%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL714^1 : TPTP v9.3.1. Bugfixed v5.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.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 11:23:41 AM UTC 2026 % Result : Theorem 0.29s 0.60s % Output : Proof 0.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL714^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.08/0.35 % Computer : n019.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Sat Sep 5 11:59:23 UTC 2026 % 0.08/0.35 % CPUTime : % 0.13/0.42 %----Proving TH0 % 0.29/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.29/0.60 % SZS status Theorem % 0.29/0.60 % SZS output start Proof % 0.29/0.60 ( % 0.29/0.60 (declare-sort $$unsorted 0) % 0.29/0.60 (declare-sort tptp.mu 0) % 0.29/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.29/0.60 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.29/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.29/0.60 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.29/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.29/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.29/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.29/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.29/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.29/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.29/0.60 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.29/0.60 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.29/0.60 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.29/0.60 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.29/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.29/0.60 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.29/0.60 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.29/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.29/0.60 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.29/0.60 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.29/0.60 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.29/0.60 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.29/0.60 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.29/0.60 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.29/0.60 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.29/0.60 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.29/0.60 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.29/0.60 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.29/0.60 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.29/0.60 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.29/0.60 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.29/0.60 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.29/0.60 (define @t2 () (@var "__flatten_var_0" $$unsorted)) % 0.29/0.60 (define @t3 () (@var "A" (-> $$unsorted Bool))) % 0.29/0.60 (define @t4 () (_ tptp.mbox @t1)) % 0.29/0.60 (define @t5 () (@list @t3 @t2)) % 0.29/0.60 (define @t6 () (lambda @t5 (_ (_ (_ tptp.mimplies (_ (_ tptp.mdia @t1) @t3)) (_ @t4 @t3)) @t2))) % 0.29/0.60 (define @t7 () (=> (_ tptp.mvalid (_ tptp.mforall_prop @t6)) (_ tptp.mpartially_functional @t1))) % 0.29/0.60 (define @t8 () (@list @t1)) % 0.29/0.60 (define @t9 () (forall @t8 @t7)) % 0.29/0.60 (define @t10 () (not @t9)) % 0.29/0.60 (define @t11 () (@var "Y" tptp.mu)) % 0.29/0.60 (define @t12 () (@var "X" tptp.mu)) % 0.29/0.60 (define @t13 () (@var "W" $$unsorted)) % 0.29/0.60 (define @t14 () (lambda (@list @t12 @t11 @t13) (= @t12 @t11))) % 0.29/0.60 (define @t15 () (@var "Y" (-> $$unsorted Bool))) % 0.29/0.60 (define @t16 () (@var "X" (-> $$unsorted Bool))) % 0.29/0.60 (define @t17 () (lambda (@list @t16 @t15 @t13) (= (_ @t16 @t13) (_ @t15 @t13)))) % 0.29/0.60 (define @t18 () (@var "Phi" (-> $$unsorted Bool))) % 0.29/0.60 (define @t19 () (_ @t18 @t13)) % 0.29/0.60 (define @t20 () (not @t19)) % 0.29/0.60 (define @t21 () (@list @t18 @t13)) % 0.29/0.60 (define @t22 () (lambda @t21 @t20)) % 0.29/0.60 (define @t23 () (@var "Psi" (-> $$unsorted Bool))) % 0.29/0.60 (define @t24 () (_ @t23 @t13)) % 0.29/0.60 (define @t25 () (lambda (@list @t18 @t23 @t13) (or @t19 @t24))) % 0.29/0.60 (define @t26 () (_ tptp.mnot @t23)) % 0.29/0.60 (define @t27 () (_ tptp.mnot @t18)) % 0.29/0.60 (define @t28 () (_ tptp.mor @t27)) % 0.29/0.60 (define @t29 () (@list @t18 @t23 @t2)) % 0.29/0.60 (define @t30 () (lambda @t29 (_ (_ tptp.mnot (_ @t28 @t26)) @t2))) % 0.29/0.60 (define @t31 () (lambda @t29 (_ (_ @t28 @t23) @t2))) % 0.29/0.60 (define @t32 () (lambda @t29 (_ (_ (_ tptp.mor @t26) @t18) @t2))) % 0.29/0.60 (define @t33 () (lambda @t29 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t18) @t23)) (_ (_ tptp.mimplies @t23) @t18)) @t2))) % 0.29/0.60 (define @t34 () (lambda @t29 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t18) @t23)) @t2))) % 