%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL705^1 : 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 : n020.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 11:23:40 AM UTC 2026 % Result : Theorem 6.00s 6.32s % Output : Proof 6.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL705^1 : 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 % 0.09/0.35 % Computer : n020.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 15:25:42 UTC 2026 % 0.09/0.35 % CPUTime : % 0.12/0.43 %----Proving TH0 % 6.00/6.32 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 6.00/6.32 % SZS status Theorem % 6.00/6.32 % SZS output start Proof % 6.00/6.32 ( % 6.00/6.32 (declare-sort $$unsorted 0) % 6.00/6.32 (declare-sort tptp.mu 0) % 6.00/6.32 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 6.00/6.32 (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" $$unsorted)) (= _let_2 _let_1))))) % 6.00/6.32 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 6.00/6.32 (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)))))) % 6.00/6.32 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 6.00/6.32 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 6.00/6.32 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 6.00/6.32 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 6.00/6.32 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 6.00/6.32 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 6.00/6.32 (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))))))) % 6.00/6.32 (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))))))) % 6.00/6.32 (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)))))) % 6.00/6.32 (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)))))) % 6.00/6.32 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 6.00/6.32 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 6.00/6.32 (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)))))) % 6.00/6.32 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 6.00/6.32 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 6.00/6.32 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 6.00/6.32 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 6.00/6.32 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 6.00/6.32 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 6.00/6.32 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 6.00/6.32 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 6.00/6.32 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 6.00/6.32 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 6.00/6.32 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 6.00/6.32 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 6.00/6.32 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 6.00/6.32 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 6.00/6.32 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 6.00/6.32 (define @t2 () (@var "A" (-> $$unsorted Bool))) % 6.00/6.32 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 6.00/6.32 (define @t4 () (_ tptp.mbox @t3)) % 6.00/6.32 (define @t5 () (@list @t2 @t1)) % 6.00/6.32 (define @t6 () (lambda @t5 (_ (_ (_ tptp.mequiv (_ (_ tptp.mdia @t3) @t2)) (_ @t4 @t2)) @t1))) % 6.00/6.32 (define @t7 () (=> (_ tptp.mfunctional @t3) (_ tptp.mvalid (_ tptp.mforall_prop @t6)))) % 6.00/6.32 (define @t8 () (@list @t3)) % 6.00/6.32 (define @t9 () (forall @t8 @t7)) % 6.00/6.32 (define @t10 () (not @t9)) % 6.00/6.32 (define @t11 () (@var "Y" tptp.mu)) % 6.00/6.32 (define @t12 () (@var "X" tptp.mu)) % 6.00/6.32 (define @t13 () (@var "W" $$unsorted)) % 6.00/6.32 (define @t14 () (lambda (@list @t12 @t11 @t13) (= @t12 @t11))) % 6.00/6.32 (define @t15 () (@var "Y" (-> $$unsorted Bool))) % 6.00/6.32 (define @t16 () (@var "X" (-> $$unsorted Bool))) % 6.00/6.32 (define @t17 () (lambda (@list @t16 @t15 @t13) (= (_ @t16 @t13) (_ @t15 @t13)))) % 6.00/6.32 (define @t18 () (@var "Phi" (-> $$unsorted Bool))) % 6.00/6.32 (define @t19 () (_ @t18 @t13)) % 6.00/6.32 (define @t20 () (not @t19)) % 6.00/6.32 (define @t21 () (@list @t18 @t13)) % 6.00/6.32 (define @t22 () (lambda @t21 @t20)) % 6.00/6.32 (define @t23 () (@var "Psi" (-> $$unsorted Bool))) % 6.00/6.32 (define @t24 () (_ @t23 @t13)) % 6.00/6.32 (define @t25 () (lambda (@list @t18 @t23 @t13) (or @t19 @t24))) % 6.00/6.32 (define @t26 () (_ tptp.mnot @t23)) % 6.00/6.32 (define @t27 () (_ tptp.mnot @t18)) % 6.00/6.32 (define @t28 () (_ tptp.mor @t27)) % 6.00/6.32 (define @t29 () (@list @t18 @t23 @t1)) % 6.00/6.32 (define @t30 () (lambda @t29 (_ (_ tptp.mnot (_ @t28 @t26)) @t1))) % 6.00/6.32 (define @t31 () (lambda @t29 (_ (_ @t28 @t23) @t1))) % 6.00/6.32 (define @t32 () (lambda @t29 (_ (_ (_ tptp.mor @t26) @t18) @t1))) % 6.00/6.32 (define @t33 () (lambda @t29 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t18) @t23)) (_ (_ tptp.mimplies @t23) @t18)) @t1))) % 6.00/6.32 (define @t34 () (lambda @t29 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t18) @t23)) @t1))) % 6.00/6.32 (define @t35 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 6.00/6.32 (define @t36 () (_ @t35 @t12)) % 6.00/6.32 (define @t37 () (lambda (@list @t35 @t13) (forall (@list @t12) (_ @t36 @t13)))) % 6.00/6.32 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 6.00/6.32 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 6.00/6.32 (define @t40 () (_ @t39 @t38)) % 6.00/6.32 (define @t41 () (_ @t40 @t13)) % 6.00/6.32 (define @t42 () (@list @t38)) % 6.00/6.32 (define @t43 () (forall @t42 @t41)) % 6.00/6.32 (define @t44 () (@list @t39 @t13)) % 6.00/6.32 (define @t45 () (lambda @t44 @t43)) % 6.00/6.32 (define @t46 () (lambda (@list @t35 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t12 @t1) (_ (_ tptp.mnot @t36) @t1)))) @t1))) % 6.00/6.32 (define @t47 () (lambda (@list @t39 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t1) (_ (_ tptp.mnot @t40) @t1)))) @t1))) % 6.00/6.32 (define @t48 () (@list @t13)) % 6.00/6.32 (define @t49 () (lambda @t48 true)) % 6.00/6.32 (define @t50 () (@var "V" $$unsorted)) % 6.00/6.32 (define @t51 () (_ @t18 @t50)) % 6.00/6.32 (define @t52 () (_ (_ @t3 @t13) @t50)) % 6.00/6.32 (define @t53 () (not @t52)) % 6.00/6.32 (define @t54 () (or @t53 @t51)) % 6.00/6.32 (define @t55 () (@list @t50)) % 6.00/6.32 (define @t56 () (forall @t55 @t54)) % 6.00/6.32 (define @t57 () (@list @t3 @t18 @t13)) % 6.00/6.32 (define @t58 () (lambda @t57 @t56)) % 6.00/6.32 (define @t59 () (@list @t3 @t18 @t1)) % 6.00/6.32 (define @t60 () (lambda @t59 (_ (_ tptp.mnot (_ @t4 @t27)) @t1))) % 6.00/6.32 (define @t61 () (@var "S" $$unsorted)) % 6.00/6.32 (define @t62 () (_ @t3 @t61)) % 6.00/6.32 (define @t63 () (@list @t61)) % 6.00/6.32 (define @t64 () (lambda @t8 (forall @t63 (_ @t62 @t61)))) % 6.00/6.32 (define @t65 () (@var "T" $$unsorted)) % 6.00/6.32 (define @t66 () (_ @t3 @t65)) % 6.00/6.32 (define @t67 () (_ @t62 @t65)) % 6.00/6.32 (define @t68 () (lambda @t8 (forall (@list @t61 @t65) (=> @t67 (_ @t66 @t61))))) % 6.00/6.32 (define @t69 () (@list @t65)) % 6.00/6.32 (define @t70 () (lambda @t8 (forall @t63 (exists @t69 @t67)))) % 6.00/6.32 (define @t71 () (@var "U" $$unsorted)) % 6.00/6.32 (define @t72 () (_ @t62 @t71)) % 6.00/6.32 (define @t73 () (_ @t66 @t71)) % 6.00/6.32 (define @t74 () (@list @t61 @t65 @t71)) % 6.00/6.32 (define @t75 () (lambda @t8 (forall @t74 (=> (and @t67 @t73) @t72)))) % 6.00/6.32 (define @t76 () (and @t67 @t72)) % 6.00/6.32 (define @t77 () (lambda @t8 (forall @t74 (=> @t76 @t73)))) % 6.00/6.32 (define @t78 () (= @t65 @t71)) % 6.00/6.32 (define @t79 () (lambda @t8 (forall @t74 (=> @t76 @t78)))) % 6.00/6.32 (define @t80 () (@list @t71)) % 6.00/6.32 (define @t81 () (forall @t80 (=> @t72 @t78))) % 6.00/6.32 (define @t82 () (and @t67 @t81)) % 6.00/6.32 (define @t83 () (exists @t69 @t82)) % 6.00/6.32 (define @t84 () (forall @t63 @t83)) % 6.00/6.32 (define @t85 () (lambda @t8 @t84)) % 6.00/6.32 (define @t86 () (_ @t3 @t71)) % 6.00/6.32 (define @t87 () (_ @t86 @t65)) % 6.00/6.32 (define @t88 () (lambda @t8 (forall @t74 (=> @t67 (exists @t80 (and @t72 @t87)))))) % 6.00/6.32 (define @t89 () (lambda @t8 (forall @t74 (=> @t76 (or @t73 @t78 @t87))))) % 6.00/6.32 (define @t90 () (lambda @t8 (forall @t74 (=> @t76 (exists @t55 (and (_ @t66 @t50) (_ @t86 @t50))))))) % 6.00/6.32 (define @t91 () (forall @t48 @t19)) % 6.00/6.32 (define @t92 () (@list @t18)) % 6.00/6.32 (define @t93 () (lambda @t92 @t91)) % 6.00/6.32 (define @t94 () (lambda @t92 (forall @t48 @t20))) % 6.00/6.32 (define @t95 () (lambda @t92 (exists @t48 @t19))) % 6.00/6.32 (define @t96 () (lambda @t92 (exists @t48 @t20))) % 6.00/6.32 (define @t97 () (@var "BOUND_VARIABLE_8521" (-> $$unsorted Bool))) % 6.00/6.32 (define @t98 () (_ @t97 @t50)) % 6.00/6.32 (define @t99 () (@var "BOUND_VARIABLE_8519" $$unsorted)) % 6.00/6.32 (define @t100 () (not (_ @t3 @t99 @t50))) % 6.00/6.32 (define @t101 () (or (not (forall @t55 (or @t100 @t98))) (not (forall @t55 (or @t100 (not @t98)))))) % 6.00/6.32 (define @t102 () (@var "BOUND_VARIABLE_8509" $$unsorted)) % 6.00/6.32 (define @t103 () (@var "BOUND_VARIABLE_8505" (-> $$unsorted Bool))) % 6.00/6.32 (define @t104 () (@var "BOUND_VARIABLE_8503" $$unsorted)) % 6.00/6.32 (define @t105 () (@var "BOUND_VARIABLE_8507" $$unsorted)) % 6.00/6.32 (define @t106 () (or (not (_ @t3 @t104 @t105)) (not (_ @t103 @t105)) (not (_ @t3 @t104 @t102)) (_ @t103 @t102))) % 6.00/6.32 (define @t107 () (and @t106 @t101)) % 6.00/6.32 (define @t108 () (_ @t3 @t61 @t71)) % 6.00/6.32 (define @t109 () (forall @t80 (or (not @t108) @t78))) % 6.00/6.32 (define @t110 () (not @t109)) % 6.00/6.32 (define @t111 () (_ @t3 @t61 @t65)) % 6.00/6.32 (define @t112 () (forall @t63 (not (forall @t69 (or (not @t111) @t110))))) % 6.00/6.32 (define @t113 () (not @t112)) % 6.00/6.32 (define @t114 () (or @t113 @t107)) % 6.00/6.32 (define @t115 () (forall (@list @t3 @t104 @t103 @t105 @t102 @t99 @t97) @t114)) % 6.00/6.32 (define @t116 () (@list @t104 @t103 @t105 @t102 @t99 @t97)) % 6.00/6.32 (define @t117 () (forall @t116 @t114)) % 6.00/6.32 (define @t118 () (forall (@list @t99 @t97) @t101)) % 6.00/6.32 (define @t119 () (@var "BOUND_VARIABLE_8430" (-> $$unsorted Bool))) % 6.00/6.32 (define @t120 () (@var "BOUND_VARIABLE_8478" $$unsorted)) % 6.00/6.32 (define @t121 () (forall @t116 @t101)) % 6.00/6.32 (define @t122 () (forall (@list @t104 @t103 @t105 @t102) @t106)) % 6.00/6.32 (define @t123 () (@var "BOUND_VARIABLE_8451" $$unsorted)) % 6.00/6.32 (define @t124 () (@var "BOUND_VARIABLE_8444" $$unsorted)) % 6.00/6.32 (define @t125 () (@var "BOUND_VARIABLE_8419" (-> $$unsorted Bool))) % 6.00/6.32 (define @t126 () (@var "BOUND_VARIABLE_8468" $$unsorted)) % 6.00/6.32 (define @t127 () (forall @t116 @t106)) % 6.00/6.32 (define @t128 () (and @t127 @t121)) % 6.00/6.32 (define @t129 () (forall @t116 @t107)) % 6.00/6.32 (define @t130 () (or @t113 @t129)) % 6.00/6.32 (define @t131 () (_ @t119 @t50)) % 6.00/6.32 (define @t132 () (not @t131)) % 6.00/6.32 (define @t133 () (not (_ @t3 @t120 @t50))) % 6.00/6.32 (define @t134 () (or (not (forall @t55 (or @t133 @t131))) (not (forall @t55 (or @t133 @t132))))) % 6.00/6.32 (define @t135 () (forall (@list @t120 @t119) @t134)) % 6.00/6.32 (define @t136 () (_ @t125 @t123)) % 6.00/6.32 (define @t137 () (not (_ @t125 @t124))) % 6.00/6.32 (define @t138 () (or (not (_ @t3 @t126 @t124)) @t137 (not (_ @t3 @t126 @t123)) @t136)) % 6.00/6.32 (define @t139 () (forall (@list @t126 @t125 @t124 @t123) @t138)) % 6.00/6.32 (define @t140 () (and @t139 @t135)) % 6.00/6.32 (define @t141 () (@list @t119)) % 6.00/6.32 (define @t142 () (forall (@list @t120) (forall @t141 @t134))) % 6.00/6.32 (define @t143 () (@list @t125 @t124 @t123)) % 6.00/6.32 (define @t144 () (forall (@list @t126) (forall @t143 @t138))) % 6.00/6.32 (define @t145 () (_ @t3 @t13 @t50)) % 6.00/6.32 (define @t146 () (not @t145)) % 6.00/6.32 (define @t147 () (forall @t141 (or (not (forall @t55 (or @t146 @t131))) (not (forall @t55 (or @t146 @t132)))))) % 6.00/6.32 (define @t148 () (forall @t48 @t147)) % 6.00/6.32 (define @t149 () (@list @t13)) % 6.00/6.32 (define @t150 () (not (_ @t3 @t13 @t123))) % 6.00/6.32 (define @t151 () (not (_ @t3 @t13 @t124))) % 6.00/6.32 (define @t152 () (or @t151 @t137 @t150 @t136)) % 6.00/6.32 (define @t153 () (forall @t143 @t152)) % 6.00/6.32 (define @t154 () (forall @t48 @t153)) % 6.00/6.32 (define @t155 () (and @t154 @t148)) % 6.00/6.32 (define @t156 () (and @t153 @t147)) % 6.00/6.32 (define @t157 () (lambda @t48 @t156)) % 6.00/6.32 (define @t158 () (_ @t157 @t13)) % 6.00/6.32 (define @t159 () (forall @t48 @t158)) % 6.00/6.32 (define @t160 () (_ @t18 @t13)) % 6.00/6.32 (define @t161 () (lambda @t92 (forall @t48 @t160))) % 6.00/6.32 (define @t162 () (or @t150 @t136)) % 6.00/6.32 (define @t163 () (or @t151 @t137)) % 6.00/6.32 (define @t164 () (or @t163 @t162)) % 6.00/6.32 (define @t165 () (forall @t143 @t164)) % 6.00/6.32 (define @t166 () (forall (@list @t124 @t123) @t164)) % 6.00/6.32 (define @t167 () (@list @t125)) % 6.00/6.32 (define @t168 () (forall (@list @t123) @t162)) % 6.00/6.32 (define @t169 () (@list @t50)) % 6.00/6.32 (define @t170 () (forall (@list @t124) @t163)) % 6.00/6.32 (define @t171 () (or @t170 @t168)) % 6.00/6.32 (define @t172 () (_ @t125 @t50)) % 6.00/6.32 (define @t173 () (forall @t167 (or (forall @t55 (or @t146 (not @t172))) (forall @t55 (or @t146 @t172))))) % 6.00/6.32 (define @t174 () (_ @t38 @t50)) % 6.00/6.32 (define @t175 () (forall @t55 (or @t146 (not @t174)))) % 6.00/6.32 (define @t176 () (forall @t55 (or @t146 @t174))) % 6.00/6.32 (define @t177 () (or (not @t176) (not @t175))) % 6.00/6.32 (define @t178 () (forall @t42 @t177)) % 6.00/6.32 (define @t179 () (@list @t38)) % 6.00/6.32 (define @t180 () (or @t175 @t176)) % 6.00/6.32 (define @t181 () (forall @t42 @t180)) % 6.00/6.32 (define @t182 () (and @t181 @t178)) % 6.00/6.32 (define @t183 () (not @t177)) % 6.00/6.32 (define @t184 () (not @t180)) % 6.00/6.32 (define @t185 () (not (or @t184 @t183))) % 6.00/6.32 (define @t186 () (_ @t2 @t50)) % 6.00/6.32 (define @t187 () (not (_ @t3 @t1 @t50))) % 6.00/6.32 (define @t188 () (forall @t55 (or @t187 (not @t186)))) % 6.00/6.32 (define @t189 () (not @t188)) % 6.00/6.32 (define @t190 () (forall @t55 (or @t187 @t186))) % 6.00/6.32 (define @t191 () (not (or (not (or @t188 @t190)) (not (or (not @t190) @t189))))) % 6.00/6.32 (define @t192 () (lambda @t5 @t191)) % 6.00/6.32 (define @t193 () (_ @t192 @t38 @t13)) % 6.00/6.32 (define @t194 () (forall @t42 @t193)) % 6.00/6.32 (define @t195 () (lambda @t48 @t194)) % 6.00/6.32 (define @t196 () (_ @t39 @t38 @t13)) % 6.00/6.32 (define @t197 () (lambda @t44 (forall @t42 @t196))) % 6.00/6.32 (define @t198 () (@list @t1)) % 6.00/6.32 (define @t199 () (lambda @t48 (forall @t55 (or @t146 @t186)))) % 6.00/6.32 (define @t200 () (_ @t199 @t1)) % 6.00/6.32 (define @t201 () (not @t200)) % 6.00/6.32 (define @t202 () (or @t201 @t189)) % 6.00/6.32 (define @t203 () (not @t202)) % 6.00/6.32 (define @t204 () (or @t188 @t200)) % 6.00/6.32 (define @t205 () (not @t204)) % 6.00/6.32 (define @t206 () (or @t205 @t203)) % 6.00/6.32 (define @t207 () (not @t206)) % 6.00/6.32 (define @t208 () (lambda @t198 @t207)) % 6.00/6.32 (define @t209 () (_ @t23 @t1)) % 6.00/6.32 (define @t210 () (not @t209)) % 6.00/6.32 (define @t211 () (@list @t23 @t1)) % 6.00/6.32 (define @t212 () (_ @t18 @t50)) % 6.00/6.32 (define @t213 () (forall @t55 (or @t146 @t212))) % 6.00/6.32 (define @t214 () (lambda @t21 @t213)) % 6.00/6.32 (define @t215 () (_ (lambda @t57 @t213) @t3)) % 6.00/6.32 (define @t216 () (lambda @t198 @t189)) % 6.00/6.32 (define @t217 () (_ @t216 @t1)) % 6.00/6.32 (define @t218 () (or @t210 @t217)) % 6.00/6.32 (define @t219 () (not @t218)) % 6.00/6.32 (define @t220 () (not @t217)) % 6.00/6.32 (define @t221 () (or @t220 @t209)) % 6.00/6.32 (define @t222 () (not @t221)) % 6.00/6.32 (define @t223 () (or @t222 @t219)) % 6.00/6.32 (define @t224 () (not @t223)) % 6.00/6.32 (define @t225 () (lambda @t211 @t224)) % 6.00/6.32 (define @t226 () (_ @t18 @t1)) % 6.00/6.32 (define @t227 () (or @t210 @t226)) % 6.00/6.32 (define @t228 () (not @t226)) % 6.00/6.32 (define @t229 () (or @t228 @t209)) % 6.00/6.32 (define @t230 () (not @t229)) % 6.00/6.32 (define @t231 () (not (or @t230 (not @t227)))) % 6.00/6.32 (define @t232 () (lambda @t29 @t231)) % 