (exists @t55 (and (_ @t66 @t50) (_ @t85 @t50))))))) % 0.18/0.52 (define @t90 () (forall @t48 @t19)) % 0.18/0.52 (define @t91 () (@list @t18)) % 0.18/0.52 (define @t92 () (lambda @t91 @t90)) % 0.18/0.52 (define @t93 () (lambda @t91 (forall @t48 @t20))) % 0.18/0.52 (define @t94 () (lambda @t91 (exists @t48 @t19))) % 0.18/0.52 (define @t95 () (lambda @t91 (exists @t48 @t20))) % 0.18/0.52 (define @t96 () (@var "BOUND_VARIABLE_8362" $$unsorted)) % 0.18/0.52 (define @t97 () (@var "BOUND_VARIABLE_8441" (-> $$unsorted Bool))) % 0.18/0.52 (define @t98 () (@var "BOUND_VARIABLE_8443" $$unsorted)) % 0.18/0.52 (define @t99 () (@list @t96)) % 0.18/0.52 (define @t100 () (not (forall @t99 (or (not (_ @t3 @t98 @t96)) (not (_ @t97 @t96)))))) % 0.18/0.52 (define @t101 () (@var "BOUND_VARIABLE_8439" $$unsorted)) % 0.18/0.52 (define @t102 () (not (_ @t3 @t101 @t98))) % 0.18/0.52 (define @t103 () (not (_ @t97 @t101))) % 0.18/0.52 (define @t104 () (_ @t3 @t65 @t61)) % 0.18/0.52 (define @t105 () (_ @t3 @t61 @t65)) % 0.18/0.52 (define @t106 () (forall @t69 (or (not @t105) @t104))) % 0.18/0.52 (define @t107 () (not @t106)) % 0.18/0.52 (define @t108 () (or @t107 @t103 @t102 @t100)) % 0.18/0.52 (define @t109 () (or @t103 @t102 @t100)) % 0.18/0.52 (define @t110 () (or @t107 @t109)) % 0.18/0.52 (define @t111 () (@list @t3 @t101 @t97 @t98)) % 0.18/0.52 (define @t112 () (forall @t111 @t110)) % 0.18/0.52 (define @t113 () (@list @t101 @t97 @t98)) % 0.18/0.52 (define @t114 () (forall @t113 @t110)) % 0.18/0.52 (define @t115 () (forall @t113 @t109)) % 0.18/0.52 (define @t116 () (@var "BOUND_VARIABLE_8412" $$unsorted)) % 0.18/0.52 (define @t117 () (or @t107 @t115)) % 0.18/0.52 (define @t118 () (not (_ @t38 @t96))) % 0.18/0.52 (define @t119 () (not (forall @t99 (or (not (_ @t3 @t116 @t96)) @t118)))) % 0.18/0.52 (define @t120 () (not (_ @t3 @t13 @t116))) % 0.18/0.52 (define @t121 () (_ @t38 @t13)) % 0.18/0.52 (define @t122 () (not @t121)) % 0.18/0.52 (define @t123 () (or @t122 @t120 @t119)) % 0.18/0.52 (define @t124 () (forall (@list @t13 @t38 @t116) @t123)) % 0.18/0.52 (define @t125 () (@list @t38 @t116)) % 0.18/0.52 (define @t126 () (forall @t125 @t123)) % 0.18/0.52 (define @t127 () (lambda @t48 @t126)) % 0.18/0.52 (define @t128 () (_ @t127 @t13)) % 0.18/0.52 (define @t129 () (forall @t48 @t128)) % 0.18/0.52 (define @t130 () (_ @t18 @t13)) % 0.18/0.52 (define @t131 () (lambda @t91 (forall @t48 @t130))) % 0.18/0.52 (define @t132 () (or @t120 @t119)) % 0.18/0.52 (define @t133 () (or @t122 @t132)) % 0.18/0.52 (define @t134 () (forall @t125 @t133)) % 0.18/0.52 (define @t135 () (@list @t116)) % 0.18/0.52 (define @t136 () (forall @t135 @t133)) % 0.18/0.52 (define @t137 () (forall @t135 @t132)) % 0.18/0.52 (define @t138 () (@list @t50)) % 0.18/0.52 (define @t139 () (or @t122 @t137)) % 0.18/0.52 (define @t140 () (not (_ @t3 @t50 @t96))) % 0.18/0.52 (define @t141 () (_ @t3 @t13 @t50)) % 0.18/0.52 (define @t142 () (not @t141)) % 0.18/0.52 (define @t143 () (forall @t55 (or @t142 (not (forall @t99 (or @t140 @t118)))))) % 0.18/0.52 (define @t144 () (_ @t38 @t13)) % 0.18/0.52 (define @t145 () (not @t144)) % 0.18/0.52 (define @t146 () (or @t145 @t143)) % 0.18/0.52 (define @t147 () (not (_ @t2 @t96))) % 0.18/0.52 (define @t148 () (not (forall @t99 (or @t140 @t147)))) % 0.18/0.52 (define @t149 () (not (_ @t3 @t1 @t50))) % 0.18/0.52 (define @t150 () (forall @t55 (or @t149 @t148))) % 0.18/0.52 (define @t151 () (not (_ @t2 @t1))) % 0.18/0.52 (define @t152 () (or @t151 @t150)) % 0.18/0.52 (define @t153 () (lambda @t5 @t152)) % 0.18/0.52 (define @t154 () (_ @t153 @t38 @t13)) % 0.18/0.52 (define @t155 () (forall @t42 @t154)) % 0.18/0.52 (define @t156 () (lambda @t48 @t155)) % 0.18/0.52 (define @t157 () (_ @t39 @t38 @t13)) % 0.18/0.52 (define @t158 () (lambda @t44 (forall @t42 @t157))) % 0.18/0.52 (define @t159 () (@list @t1)) % 0.18/0.52 (define @t160 () (lambda @t48 (forall @t55 (or @t142 @t148)))) % 0.18/0.52 (define @t161 () (_ @t160 @t1)) % 0.18/0.52 (define @t162 () (or @t151 @t161)) % 0.18/0.52 (define @t163 () (lambda @t159 @t162)) % 0.18/0.52 (define @t164 () (_ @t23 @t1)) % 0.18/0.52 (define @t165 () (lambda (@list @t23 @t1) (or @t151 @t164))) % 0.18/0.52 (define @t166 () (forall @t55 (or @t149 (not (_ @t2 @t50))))) % 0.18/0.52 (define @t167 () (not @t166)) % 0.18/0.52 (define @t168 () (lambda @t159 @t167)) % 0.18/0.52 (define @t169 () (or @t142 (_ @t168 @t50))) % 0.18/0.52 (define @t170 () (forall @t55 @t169)) % 0.18/0.52 (define @t171 () (lambda @t48 @t170)) % 0.18/0.52 (define @t172 () (_ @t18 @t50)) % 0.18/0.52 (define @t173 () (forall @t55 (or @t142 @t172))) % 0.18/0.52 (define @t174 () (lambda @t21 @t173)) % 0.18/0.52 (define @t175 () (not @t172)) % 0.18/0.52 (define @t176 () (not (forall @t55 (or @t149 @t175)))) % 0.18/0.52 (define @t177 () (lambda (@list @t18 @t1) @t176)) % 0.18/0.52 (define @t178 () (_ (lambda @t59 @t176) @t3)) % 0.18/0.52 (define @t179 () (_ (lambda @t57 @t173) @t3)) % 0.18/0.52 (define @t180 () (or (not (_ @t18 @t1)) @t164)) % 0.18/0.52 (define @t181 () (_ (lambda @t29 @t180) @t2)) % 0.18/0.52 (define @t182 () (lambda @t5 (_ (_ @t181 (_ @t179 (_ @t178 @t2))) @t1))) % 0.18/0.52 (define @t183 () (_ (lambda @t8 @t106) @t3)) % 0.18/0.52 (define @t184 () (=> @t183 (_ @t131 (_ @t158 @t182)))) % 0.18/0.52 (define @t185 () (forall @t8 @t184)) % 0.18/0.52 (define @t186 () (forall @t55 (or @t142 @t175))) % 0.18/0.52 (define @t187 () (lambda @t48 @t186)) % 0.18/0.52 (define @t188 () (_ @t187 @t13)) % 0.18/0.52 (define @t189 () (not @t188)) % 0.18/0.52 (define @t190 () (lambda @t48 @t189)) % 0.18/0.52 (define @t191 () (not @t51)) % 0.18/0.52 (define @t192 () (or @t142 @t191)) % 0.18/0.52 (define @t193 () (lambda @t48 @t20)) % 0.18/0.52 (define @t194 () (_ @t193 @t50)) % 0.18/0.52 (define @t195 () (or @t142 @t194)) % 0.18/0.52 (define @t196 () (forall @t55 @t195)) % 0.18/0.52 (define @t197 () (lambda @t48 @t196)) % 0.18/0.52 (define @t198 () (or @t20 @t24)) % 0.18/0.52 (define @t199 () (lambda @t48 @t198)) % 0.18/0.52 (define @t200 () (@list @t23 @t13)) % 0.18/0.52 (define @t201 () (_ @t193 @t13)) % 0.18/0.52 (define @t202 () (or @t201 @t24)) % 0.18/0.52 (define @t203 () (lambda @t200 @t202)) % 0.18/0.52 (define @t204 () (not @t68)) % 0.18/0.52 (define @t205 () (or @t204 @t67)) % 0.18/0.52 (define @t206 () (forall @t111 @t108)) % 0.18/0.52 (define @t207 () (@quantifiers_skolemize @t206 1)) % 0.18/0.52 (define @t208 () (@quantifiers_skolemize @t206 2)) % 0.18/0.52 (define @t209 () (_ @t208 @t207)) % 0.18/0.52 (define @t210 () (@quantifiers_skolemize @t206 3)) % 0.18/0.52 (define @t211 () (@quantifiers_skolemize @t206 0)) % 0.18/0.52 (define @t212 () (forall @t99 (or (not (_ @t211 @t210 @t96)) (not (_ @t208 @t96))))) % 0.18/0.52 (define @t213 () (not @t212)) % 0.18/0.52 (define @t214 () (_ @t211 @t207 @t210)) % 0.18/0.52 (define @t215 () (not @t214)) % 0.18/0.52 (define @t216 () (not @t209)) % 0.18/0.52 (define @t217 () (forall @t69 (or (not (_ @t211 @t61 @t65)) (_ @t211 @t65 @t61)))) % 0.18/0.52 (define @t218 () (not @t217)) % 0.18/0.52 (define @t219 () (or @t218 @t216 @t215 @t213)) % 0.18/0.52 (define @t220 () (@list true)) % 0.18/0.52 (define @t221 () (@list @t219)) % 0.18/0.52 (define @t222 () (_ @t211 @t210 @t207)) % 0.18/0.52 (define @t223 () (or @t215 @t222)) % 0.18/0.52 (define @t224 () (not @t222)) % 0.18/0.52 (define @t225 () (or @t224 @t216)) % 0.18/0.52 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.18/0.52 (assume @p2 @t10) % 0.18/0.52 (assume @p3 true) % 0.18/0.52 (step @p4 (= tptp.meq_ind @t14) :rule refl :args (@t14)) % 0.18/0.52 (step @p5 (= tptp.meq_prop @t17) :rule refl :args (@t17)) % 0.18/0.52 (step @p6 (= tptp.mnot @t22) :rule refl :args (@t22)) % 0.18/0.52 (step @p7 (= tptp.mor @t25) :rule refl :args (@t25)) % 0.18/0.52 (step @p8 (= tptp.mand @t30) :rule refl :args (@t30)) % 0.18/0.52 (step @p9 (= tptp.mimplies @t31) :rule refl :args (@t31)) % 0.18/0.52 (step @p10 (= tptp.mimplied @t32) :rule refl :args (@t32)) % 0.18/0.52 (step @p11 (= tptp.mequiv @t33) :rule refl :args (@t33)) % 0.18/0.52 (step @p12 (= tptp.mxor @t34) :rule refl :args (@t34)) % 0.18/0.52 (step @p13 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 0.18/0.52 (step @p14 (= tptp.mforall_prop @t45) :rule refl :args (@t45)) % 0.18/0.52 (step @p15 (= tptp.mexists_ind @t46) :rule refl :args (@t46)) % 0.18/0.52 (step @p16 (= tptp.mexists_prop @t47) :rule refl :args (@t47)) % 0.18/0.52 (step @p17 (= tptp.mtrue @t49) :rule refl :args (@t49)) % 0.18/0.52 (step @p18 (= tptp.mbox @t58) :rule refl :args (@t58)) % 0.18/0.52 (step @p19 (= tptp.mdia @t60) :rule refl :args (@t60)) % 0.18/0.52 (step @p20 (= tptp.mreflexive @t64) :rule refl :args (@t64)) % 0.18/0.52 (step @p21 (= tptp.msymmetric @t71) :rule refl :args (@t71)) % 0.18/0.52 (step @p22 (= tptp.mserial @t73) :rule refl :args (@t73)) % 0.18/0.52 (step @p23 (= tptp.mtransitive @t78) :rule refl :args (@t78)) % 0.18/0.52 (step @p24 (= tptp.meuclidean @t80) :rule refl :args (@t80)) % 0.18/0.52 (step @p25 (= tptp.mpartially_functional @t82) :rule refl :args (@t82)) % 0.18/0.52 (step @p26 (= tptp.mfunctional @t84) :rule refl :args (@t84)) % 0.18/0.52 (step @p27 (= tptp.mweakly_dense @t87) :rule refl :args (@t87)) % 0.18/0.52 (step @p28 (= tptp.mweakly_connected @t88) :rule refl :args (@t88)) % 0.18/0.52 (step @p29 (= tptp.mweakly_directed @t89) :rule refl :args (@t89)) % 0.18/0.52 (step @p30 (= tptp.mvalid @t92) :rule refl :args (@t92)) % 0.18/0.52 (step @p31 (= tptp.minvalid @t93) :rule refl :args (@t93)) % 0.18/0.52 (step @p32 (= tptp.msatisfiable @t94) :rule refl :args (@t94)) % 0.18/0.52 (step @p33 (= tptp.mcountersatisfiable @t95) :rule refl :args (@t95)) % 0.18/0.52 (step @p34 :rule aci_norm :args ((= @t110 @t108))) % 0.18/0.52 (step @p35 :rule cong :premises (@p34) :args (@t112)) % 0.18/0.52 (step @p36 :rule quant-merge-prenex :args ((= (forall @t8 @t114) @t112))) % 0.18/0.52 (step @p37 :rule alpha_equiv :args (@t115 (@list @t101 @t97 @t98) (@list @t13 @t38 @t116))) % 0.18/0.52 (step @p38 :rule refl :args (@t107)) % 0.18/0.52 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t117)) % 0.18/0.52 (step @p40 :rule quant-miniscope-or :args ((= @t114 @t117))) % 0.18/0.52 (step @p41 :rule trans :premises (@p40 @p39)) % 0.18/0.52 (step @p42 :rule symm :premises (@p41)) % 0.18/0.52 (step @p43 :rule cong :premises (@p42) :args ((forall @t8 (or @t107 @t124)))) % 0.18/0.52 (step @p44 :rule trans :premises (@p43 @p36)) % 0.18/0.52 (step @p45 :rule trans :premises (@p44 @p35)) % 0.18/0.52 (step @p46 :rule bool-impl-elim :args (@t106 @t124)) % 0.18/0.52 (step @p47 :rule cong :premises (@p46) :args ((forall @t8 (=> @t106 @t124)))) % 0.18/0.52 (step @p48 :rule trans :premises (@p47 @p45)) % 0.18/0.52 (step @p49 :rule quant-merge-prenex :args ((= (forall @t48 @t126) @t124))) % 0.18/0.52 (step @p50 :rule beta-reduce :args ((= @t128 @t126))) % 0.18/0.52 (step @p51 :rule cong :premises (@p50) :args (@t129)) % 0.18/0.52 (step @p52 :rule trans :premises (@p51 @p49)) % 0.18/0.52 (step @p53 :rule beta-reduce :args ((= (_ @t131 @t127) @t129))) % 0.18/0.52 (step @p54 :rule trans :premises (@p53 @p52)) % 0.18/0.52 (step @p55 :rule aci_norm :args ((= @t133 @t123))) % 0.18/0.52 (step @p56 :rule cong :premises (@p55) :args (@t134)) % 0.18/0.52 (step @p57 :rule quant-merge-prenex :args ((= (forall @t42 @t136) @t134))) % 0.18/0.52 (step @p58 :rule alpha_equiv :args (@t137 (@list @t116) @t138)) % 0.18/0.52 (step @p59 :rule refl :args (@t122)) % 0.18/0.52 (step @p60 :rule nary_cong :premises (@p59 @p58) :args (@t139)) % 0.18/0.52 (step @p61 :rule quant-miniscope-or :args ((= @t136 @t139))) % 0.18/0.52 (step @p62 :rule trans :premises (@p61 @p60)) % 0.18/0.52 (step @p63 :rule symm :premises (@p62)) % 0.18/0.52 (step @p64 :rule cong :premises (@p63) :args ((forall @t42 (or @t122 @t143)))) % 0.18/0.52 (step @p65 :rule trans :premises (@p64 @p57)) % 0.18/0.52 (step @p66 :rule trans :premises (@p65 @p56)) % 0.18/0.52 (step @p67 :rule refl :args (@t143)) % 0.18/0.52 (step @p68 :rule refl :args (@t121)) % 0.18/0.52 (step @p69 :rule refl :args (@t144)) % 0.18/0.52 (step @p70 :rule cong :premises (@p69 @p68) :args ((= @t144 @t121))) % 0.18/0.52 (step @p71 :rule symm :premises (@p70)) % 0.18/0.52 (step @p72 :rule eq_resolve :premises (@p69 @p71)) % 0.18/0.52 (step @p73 :rule cong :premises (@p72) :args (@t145)) % 0.18/0.52 (step @p74 :rule nary_cong :premises (@p73 @p67) :args (@t146)) % 0.18/0.52 (step @p75 :rule cong :premises (@p74) :args ((forall @t42 @t146))) % 0.18/0.52 (step @p76 :rule trans :premises (@p75 @p66)) % 0.18/0.52 (step @p77 :rule beta-reduce :args ((= @t154 @t146))) % 0.18/0.52 (step @p78 :rule cong :premises (@p77) :args (@t155)) % 0.18/0.52 (step @p79 :rule trans :premises (@p78 @p76)) % 0.18/0.52 (step @p80 :rule cong :premises (@p79) :args (@t156)) % 0.18/0.52 (step @p81 :rule beta-reduce :args ((= (_ @t158 @t153) @t156))) % 0.18/0.52 (step @p82 :rule trans :premises (@p81 @p80)) % 0.18/0.52 (step @p83 :rule beta-reduce :args ((= (_ (lambda @t159 @t152) @t1) @t152))) % 0.18/0.52 (step @p84 :rule refl :args (@t1)) % 0.18/0.52 (step @p85 :rule beta-reduce :args ((= @t161 @t150))) % 0.18/0.52 (step @p86 :rule refl :args (@t151)) % 0.18/0.52 (step @p87 :rule nary_cong :premises (@p86 @p85) :args (@t162)) % 0.18/0.52 (step @p88 :rule cong :premises (@p87) :args (@t163)) % 0.18/0.52 (step @p89 :rule beta-reduce :args ((= (_ @t165 @t160) @t163))) % 0.18/0.52 (step @p90 :rule trans :premises (@p89 @p88)) % 0.18/0.52 (step @p91 :rule beta-reduce :args ((= (_ (lambda @t159 (not (forall @t99 (or (not (_ @t3 @t1 @t96)) @t147)))) @t50) @t148))) % 0.18/0.52 (step @p92 :rule refl :args (@t50)) % 0.18/0.52 (step @p93 :rule alpha_equiv :args (@t166 @t138 (@list @t96))) % 0.18/0.52 (step @p94 :rule cong :premises (@p93) :args (@t167)) % 0.18/0.52 (step @p95 :rule cong :premises (@p94) :args (@t168)) % 0.18/0.52 (step @p96 :rule ho_cong :premises (@p95 @p92)) % 0.18/0.52 (step @p97 :rule trans :premises (@p96 @p91)) % 0.18/0.52 (step @p98 :rule refl :args (@t142)) % 0.18/0.52 (step @p99 :rule nary_cong :premises (@p98 @p97) :args (@t169)) % 0.18/0.52 (step @p100 :rule cong :premises (@p99) :args (@t170)) % 0.18/0.52 (step @p101 :rule cong :premises (@p100) :args (@t171)) % 0.18/0.52 (step @p102 :rule beta-reduce :args ((= (_ @t174 @t168) @t171))) % 0.18/0.52 (step @p103 :rule trans :premises (@p102 @p101)) % 0.18/0.52 (step @p104 :rule beta-reduce :args ((= (_ @t177 @t2) @t168))) % 0.18/0.52 (step @p105 :rule refl :args (@t2)) % 0.18/0.52 (step @p106 :rule beta-reduce :args ((= @t178 @t177))) % 0.18/0.52 (step @p107 :rule ho_cong :premises (@p106 @p105)) % 0.18/0.52 (step @p108 :rule trans :premises (@p107 @p104)) % 0.18/0.52 (step @p109 :rule beta-reduce :args ((= @t179 @t174))) % 0.18/0.52 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 0.18/0.52 (step @p111 :rule trans :premises (@p110 @p103)) % 0.18/0.52 (step @p112 :rule beta-reduce :args ((= @t181 @t165))) % 0.18/0.52 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 0.18/0.52 (step @p114 :rule trans :premises (@p113 @p90)) % 0.18/0.52 (step @p115 :rule ho_cong :premises (@p114 @p84)) % 0.18/0.52 (step @p116 :rule trans :premises (@p115 @p83)) % 0.18/0.52 (step @p117 :rule cong :premises (@p116) :args (@t182)) % 0.18/0.52 (step @p118 :rule refl :args (@t158)) % 0.18/0.52 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 0.18/0.52 (step @p120 :rule trans :premises (@p119 @p82)) % 0.18/0.52 (step @p121 :rule refl :args (@t131)) % 0.18/0.52 (step @p122 :rule ho_cong :premises (@p121 @p120)) % 0.18/0.52 (step @p123 :rule trans :premises (@p122 @p54)) % 0.18/0.52 (step @p124 :rule beta-reduce :args ((= @t183 @t106))) % 0.18/0.52 (step @p125 :rule cong :premises (@p124 @p123) :args (@t184)) % 0.18/0.52 (step @p126 :rule cong :premises (@p125) :args (@t185)) % 0.18/0.52 (step @p127 :rule trans :premises (@p126 @p48)) % 0.18/0.52 (step @p128 :rule cong :premises (@p127) :args ((not @t185))) % 0.18/0.52 (step @p129 :rule refl :args (@t3)) % 0.18/0.52 (step @p130 :rule beta-reduce :args ((= (_ (lambda @t48 (not @t186)) @t1) @t176))) % 0.18/0.52 (step @p131 :rule beta-reduce :args ((= @t188 @t186))) % 0.18/0.52 (step @p132 :rule cong :premises (@p131) :args (@t189)) % 0.18/0.52 (step @p133 :rule cong :premises (@p132) :args (@t190)) % 0.18/0.52 (step @p134 :rule beta-reduce :args ((= (_ @t22 @t187) @t190))) % 0.18/0.52 (step @p135 :rule trans :premises (@p134 @p133)) % 0.18/0.52 (step @p136 :rule refl :args (@t172)) % 0.18/0.52 (step @p137 :rule refl :args (@t51)) % 0.18/0.52 (step @p138 :rule cong :premises (@p137 @p136) :args ((= @t51 @t172))) % 0.18/0.52 (step @p139 :rule symm :premises (@p138)) % 0.18/0.52 (step @p140 :rule eq_resolve :premises (@p137 @p139)) % 0.18/0.52 (step @p141 :rule cong :premises (@p140) :args (@t191)) % 0.18/0.52 (step @p142 :rule refl :args (@t142)) % 0.18/0.52 (step @p143 :rule nary_cong :premises (@p142 @p141) :args (@t192)) % 0.18/0.52 (step @p144 :rule cong :premises (@p143) :args ((forall @t55 @t192))) % 0.18/0.52 (step @p145 :rule beta-reduce :args ((= @t194 @t191))) % 0.18/0.52 (step @p146 :rule nary_cong :premises (@p98 @p145) :args (@t195)) % 0.18/0.52 (step @p147 :rule cong :premises (@p146) :args (@t196)) % 0.18/0.52 (step @p148 :rule trans :premises (@p147 @p144)) % 0.18/0.52 (step @p149 :rule cong :premises (@p148) :args (@t197)) % 0.18/0.52 (step @p150 :rule beta-reduce :args ((= (_ @t174 @t193) @t197))) % 0.18/0.52 (step @p151 :rule trans :premises (@p150 @p149)) % 0.18/0.52 (step @p152 :rule beta-reduce :args ((= (_ @t22 @t18) @t193))) % 0.18/0.52 (step @p153 :rule ho_cong :premises (@p109 @p152)) % 0.18/0.52 (step @p154 :rule trans :premises (@p153 @p151)) % 0.18/0.52 (step @p155 :rule refl :args (@t22)) % 0.18/0.52 (step @p156 :rule ho_cong :premises (@p155 @p154)) % 0.18/0.52 (step @p157 :rule trans :premises (@p156 @p135)) % 0.18/0.52 (step @p158 :rule ho_cong :premises (@p157 @p84)) % 0.18/0.52 (step @p159 :rule trans :premises (@p158 @p130)) % 0.18/0.52 (step @p160 :rule refl :args (@t18)) % 0.18/0.52 (step @p161 :rule ho_cong :premises (@p6 @p160)) % 0.18/0.52 (step @p162 :rule refl :args (@t141)) % 0.18/0.52 (step @p163 :rule refl :args (@t52)) % 0.18/0.52 (step @p164 :rule cong :premises (@p163 @p162) :args ((= @t52 @t141))) % 0.18/0.52 (step @p165 :rule symm :premises (@p164)) % 0.18/0.52 (step @p166 :rule eq_resolve :premises (@p163 @p165)) % 0.18/0.52 (step @p167 :rule cong :premises (@p166) :args (@t53)) % 0.18/0.52 (step @p168 :rule nary_cong :premises (@p167 @p140) :args (@t54)) % 0.18/0.52 (step @p169 :rule cong :premises (@p168) :args (@t56)) % 0.18/0.52 (step @p170 :rule cong :premises (@p169) :args (@t58)) % 0.18/0.52 (step @p171 :rule trans :premises (@p18 @p170)) % 0.18/0.52 (step @p172 :rule ho_cong :premises (@p171 @p129)) % 0.18/0.52 (step @p173 :rule ho_cong :premises (@p172 @p161)) % 0.18/0.52 (step @p174 :rule ho_cong :premises (@p6 @p173)) % 0.18/0.52 (step @p175 :rule ho_cong :premises (@p174 @p84)) % 0.18/0.52 (step @p176 :rule trans :premises (@p175 @p159)) % 0.18/0.52 (step @p177 :rule cong :premises (@p176) :args (@t60)) % 0.18/0.52 (step @p178 :rule trans :premises (@p19 @p177)) % 0.18/0.52 (step @p179 :rule ho_cong :premises (@p178 @p129)) % 0.18/0.52 (step @p180 :rule ho_cong :premises (@p179 @p105)) % 0.18/0.52 (step @p181 :rule ho_cong :premises (@p172 @p180)) % 0.18/0.52 (step @p182 :rule beta-reduce :args ((= (_ @t199 @t1) @t180))) % 0.18/0.52 (step @p183 :rule beta-reduce :args ((= (_ (lambda @t200 @t198) @t23) @t199))) % 0.18/0.52 (step @p184 :rule refl :args (@t23)) % 0.18/0.52 (step @p185 :rule refl :args (@t24)) % 0.18/0.52 (step @p186 :rule beta-reduce :args ((= @t201 @t20))) % 0.18/0.52 (step @p187 :rule nary_cong :premises (@p186 @p185) :args (@t202)) % 0.18/0.52 (step @p188 :rule cong :premises (@p187) :args (@t203)) % 0.18/0.52 (step @p189 :rule beta-reduce :args ((= (_ @t25 @t193) @t203))) % 0.18/0.52 (step @p190 :rule trans :premises (@p189 @p188)) % 0.18/0.52 (step @p191 :rule refl :args (@t25)) % 0.18/0.52 (step @p192 :rule ho_cong :premises (@p191 @p152)) % 0.18/0.52 (step @p193 :rule trans :premises (@p192 @p190)) % 0.18/0.52 (step @p194 :rule ho_cong :premises (@p193 @p184)) % 0.18/0.52 (step @p195 :rule trans :premises (@p194 @p183)) % 0.18/0.52 (step @p196 :rule ho_cong :premises (@p195 @p84)) % 0.18/0.52 (step @p197 :rule trans :premises (@p196 @p182)) % 0.18/0.52 (step @p198 :rule ho_cong :premises (@p7 @p161)) % 0.18/0.52 (step @p199 :rule ho_cong :premises (@p198 @p184)) % 0.18/0.52 (step @p200 :rule ho_cong :premises (@p199 @p84)) % 0.18/0.52 (step @p201 :rule trans :premises (@p200 @p197)) % 0.18/0.52 (step @p202 :rule cong :premises (@p201) :args (@t31)) % 0.18/0.52 (step @p203 :rule trans :premises (@p9 @p202)) % 0.18/0.52 (step @p204 :rule ho_cong :premises (@p203 @p105)) % 0.18/0.52 (step @p205 :rule ho_cong :premises (@p204 @p181)) % 0.18/0.52 (step @p206 :rule ho_cong :premises (@p205 @p84)) % 0.18/0.52 (step @p207 :rule cong :premises (@p206) :args (@t6)) % 0.18/0.52 (step @p208 :rule refl :args (@t157)) % 0.18/0.52 (step @p209 :rule refl :args (@t41)) % 0.18/0.52 (step @p210 :rule cong :premises (@p209 @p208) :args ((= @t41 @t157))) % 0.18/0.52 (step @p211 :rule symm :premises (@p210)) % 0.18/0.52 (step @p212 :rule eq_resolve :premises (@p209 @p211)) % 0.18/0.52 (step @p213 :rule cong :premises (@p212) :args (@t43)) % 0.18/0.52 (step @p214 :rule cong :premises (@p213) :args (@t45)) % 0.18/0.52 (step @p215 :rule trans :premises (@p14 @p214)) % 0.18/0.52 (step @p216 :rule ho_cong :premises (@p215 @p207)) % 0.18/0.52 (step @p217 :rule refl :args (@t130)) % 0.18/0.52 (step @p218 :rule refl :args (@t19)) % 0.18/0.52 (step @p219 :rule cong :premises (@p218 @p217) :args ((= @t19 @t130))) % 0.18/0.52 (step @p220 :rule symm :premises (@p219)) % 0.18/0.52 (step @p221 :rule eq_resolve :premises (@p218 @p220)) % 0.18/0.52 (step @p222 :rule cong :premises (@p221) :args (@t90)) % 0.18/0.52 (step @p223 :rule cong :premises (@p222) :args (@t92)) % 0.18/0.52 (step @p224 :rule trans :premises (@p30 @p223)) % 0.18/0.52 (step @p225 :rule ho_cong :premises (@p224 @p216)) % 0.18/0.52 (step @p226 :rule refl :args (@t104)) % 0.18/0.52 (step @p227 :rule refl :args (@t67)) % 0.18/0.52 (step @p228 :rule cong :premises (@p227 @p226) :args ((= @t67 @t104))) % 0.18/0.52 (step @p229 :rule symm :premises (@p228)) % 0.18/0.52 (step @p230 :rule eq_resolve :premises (@p227 @p229)) % 0.18/0.52 (step @p231 :rule refl :args (@t105)) % 0.18/0.52 (step @p232 :rule refl :args (@t68)) % 0.18/0.52 (step @p233 :rule cong :premises (@p232 @p231) :args ((= @t68 @t105))) % 0.18/0.52 (step @p234 :rule symm :premises (@p233)) % 0.18/0.52 (step @p235 :rule eq_resolve :premises (@p232 @p234)) % 0.18/0.52 (step @p236 :rule cong :premises (@p235) :args (@t204)) % 0.18/0.52 (step @p237 :rule nary_cong :premises (@p236 @p230) :args (@t205)) % 0.18/0.52 (step @p238 :rule cong :premises (@p237) :args ((forall @t69 @t205))) % 0.18/0.52 (step @p239 :rule bool-impl-elim :args (@t68 @t67)) % 0.18/0.52 (step @p240 :rule cong :premises (@p239) :args (@t70)) % 0.18/0.52 (step @p241 :rule trans :premises (@p240 @p238)) % 0.18/0.52 (step @p242 :rule cong :premises (@p241) :args (@t71)) % 0.18/0.52 (step @p243 :rule trans :premises (@p21 @p242)) % 0.18/0.52 (step @p244 :rule ho_cong :premises (@p243 @p129)) % 0.18/0.52 (step @p245 :rule cong :premises (@p244 @p225) :args (@t7)) % 0.18/0.52 (step @p246 :rule cong :premises (@p245) :args (@t9)) % 0.18/0.52 (step @p247 :rule cong :premises (@p246) :args (@t10)) % 0.18/0.52 (step @p248 :rule trans :premises (@p247 @p128)) % 0.18/0.52 (step @p249 :rule eq_resolve :premises (@p2 @p248)) % 0.18/0.52 (step @p250 :rule skolemize :premises (@p249)) % 0.18/0.52 (step @p251 :rule bool-double-not-elim :args (@t209)) % 0.18/0.52 (step @p252 :rule refl :args (@t219)) % 0.18/0.52 (step @p253 :rule nary_cong :premises (@p252 @p251) :args ((or @t219 (not @t216)))) % 0.18/0.52 (step @p254 :rule cnf_or_neg :args (@t219 1)) % 0.18/0.52 (step @p255 :rule eq_resolve :premises (@p254 @p253)) % 0.18/0.52 (step @p256 :rule reordering :premises (@p255) :args ((or @t209 @t219))) % 0.18/0.52 (step @p257 :rule chain_m_resolution :premises (@p256 @p250) :args (@t209 @t220 @t221)) % 0.18/0.52 (step @p258 :rule bool-double-not-elim :args (@t212)) % 0.18/0.52 (step @p259 :rule nary_cong :premises (@p252 @p258) :args ((or @t219 (not @t213)))) % 0.18/0.52 (step @p260 :rule cnf_or_neg :args (@t219 3)) % 0.18/0.52 (step @p261 :rule eq_resolve :premises (@p260 @p259)) % 0.18/0.52 (step @p262 :rule reordering :premises (@p261) :args ((or @t212 @t219))) % 0.18/0.52 (step @p263 :rule chain_m_resolution :premises (@p262 @p250) :args (@t212 @t220 @t221)) % 0.18/0.52 (step @p264 :rule instantiate :premises (@p263) :args ((@list @t207))) % 0.18/0.52 (step @p265 :rule bool-double-not-elim :args (@t217)) % 0.18/0.52 (step @p266 :rule nary_cong :premises (@p252 @p265) :args ((or @t219 (not @t218)))) % 0.18/0.52 (step @p267 :rule cnf_or_neg :args (@t219 0)) % 0.18/0.52 (step @p268 :rule eq_resolve :premises (@p267 @p266)) % 0.18/0.52 (step @p269 :rule reordering :premises (@p268) :args ((or @t217 @t219))) % 0.18/0.52 (step @p270 :rule chain_m_resolution :premises (@p269 @p250) :args (@t217 @t220 @t221)) % 0.18/0.52 (step @p271 :rule instantiate :premises (@p270) :args ((@list @t207 @t210))) % 0.18/0.52 (step @p272 :rule bool-double-not-elim :args (@t214)) % 0.18/0.52 (step @p273 :rule nary_cong :premises (@p252 @p272) :args ((or @t219 (not @t215)))) % 0.18/0.52 (step @p274 :rule cnf_or_neg :args (@t219 2)) % 0.18/0.52 (step @p275 :rule eq_resolve :premises (@p274 @p273)) % 0.18/0.52 (step @p276 :rule reordering :premises (@p275) :args ((or @t214 @t219))) % 0.18/0.52 (step @p277 :rule chain_m_resolution :premises (@p276 @p250) :args (@t214 @t220 @t221)) % 0.18/0.52 (step @p278 :rule cnf_or_pos :args (@t223)) % 0.18/0.52 (step @p279 :rule reordering :premises (@p278) :args ((or @t215 @t222 (not @t223)))) % 0.18/0.52 (step @p280 :rule chain_m_resolution :premises (@p279 @p277 @p271) :args (@t222 (@list false false) (@list @t214 @t223))) % 0.18/0.52 (step @p281 :rule cnf_or_pos :args (@t225)) % 0.18/0.52 (step @p282 :rule reordering :premises (@p281) :args ((or @t216 @t224 (not @t225)))) % 0.18/0.52 (step @p283 false :rule chain_m_resolution :premises (@p282 @p280 @p264 @p257) :args (false (@list false false false) (@list @t222 @t225 @t209))) % 0.18/0.52 ) % 0.18/0.52 % SZS output end Proof % 0.18/0.52 % cvc5 exiting %------------------------------------------------------------------------------