6.00/6.32 (define @t233 () (not @t212)) % 6.00/6.32 (define @t234 () (not (forall @t55 (or @t187 @t233)))) % 6.00/6.33 (define @t235 () (lambda (@list @t18 @t1) @t234)) % 6.00/6.33 (define @t236 () (_ (lambda @t59 @t234) @t3)) % 6.00/6.33 (define @t237 () (lambda @t5 (_ (_ (_ @t232 (_ @t236 @t2)) (_ @t215 @t2)) @t1))) % 6.00/6.33 (define @t238 () (_ (lambda @t8 @t112) @t3)) % 6.00/6.33 (define @t239 () (=> @t238 (_ @t161 (_ @t197 @t237)))) % 6.00/6.33 (define @t240 () (forall @t8 @t239)) % 6.00/6.33 (define @t241 () (forall @t55 (or @t146 @t233))) % 6.00/6.33 (define @t242 () (lambda @t48 @t241)) % 6.00/6.33 (define @t243 () (_ @t242 @t13)) % 6.00/6.33 (define @t244 () (not @t243)) % 6.00/6.33 (define @t245 () (lambda @t48 @t244)) % 6.00/6.33 (define @t246 () (not @t51)) % 6.00/6.33 (define @t247 () (or @t146 @t246)) % 6.00/6.33 (define @t248 () (lambda @t48 @t20)) % 6.00/6.33 (define @t249 () (_ @t248 @t50)) % 6.00/6.33 (define @t250 () (or @t146 @t249)) % 6.00/6.33 (define @t251 () (forall @t55 @t250)) % 6.00/6.33 (define @t252 () (lambda @t48 @t251)) % 6.00/6.33 (define @t253 () (lambda @t198 @t227)) % 6.00/6.33 (define @t254 () (_ @t253 @t1)) % 6.00/6.33 (define @t255 () (not @t254)) % 6.00/6.33 (define @t256 () (or @t230 @t255)) % 6.00/6.33 (define @t257 () (not @t256)) % 6.00/6.33 (define @t258 () (lambda @t198 @t257)) % 6.00/6.33 (define @t259 () (@var "BOUND_VARIABLE_7581" (-> $$unsorted Bool))) % 6.00/6.33 (define @t260 () (not (_ @t259 @t1))) % 6.00/6.33 (define @t261 () (@list @t259 @t1)) % 6.00/6.33 (define @t262 () (@var "BOUND_VARIABLE_7601" (-> $$unsorted Bool))) % 6.00/6.33 (define @t263 () (_ @t262 @t1)) % 6.00/6.33 (define @t264 () (lambda (@list @t262 @t1) (or @t210 @t263))) % 6.00/6.33 (define @t265 () (lambda @t29 @t229)) % 6.00/6.33 (define @t266 () (@list @t23)) % 6.00/6.33 (define @t267 () (lambda @t198 @t229)) % 6.00/6.33 (define @t268 () (_ @t267 @t1)) % 6.00/6.33 (define @t269 () (not @t268)) % 6.00/6.33 (define @t270 () (or @t269 @t260)) % 6.00/6.33 (define @t271 () (not @t270)) % 6.00/6.33 (define @t272 () (lambda @t261 @t271)) % 6.00/6.33 (define @t273 () (not (or @t228 @t210))) % 6.00/6.33 (define @t274 () (lambda @t29 @t273)) % 6.00/6.33 (define @t275 () (lambda @t211 @t229)) % 6.00/6.33 (define @t276 () (or @t20 @t24)) % 6.00/6.33 (define @t277 () (lambda @t48 @t276)) % 6.00/6.33 (define @t278 () (@list @t23 @t13)) % 6.00/6.33 (define @t279 () (lambda @t278 @t276)) % 6.00/6.33 (define @t280 () (_ @t248 @t13)) % 6.00/6.33 (define @t281 () (or @t280 @t24)) % 6.00/6.33 (define @t282 () (lambda @t278 @t281)) % 6.00/6.33 (define @t283 () (not @t24)) % 6.00/6.33 (define @t284 () (or @t20 @t283)) % 6.00/6.33 (define @t285 () (lambda @t48 @t284)) % 6.00/6.33 (define @t286 () (_ @t285 @t13)) % 6.00/6.33 (define @t287 () (not @t286)) % 6.00/6.33 (define @t288 () (lambda @t48 @t287)) % 6.00/6.33 (define @t289 () (lambda @t48 @t283)) % 6.00/6.33 (define @t290 () (_ @t289 @t13)) % 6.00/6.33 (define @t291 () (or @t20 @t290)) % 6.00/6.33 (define @t292 () (lambda @t48 @t291)) % 6.00/6.33 (define @t293 () (not @t67)) % 6.00/6.33 (define @t294 () (or @t293 @t110)) % 6.00/6.33 (define @t295 () (and @t67 @t109)) % 6.00/6.33 (define @t296 () (forall @t69 (not @t295))) % 6.00/6.33 (define @t297 () (not @t296)) % 6.00/6.33 (define @t298 () (not @t72)) % 6.00/6.33 (define @t299 () (or @t298 @t78)) % 6.00/6.33 (define @t300 () (@quantifiers_skolemize @t115 0)) % 6.00/6.33 (define @t301 () (forall @t63 (not (forall @t69 (or (not (_ @t300 @t61 @t65)) (not (forall @t80 (or (not (_ @t300 @t61 @t71)) @t78)))))))) % 6.00/6.33 (define @t302 () (@quantifiers_skolemize @t115 6)) % 6.00/6.33 (define @t303 () (_ @t302 @t50)) % 6.00/6.33 (define @t304 () (@quantifiers_skolemize @t115 5)) % 6.00/6.33 (define @t305 () (not (_ @t300 @t304 @t50))) % 6.00/6.33 (define @t306 () (forall @t55 (or @t305 (not @t303)))) % 6.00/6.33 (define @t307 () (not @t306)) % 6.00/6.33 (define @t308 () (forall @t55 (or @t305 @t303))) % 6.00/6.33 (define @t309 () (not @t308)) % 6.00/6.33 (define @t310 () (or @t309 @t307)) % 6.00/6.33 (define @t311 () (@quantifiers_skolemize @t115 4)) % 6.00/6.33 (define @t312 () (@quantifiers_skolemize @t115 2)) % 6.00/6.33 (define @t313 () (_ @t312 @t311)) % 6.00/6.33 (define @t314 () (@quantifiers_skolemize @t115 1)) % 6.00/6.33 (define @t315 () (_ @t300 @t314 @t311)) % 6.00/6.33 (define @t316 () (not @t315)) % 6.00/6.33 (define @t317 () (@quantifiers_skolemize @t115 3)) % 6.00/6.33 (define @t318 () (_ @t312 @t317)) % 6.00/6.33 (define @t319 () (not @t318)) % 6.00/6.33 (define @t320 () (_ @t300 @t314 @t317)) % 6.00/6.33 (define @t321 () (not @t320)) % 6.00/6.33 (define @t322 () (or @t321 @t319 @t316 @t313)) % 6.00/6.33 (define @t323 () (and @t322 @t310)) % 6.00/6.33 (define @t324 () (not @t301)) % 6.00/6.33 (define @t325 () (or @t324 @t323)) % 6.00/6.33 (define @t326 () (@list true)) % 6.00/6.33 (define @t327 () (@list @t325)) % 6.00/6.33 (define @t328 () (not (_ @t300 @t314 @t71))) % 6.00/6.33 (define @t329 () (forall @t69 (or (not (_ @t300 @t314 @t65)) (not (forall @t80 (or @t328 @t78)))))) % 6.00/6.33 (define @t330 () (@quantifiers_skolemize @t329 0)) % 6.00/6.33 (define @t331 () (forall @t80 (or @t328 (= @t71 @t330)))) % 6.00/6.33 (define @t332 () (not @t331)) % 6.00/6.33 (define @t333 () (not (_ @t300 @t314 @t330))) % 6.00/6.33 (define @t334 () (or @t333 @t332)) % 6.00/6.33 (define @t335 () (not @t334)) % 6.00/6.33 (define @t336 () (not @t329)) % 6.00/6.33 (define @t337 () (or @t328 (= @t330 @t71))) % 6.00/6.33 (define @t338 () (forall @t80 @t337)) % 6.00/6.33 (define @t339 () (not @t338)) % 6.00/6.33 (define @t340 () (or @t333 @t339)) % 6.00/6.33 (define @t341 () (not @t340)) % 6.00/6.33 (define @t342 () (not (_ @t300 @t304 @t71))) % 6.00/6.33 (define @t343 () (forall @t69 (or (not (_ @t300 @t304 @t65)) (not (forall @t80 (or @t342 @t78)))))) % 6.00/6.33 (define @t344 () (@quantifiers_skolemize @t343 0)) % 6.00/6.33 (define @t345 () (@list @t344)) % 6.00/6.33 (define @t346 () (_ @t302 @t344)) % 6.00/6.33 (define @t347 () (not @t346)) % 6.00/6.33 (define @t348 () (_ @t300 @t304 @t344)) % 6.00/6.33 (define @t349 () (not @t348)) % 6.00/6.33 (define @t350 () (or @t349 @t347)) % 6.00/6.33 (define @t351 () (or @t349 @t346)) % 6.00/6.33 (define @t352 () (or @t349 (not (forall @t80 (or @t342 (= @t71 @t344)))))) % 6.00/6.33 (define @t353 () (not @t352)) % 6.00/6.33 (define @t354 () (not @t343)) % 6.00/6.33 (define @t355 () (or @t342 (= @t344 @t71))) % 6.00/6.33 (define @t356 () (forall @t80 @t355)) % 6.00/6.33 (define @t357 () (not @t356)) % 6.00/6.33 (define @t358 () (or @t349 @t357)) % 6.00/6.33 (define @t359 () (not @t358)) % 6.00/6.33 (define @t360 () (@list @t322)) % 6.00/6.33 (define @t361 () (= @t317 @t330)) % 6.00/6.33 (define @t362 () (or @t321 @t361)) % 6.00/6.33 (define @t363 () (@list false false)) % 6.00/6.33 (define @t364 () (= @t311 @t330)) % 6.00/6.33 (define @t365 () (or @t316 @t364)) % 6.00/6.33 (define @t366 () (and @t318 @t361 @t364)) % 6.00/6.33 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 6.00/6.33 (assume @p2 @t10) % 6.00/6.33 (assume @p3 true) % 6.00/6.33 (step @p4 (= tptp.meq_ind @t14) :rule refl :args (@t14)) % 6.00/6.33 (step @p5 (= tptp.meq_prop @t17) :rule refl :args (@t17)) % 6.00/6.33 (step @p6 (= tptp.mnot @t22) :rule refl :args (@t22)) % 6.00/6.33 (step @p7 (= tptp.mor @t25) :rule refl :args (@t25)) % 6.00/6.33 (step @p8 (= tptp.mand @t30) :rule refl :args (@t30)) % 6.00/6.33 (step @p9 (= tptp.mimplies @t31) :rule refl :args (@t31)) % 6.00/6.33 (step @p10 (= tptp.mimplied @t32) :rule refl :args (@t32)) % 6.00/6.33 (step @p11 (= tptp.mequiv @t33) :rule refl :args (@t33)) % 6.00/6.33 (step @p12 (= tptp.mxor @t34) :rule refl :args (@t34)) % 6.00/6.33 (step @p13 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 6.00/6.33 (step @p14 (= tptp.mforall_prop @t45) :rule refl :args (@t45)) % 6.00/6.33 (step @p15 (= tptp.mexists_ind @t46) :rule refl :args (@t46)) % 6.00/6.33 (step @p16 (= tptp.mexists_prop @t47) :rule refl :args (@t47)) % 6.00/6.33 (step @p17 (= tptp.mtrue @t49) :rule refl :args (@t49)) % 6.00/6.33 (step @p18 (= tptp.mbox @t58) :rule refl :args (@t58)) % 6.00/6.33 (step @p19 (= tptp.mdia @t60) :rule refl :args (@t60)) % 6.00/6.33 (step @p20 (= tptp.mreflexive @t64) :rule refl :args (@t64)) % 6.00/6.33 (step @p21 (= tptp.msymmetric @t68) :rule refl :args (@t68)) % 6.00/6.33 (step @p22 (= tptp.mserial @t70) :rule refl :args (@t70)) % 6.00/6.33 (step @p23 (= tptp.mtransitive @t75) :rule refl :args (@t75)) % 6.00/6.33 (step @p24 (= tptp.meuclidean @t77) :rule refl :args (@t77)) % 6.00/6.33 (step @p25 (= tptp.mpartially_functional @t79) :rule refl :args (@t79)) % 6.00/6.33 (step @p26 (= tptp.mfunctional @t85) :rule refl :args (@t85)) % 6.00/6.33 (step @p27 (= tptp.mweakly_dense @t88) :rule refl :args (@t88)) % 6.00/6.33 (step @p28 (= tptp.mweakly_connected @t89) :rule refl :args (@t89)) % 6.00/6.33 (step @p29 (= tptp.mweakly_directed @t90) :rule refl :args (@t90)) % 6.00/6.33 (step @p30 (= tptp.mvalid @t93) :rule refl :args (@t93)) % 6.00/6.33 (step @p31 (= tptp.minvalid @t94) :rule refl :args (@t94)) % 6.00/6.33 (step @p32 (= tptp.msatisfiable @t95) :rule refl :args (@t95)) % 6.00/6.33 (step @p33 (= tptp.mcountersatisfiable @t96) :rule refl :args (@t96)) % 6.00/6.33 (step @p34 :rule quant-merge-prenex :args ((= (forall @t8 @t117) @t115))) % 6.00/6.33 (step @p35 :rule alpha_equiv :args (@t118 (@list @t99 @t97) (@list @t120 @t119))) % 6.00/6.33 (step @p36 :rule quant-unused-vars :args ((= @t121 @t118))) % 6.00/6.33 (step @p37 :rule trans :premises (@p36 @p35)) % 6.00/6.33 (step @p38 :rule alpha_equiv :args (@t122 (@list @t104 @t103 @t105 @t102) (@list @t126 @t125 @t124 @t123))) % 6.00/6.33 (step @p39 :rule quant-unused-vars :args ((= @t127 @t122))) % 6.00/6.33 (step @p40 :rule trans :premises (@p39 @p38)) % 6.00/6.33 (step @p41 :rule nary_cong :premises (@p40 @p37) :args (@t128)) % 6.00/6.33 (step @p42 :rule quant-miniscope-and :args ((= @t129 @t128))) % 6.00/6.33 (step @p43 :rule trans :premises (@p42 @p41)) % 6.00/6.33 (step @p44 :rule refl :args (@t113)) % 6.00/6.33 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t130)) % 6.00/6.33 (step @p46 :rule quant-miniscope-or :args ((= @t117 @t130))) % 6.00/6.33 (step @p47 :rule trans :premises (@p46 @p45)) % 6.00/6.33 (step @p48 :rule symm :premises (@p47)) % 6.00/6.33 (step @p49 :rule cong :premises (@p48) :args ((forall @t8 (or @t113 @t140)))) % 6.00/6.33 (step @p50 :rule trans :premises (@p49 @p34)) % 6.00/6.33 (step @p51 :rule bool-impl-elim :args (@t112 @t140)) % 6.00/6.33 (step @p52 :rule cong :premises (@p51) :args ((forall @t8 (=> @t112 @t140)))) % 6.00/6.33 (step @p53 :rule trans :premises (@p52 @p50)) % 6.00/6.33 (step @p54 :rule quant-merge-prenex :args ((= @t142 @t135))) % 6.00/6.33 (step @p55 :rule quant-merge-prenex :args ((= @t144 @t139))) % 6.00/6.33 (step @p56 :rule nary_cong :premises (@p55 @p54) :args ((and @t144 @t142))) % 6.00/6.33 (step @p57 :rule alpha_equiv :args (@t148 @t149 (@list @t120))) % 6.00/6.33 (step @p58 :rule alpha_equiv :args (@t154 @t149 (@list @t126))) % 6.00/6.33 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t155)) % 6.00/6.33 (step @p60 :rule quant-miniscope-and :args ((= (forall @t48 @t156) @t155))) % 6.00/6.33 (step @p61 :rule trans :premises (@p60 @p59)) % 6.00/6.33 (step @p62 :rule trans :premises (@p61 @p56)) % 6.00/6.33 (step @p63 :rule beta-reduce :args ((= @t158 @t156))) % 6.00/6.33 (step @p64 :rule cong :premises (@p63) :args (@t159)) % 6.00/6.33 (step @p65 :rule trans :premises (@p64 @p62)) % 6.00/6.33 (step @p66 :rule beta-reduce :args ((= (_ @t161 @t157) @t159))) % 6.00/6.33 (step @p67 :rule trans :premises (@p66 @p65)) % 6.00/6.33 (step @p68 :rule refl :args (@t147)) % 6.00/6.33 (step @p69 :rule aci_norm :args ((= @t164 @t152))) % 6.00/6.33 (step @p70 :rule cong :premises (@p69) :args (@t165)) % 6.00/6.33 (step @p71 :rule quant-merge-prenex :args ((= (forall @t167 @t166) @t165))) % 6.00/6.33 (step @p72 :rule alpha_equiv :args (@t168 (@list @t123) @t169)) % 6.00/6.33 (step @p73 :rule alpha_equiv :args (@t170 (@list @t124) @t169)) % 6.00/6.33 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t171)) % 6.00/6.33 (step @p75 :rule quant-miniscope-or :args ((= @t166 @t171))) % 6.00/6.33 (step @p76 :rule trans :premises (@p75 @p74)) % 6.00/6.33 (step @p77 :rule symm :premises (@p76)) % 6.00/6.33 (step @p78 :rule cong :premises (@p77) :args (@t173)) % 6.00/6.33 (step @p79 :rule trans :premises (@p78 @p71)) % 6.00/6.33 (step @p80 :rule trans :premises (@p79 @p70)) % 6.00/6.33 (step @p81 :rule nary_cong :premises (@p80 @p68) :args ((and @t173 @t147))) % 6.00/6.33 (step @p82 :rule alpha_equiv :args (@t178 @t179 (@list @t119))) % 6.00/6.33 (step @p83 :rule alpha_equiv :args (@t181 @t179 (@list @t125))) % 6.00/6.33 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t182)) % 6.00/6.33 (step @p85 :rule quant-miniscope-and :args ((= (forall @t42 (and @t180 @t177)) @t182))) % 6.00/6.33 (step @p86 :rule trans :premises (@p85 @p84)) % 6.00/6.33 (step @p87 :rule trans :premises (@p86 @p81)) % 6.00/6.33 (step @p88 :rule bool-double-not-elim :args (@t177)) % 6.00/6.33 (step @p89 :rule bool-double-not-elim :args (@t180)) % 6.00/6.33 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((and (not @t184) (not @t183)))) % 6.00/6.33 (step @p91 :rule bool-or-de-morgan :args (@t184 @t183 false)) % 6.00/6.33 (step @p92 :rule trans :premises (@p91 @p90)) % 6.00/6.33 (step @p93 :rule cong :premises (@p92) :args ((forall @t42 @t185))) % 6.00/6.33 (step @p94 :rule trans :premises (@p93 @p87)) % 6.00/6.33 (step @p95 :rule beta-reduce :args ((= @t193 @t185))) % 6.00/6.33 (step @p96 :rule cong :premises (@p95) :args (@t194)) % 6.00/6.33 (step @p97 :rule trans :premises (@p96 @p94)) % 6.00/6.33 (step @p98 :rule cong :premises (@p97) :args (@t195)) % 6.00/6.33 (step @p99 :rule beta-reduce :args ((= (_ @t197 @t192) @t195))) % 6.00/6.33 (step @p100 :rule trans :premises (@p99 @p98)) % 6.00/6.33 (step @p101 :rule beta-reduce :args ((= (_ (lambda @t198 @t191) @t1) @t191))) % 6.00/6.33 (step @p102 :rule refl :args (@t1)) % 6.00/6.33 (step @p103 :rule refl :args (@t189)) % 6.00/6.33 (step @p104 :rule beta-reduce :args ((= @t200 @t190))) % 6.00/6.33 (step @p105 :rule cong :premises (@p104) :args (@t201)) % 6.00/6.33 (step @p106 :rule nary_cong :premises (@p105 @p103) :args (@t202)) % 6.00/6.33 (step @p107 :rule cong :premises (@p106) :args (@t203)) % 6.00/6.33 (step @p108 :rule refl :args (@t188)) % 6.00/6.33 (step @p109 :rule nary_cong :premises (@p108 @p104) :args (@t204)) % 6.00/6.33 (step @p110 :rule cong :premises (@p109) :args (@t205)) % 6.00/6.33 (step @p111 :rule nary_cong :premises (@p110 @p107) :args (@t206)) % 6.00/6.33 (step @p112 :rule cong :premises (@p111) :args (@t207)) % 6.00/6.33 (step @p113 :rule cong :premises (@p112) :args (@t208)) % 6.00/6.33 (step @p114 :rule beta-reduce :args ((= (_ (lambda @t211 (not (or (not (or @t188 @t209)) (not (or @t210 @t189))))) @t199) @t208))) % 6.00/6.33 (step @p115 :rule trans :premises (@p114 @p113)) % 6.00/6.33 (step @p116 :rule beta-reduce :args ((= (_ @t214 @t2) @t199))) % 6.00/6.33 (step @p117 :rule refl :args (@t2)) % 6.00/6.33 (step @p118 :rule beta-reduce :args ((= @t215 @t214))) % 6.00/6.33 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 6.00/6.33 (step @p120 :rule trans :premises (@p119 @p116)) % 6.00/6.33 (step @p121 :rule beta-reduce :args ((= @t217 @t189))) % 6.00/6.33 (step @p122 :rule refl :args (@t210)) % 6.00/6.33 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t218)) % 6.00/6.33 (step @p124 :rule cong :premises (@p123) :args (@t219)) % 6.00/6.33 (step @p125 :rule refl :args (@t209)) % 6.00/6.33 (step @p126 :rule bool-double-not-elim :args (@t188)) % 6.00/6.33 (step @p127 :rule cong :premises (@p121) :args (@t220)) % 6.00/6.33 (step @p128 :rule trans :premises (@p127 @p126)) % 6.00/6.33 (step @p129 :rule nary_cong :premises (@p128 @p125) :args (@t221)) % 6.00/6.33 (step @p130 :rule cong :premises (@p129) :args (@t222)) % 6.00/6.33 (step @p131 :rule nary_cong :premises (@p130 @p124) :args (@t223)) % 6.00/6.33 (step @p132 :rule cong :premises (@p131) :args (@t224)) % 6.00/6.33 (step @p133 :rule cong :premises (@p132) :args (@t225)) % 6.00/6.33 (step @p134 :rule beta-reduce :args ((= (_ @t232 @t216) @t225))) % 6.00/6.33 (step @p135 :rule trans :premises (@p134 @p133)) % 6.00/6.33 (step @p136 :rule beta-reduce :args ((= (_ @t235 @t2) @t216))) % 6.00/6.33 (step @p137 :rule beta-reduce :args ((= @t236 @t235))) % 6.00/6.33 (step @p138 :rule ho_cong :premises (@p137 @p117)) % 6.00/6.33 (step @p139 :rule trans :premises (@p138 @p136)) % 6.00/6.33 (step @p140 :rule refl :args (@t232)) % 6.00/6.33 (step @p141 :rule ho_cong :premises (@p140 @p139)) % 6.00/6.33 (step @p142 :rule trans :premises (@p141 @p135)) % 6.00/6.33 (step @p143 :rule ho_cong :premises (@p142 @p120)) % 6.00/6.33 (step @p144 :rule trans :premises (@p143 @p115)) % 6.00/6.33 (step @p145 :rule ho_cong :premises (@p144 @p102)) % 6.00/6.33 (step @p146 :rule trans :premises (@p145 @p101)) % 6.00/6.33 (step @p147 :rule cong :premises (@p146) :args (@t237)) % 6.00/6.33 (step @p148 :rule refl :args (@t197)) % 6.00/6.33 (step @p149 :rule ho_cong :premises (@p148 @p147)) % 6.00/6.33 (step @p150 :rule trans :premises (@p149 @p100)) % 6.00/6.33 (step @p151 :rule refl :args (@t161)) % 6.00/6.33 (step @p152 :rule ho_cong :premises (@p151 @p150)) % 6.00/6.33 (step @p153 :rule trans :premises (@p152 @p67)) % 6.00/6.33 (step @p154 :rule beta-reduce :args ((= @t238 @t112))) % 6.00/6.33 (step @p155 :rule cong :premises (@p154 @p153) :args (@t239)) % 6.00/6.33 (step @p156 :rule cong :premises (@p155) :args (@t240)) % 6.00/6.33 (step @p157 :rule trans :premises (@p156 @p53)) % 6.00/6.33 (step @p158 :rule cong :premises (@p157) :args ((not @t240))) % 6.00/6.33 (step @p159 :rule refl :args (@t3)) % 6.00/6.33 (step @p160 :rule refl :args (@t212)) % 6.00/6.33 (step @p161 :rule refl :args (@t51)) % 6.00/6.33 (step @p162 :rule cong :premises (@p161 @p160) :args ((= @t51 @t212))) % 6.00/6.33 (step @p163 :rule symm :premises (@p162)) % 6.00/6.33 (step @p164 :rule eq_resolve :premises (@p161 @p163)) % 6.00/6.33 (step @p165 :rule refl :args (@t145)) % 6.00/6.33 (step @p166 :rule refl :args (@t52)) % 6.00/6.33 (step @p167 :rule cong :premises (@p166 @p165) :args ((= @t52 @t145))) % 6.00/6.33 (step @p168 :rule symm :premises (@p167)) % 6.00/6.33 (step @p169 :rule eq_resolve :premises (@p166 @p168)) % 6.00/6.33 (step @p170 :rule cong :premises (@p169) :args (@t53)) % 6.00/6.33 (step @p171 :rule nary_cong :premises (@p170 @p164) :args (@t54)) % 6.00/6.33 (step @p172 :rule cong :premises (@p171) :args (@t56)) % 6.00/6.33 (step @p173 :rule cong :premises (@p172) :args (@t58)) % 6.00/6.33 (step @p174 :rule trans :premises (@p18 @p173)) % 6.00/6.33 (step @p175 :rule ho_cong :premises (@p174 @p159)) % 6.00/6.33 (step @p176 :rule ho_cong :premises (@p175 @p117)) % 6.00/6.33 (step @p177 :rule beta-reduce :args ((= (_ (lambda @t48 (not @t241)) @t1) @t234))) % 6.00/6.33 (step @p178 :rule beta-reduce :args ((= @t243 @t241))) % 6.00/6.33 (step @p179 :rule cong :premises (@p178) :args (@t244)) % 6.00/6.33 (step @p180 :rule cong :premises (@p179) :args (@t245)) % 6.00/6.33 (step @p181 :rule beta-reduce :args ((= (_ @t22 @t242) @t245))) % 6.00/6.33 (step @p182 :rule trans :premises (@p181 @p180)) % 6.00/6.33 (step @p183 :rule cong :premises (@p164) :args (@t246)) % 6.00/6.33 (step @p184 :rule refl :args (@t146)) % 6.00/6.33 (step @p185 :rule nary_cong :premises (@p184 @p183) :args (@t247)) % 6.00/6.33 (step @p186 :rule cong :premises (@p185) :args ((forall @t55 @t247))) % 6.00/6.33 (step @p187 :rule beta-reduce :args ((= @t249 @t246))) % 6.00/6.33 (step @p188 :rule refl :args (@t146)) % 6.00/6.33 (step @p189 :rule nary_cong :premises (@p188 @p187) :args (@t250)) % 6.00/6.33 (step @p190 :rule cong :premises (@p189) :args (@t251)) % 6.00/6.33 (step @p191 :rule trans :premises (@p190 @p186)) % 6.00/6.33 (step @p192 :rule cong :premises (@p191) :args (@t252)) % 6.00/6.33 (step @p193 :rule beta-reduce :args ((= (_ @t214 @t248) @t252))) % 6.00/6.33 (step @p194 :rule trans :premises (@p193 @p192)) % 6.00/6.33 (step @p195 :rule beta-reduce :args ((= (_ @t22 @t18) @t248))) % 6.00/6.33 (step @p196 :rule ho_cong :premises (@p118 @p195)) % 6.00/6.33 (step @p197 :rule trans :premises (@p196 @p194)) % 6.00/6.33 (step @p198 :rule refl :args (@t22)) % 6.00/6.33 (step @p199 :rule ho_cong :premises (@p198 @p197)) % 6.00/6.33 (step @p200 :rule trans :premises (@p199 @p182)) % 6.00/6.33 (step @p201 :rule ho_cong :premises (@p200 @p102)) % 6.00/6.33 (step @p202 :rule trans :premises (@p201 @p177)) % 6.00/6.33 (step @p203 :rule refl :args (@t18)) % 6.00/6.33 (step @p204 :rule ho_cong :premises (@p6 @p203)) % 6.00/6.33 (step @p205 :rule ho_cong :premises (@p175 @p204)) % 6.00/6.33 (step @p206 :rule ho_cong :premises (@p6 @p205)) % 6.00/6.33 (step @p207 :rule ho_cong :premises (@p206 @p102)) % 6.00/6.33 (step @p208 :rule trans :premises (@p207 @p202)) % 6.00/6.33 (step @p209 :rule cong :premises (@p208) :args (@t60)) % 6.00/6.33 (step @p210 :rule trans :premises (@p19 @p209)) % 6.00/6.33 (step @p211 :rule ho_cong :premises (@p210 @p159)) % 6.00/6.33 (step @p212 :rule ho_cong :premises (@p211 @p117)) % 6.00/6.33 (step @p213 :rule beta-reduce :args ((= (_ (lambda @t198 @t231) @t1) @t231))) % 6.00/6.33 (step @p214 :rule beta-reduce :args ((= @t254 @t227))) % 6.00/6.33 (step @p215 :rule cong :premises (@p214) :args (@t255)) % 6.00/6.33 (step @p216 :rule refl :args (@t230)) % 6.00/6.33 (step @p217 :rule nary_cong :premises (@p216 @p215) :args (@t256)) % 6.00/6.33 (step @p218 :rule cong :premises (@p217) :args (@t257)) % 6.00/6.33 (step @p219 :rule cong :premises (@p218) :args (@t258)) % 6.00/6.33 (step @p220 :rule beta-reduce :args ((= (_ (lambda @t261 (not (or @t230 @t260))) @t253) @t258))) % 6.00/6.33 (step @p221 :rule trans :premises (@p220 @p219)) % 6.00/6.33 (step @p222 :rule beta-reduce :args ((= (_ @t264 @t18) @t253))) % 6.00/6.33 (step @p223 :rule beta-reduce :args ((= (_ (lambda (@list @t18 @t262 @t1) (or @t228 @t263)) @t23) @t264))) % 6.00/6.33 (step @p224 :rule refl :args (@t23)) % 6.00/6.33 (step @p225 :rule alpha_equiv :args (@t265 @t266 (@list @t262))) % 6.00/6.33 (step @p226 :rule ho_cong :premises (@p225 @p224)) % 6.00/6.33 (step @p227 :rule trans :premises (@p226 @p223)) % 6.00/6.33 (step @p228 :rule ho_cong :premises (@p227 @p203)) % 6.00/6.33 (step @p229 :rule trans :premises (@p228 @p222)) % 6.00/6.33 (step @p230 :rule refl :args (@t260)) % 6.00/6.33 (step @p231 :rule beta-reduce :args ((= @t268 @t229))) % 6.00/6.33 (step @p232 :rule cong :premises (@p231) :args (@t269)) 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chain_m_resolution :premises (@p468 @p467 @p465) :args ((not @t322) (@list true false) (@list @t323 @t310))) % 6.00/6.33 (step @p470 :rule bool-double-not-elim :args (@t320)) % 6.00/6.33 (step @p471 :rule refl :args (@t322)) % 6.00/6.33 (step @p472 :rule nary_cong :premises (@p471 @p470) :args ((or @t322 (not @t321)))) % 6.00/6.33 (step @p473 :rule cnf_or_neg :args (@t322 0)) % 6.00/6.33 (step @p474 :rule eq_resolve :premises (@p473 @p472)) % 6.00/6.33 (step @p475 :rule reordering :premises (@p474) :args ((or @t320 @t322))) % 6.00/6.33 (step @p476 :rule chain_m_resolution :premises (@p475 @p469) :args (@t320 @t326 @t360)) % 6.00/6.33 (step @p477 :rule cnf_or_pos :args (@t362)) % 6.00/6.33 (step @p478 :rule reordering :premises (@p477) :args ((or @t321 @t361 (not @t362)))) % 6.00/6.33 (step @p479 :rule chain_m_resolution :premises (@p478 @p476 @p410) :args (@t361 @t363 (@list @t320 @t362))) % 6.00/6.33 (step @p480 :rule bool-double-not-elim :args (@t318)) % 6.00/6.33 (step @p481 :rule nary_cong :premises (@p471 @p480) :args ((or @t322 (not @t319)))) % 6.00/6.33 (step @p482 :rule cnf_or_neg :args (@t322 1)) % 6.00/6.33 (step @p483 :rule eq_resolve :premises (@p482 @p481)) % 6.00/6.33 (step @p484 :rule reordering :premises (@p483) :args ((or @t318 @t322))) % 6.00/6.33 (step @p485 :rule chain_m_resolution :premises (@p484 @p469) :args (@t318 @t326 @t360)) % 6.00/6.33 (step @p486 :rule cnf_or_neg :args (@t322 3)) % 6.00/6.33 (step @p487 :rule chain_m_resolution :premises (@p486 @p469) :args ((not @t313) @t326 @t360)) % 6.00/6.33 (step @p488 :rule instantiate :premises (@p409) :args ((@list @t311))) % 6.00/6.33 (step @p489 :rule bool-double-not-elim :args (@t315)) % 6.00/6.33 (step @p490 :rule nary_cong :premises (@p471 @p489) :args ((or @t322 (not @t316)))) % 6.00/6.33 (step @p491 :rule cnf_or_neg :args (@t322 2)) % 6.00/6.33 (step @p492 :rule eq_resolve :premises (@p491 @p490)) % 6.00/6.33 (step @p493 :rule reordering :premises (@p492) :args ((or @t315 @t322))) % 6.00/6.33 (step @p494 :rule chain_m_resolution :premises (@p493 @p469) :args (@t315 @t326 @t360)) % 6.00/6.33 (step @p495 :rule cnf_or_pos :args (@t365)) % 6.00/6.33 (step @p496 :rule reordering :premises (@p495) :args ((or @t316 @t364 (not @t365)))) % 6.00/6.33 (step @p497 :rule chain_m_resolution :premises (@p496 @p494 @p488) :args (@t364 @t363 (@list @t315 @t365))) % 6.00/6.33 (assume-push @p533 @t318) % 6.00/6.33 (assume-push @p534 @t361) % 6.00/6.33 (assume-push @p535 @t364) % 6.00/6.33 (assume-push @p536 @t318) % 6.00/6.33 (assume-push @p537 @t361) % 6.00/6.33 (assume-push @p538 @t364) % 6.00/6.33 (step @p504 :rule true_intro :premises (@p533)) % 6.00/6.33 (step @p505 :rule symm :premises (@p534)) % 6.00/6.33 (step @p506 :rule trans :premises (@p535 @p505)) % 6.00/6.33 (step @p507 :rule cong :premises (@p506) :args (@t313)) % 6.00/6.33 (step @p508 :rule trans :premises (@p507 @p504)) % 6.00/6.33 (step @p509 :rule true_elim :premises (@p508)) % 6.00/6.33 (step-pop @p539 :rule scope :premises (@p509)) % 6.00/6.33 (step-pop @p540 :rule scope :premises (@p539)) % 6.00/6.33 (step-pop @p541 :rule scope :premises (@p540)) % 6.00/6.33 (step @p510 :rule process_scope :premises (@p541) :args (@t313)) % 6.00/6.33 (step @p514 :rule and_intro :premises (@p533 @p534 @p535)) % 6.00/6.33 (step @p515 :rule modus_ponens :premises (@p514 @p510)) % 6.00/6.33 (step-pop @p542 :rule scope :premises (@p515)) % 6.00/6.33 (step-pop @p543 :rule scope :premises (@p542)) % 6.00/6.33 (step-pop @p544 :rule scope :premises (@p543)) % 6.00/6.33 (step @p516 :rule process_scope :premises (@p544) :args (@t313)) % 6.00/6.33 (step @p520 :rule implies_elim :premises (@p516)) % 6.00/6.33 (step @p521 :rule cnf_and_neg :args (@t366)) % 6.00/6.33 (step @p522 :rule resolution :premises (@p521 @p520) :args (true @t366)) % 6.00/6.33 (step @p523 :rule reordering :premises (@p522) :args ((or @t319 @t313 (not @t361) (not @t364)))) % 6.00/6.33 (step @p524 false :rule chain_m_resolution :premises (@p523 @p497 @p487 @p485 @p479) :args (false (@list false true false false) (@list @t364 @t313 @t318 @t361))) % 6.00/6.33 ) % 6.00/6.33 % SZS output end Proof % 6.00/6.33 % cvc5 exiting %------------------------------------------------------------------------------