0.29/0.60 (define @t35 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.29/0.60 (define @t36 () (_ @t35 @t12)) % 0.29/0.60 (define @t37 () (lambda (@list @t35 @t13) (forall (@list @t12) (_ @t36 @t13)))) % 0.29/0.60 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 0.29/0.60 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.29/0.60 (define @t40 () (_ @t39 @t38)) % 0.29/0.60 (define @t41 () (_ @t40 @t13)) % 0.29/0.60 (define @t42 () (@list @t38)) % 0.29/0.60 (define @t43 () (forall @t42 @t41)) % 0.29/0.60 (define @t44 () (@list @t39 @t13)) % 0.29/0.60 (define @t45 () (lambda @t44 @t43)) % 0.29/0.60 (define @t46 () (lambda (@list @t35 @t2) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t12 @t2) (_ (_ tptp.mnot @t36) @t2)))) @t2))) % 0.29/0.60 (define @t47 () (lambda (@list @t39 @t2) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t2) (_ (_ tptp.mnot @t40) @t2)))) @t2))) % 0.29/0.60 (define @t48 () (@list @t13)) % 0.29/0.60 (define @t49 () (lambda @t48 true)) % 0.29/0.60 (define @t50 () (@var "V" $$unsorted)) % 0.29/0.60 (define @t51 () (_ @t18 @t50)) % 0.29/0.60 (define @t52 () (_ (_ @t1 @t13) @t50)) % 0.29/0.60 (define @t53 () (not @t52)) % 0.29/0.60 (define @t54 () (or @t53 @t51)) % 0.29/0.60 (define @t55 () (@list @t50)) % 0.29/0.60 (define @t56 () (forall @t55 @t54)) % 0.29/0.60 (define @t57 () (@list @t1 @t18 @t13)) % 0.29/0.60 (define @t58 () (lambda @t57 @t56)) % 0.29/0.60 (define @t59 () (@list @t1 @t18 @t2)) % 0.29/0.60 (define @t60 () (lambda @t59 (_ (_ tptp.mnot (_ @t4 @t27)) @t2))) % 0.29/0.60 (define @t61 () (@var "S" $$unsorted)) % 0.29/0.60 (define @t62 () (_ @t1 @t61)) % 0.29/0.60 (define @t63 () (@list @t61)) % 0.29/0.60 (define @t64 () (lambda @t8 (forall @t63 (_ @t62 @t61)))) % 0.29/0.60 (define @t65 () (@var "T" $$unsorted)) % 0.29/0.60 (define @t66 () (_ @t1 @t65)) % 0.29/0.60 (define @t67 () (_ @t62 @t65)) % 0.29/0.60 (define @t68 () (lambda @t8 (forall (@list @t61 @t65) (=> @t67 (_ @t66 @t61))))) % 0.29/0.60 (define @t69 () (@list @t65)) % 0.29/0.60 (define @t70 () (lambda @t8 (forall @t63 (exists @t69 @t67)))) % 0.29/0.60 (define @t71 () (@var "U" $$unsorted)) % 0.29/0.60 (define @t72 () (_ @t62 @t71)) % 0.29/0.60 (define @t73 () (_ @t66 @t71)) % 0.29/0.60 (define @t74 () (@list @t61 @t65 @t71)) % 0.29/0.60 (define @t75 () (lambda @t8 (forall @t74 (=> (and @t67 @t73) @t72)))) % 0.29/0.60 (define @t76 () (and @t67 @t72)) % 0.29/0.60 (define @t77 () (lambda @t8 (forall @t74 (=> @t76 @t73)))) % 0.29/0.60 (define @t78 () (= @t65 @t71)) % 0.29/0.60 (define @t79 () (forall @t74 (=> @t76 @t78))) % 0.29/0.60 (define @t80 () (lambda @t8 @t79)) % 0.29/0.60 (define @t81 () (@list @t71)) % 0.29/0.60 (define @t82 () (lambda @t8 (forall @t63 (exists @t69 (and @t67 (forall @t81 (=> @t72 @t78))))))) % 0.29/0.60 (define @t83 () (_ @t1 @t71)) % 0.29/0.60 (define @t84 () (_ @t83 @t65)) % 0.29/0.60 (define @t85 () (lambda @t8 (forall @t74 (=> @t67 (exists @t81 (and @t72 @t84)))))) % 0.29/0.60 (define @t86 () (lambda @t8 (forall @t74 (=> @t76 (or @t73 @t78 @t84))))) % 0.29/0.60 (define @t87 () (lambda @t8 (forall @t74 (=> @t76 (exists @t55 (and (_ @t66 @t50) (_ @t83 @t50))))))) % 0.29/0.60 (define @t88 () (forall @t48 @t19)) % 0.29/0.60 (define @t89 () (@list @t18)) % 0.29/0.60 (define @t90 () (lambda @t89 @t88)) % 0.29/0.60 (define @t91 () (lambda @t89 (forall @t48 @t20))) % 0.29/0.60 (define @t92 () (lambda @t89 (exists @t48 @t19))) % 0.29/0.60 (define @t93 () (lambda @t89 (exists @t48 @t20))) % 0.29/0.60 (define @t94 () (@var "BOUND_VARIABLE_8422" $$unsorted)) % 0.29/0.60 (define @t95 () (@var "BOUND_VARIABLE_8420" $$unsorted)) % 0.29/0.60 (define @t96 () (= @t95 @t94)) % 0.29/0.60 (define @t97 () (@var "BOUND_VARIABLE_8418" $$unsorted)) % 0.29/0.60 (define @t98 () (not (_ @t1 @t97 @t94))) % 0.29/0.60 (define @t99 () (not (_ @t1 @t97 @t95))) % 0.29/0.60 (define @t100 () (@var "BOUND_VARIABLE_8395" $$unsorted)) % 0.29/0.60 (define @t101 () (_ @t38 @t100)) % 0.29/0.60 (define @t102 () (not (_ @t1 @t13 @t100))) % 0.29/0.60 (define @t103 () (@var "BOUND_VARIABLE_8388" $$unsorted)) % 0.29/0.60 (define @t104 () (not (_ @t38 @t103))) % 0.29/0.60 (define @t105 () (not (_ @t1 @t13 @t103))) % 0.29/0.60 (define @t106 () (or @t105 @t104 @t102 @t101)) % 0.29/0.60 (define @t107 () (@list @t13 @t38 @t103 @t100)) % 0.29/0.60 (define @t108 () (forall @t107 @t106)) % 0.29/0.60 (define @t109 () (not @t108)) % 0.29/0.60 (define @t110 () (or @t109 @t99 @t98 @t96)) % 0.29/0.60 (define @t111 () (or @t99 @t98 @t96)) % 0.29/0.60 (define @t112 () (or @t109 @t111)) % 0.29/0.60 (define @t113 () (@list @t1 @t97 @t95 @t94)) % 0.29/0.60 (define @t114 () (forall @t113 @t112)) % 0.29/0.60 (define @t115 () (@list @t97 @t95 @t94)) % 0.29/0.60 (define @t116 () (forall @t115 @t112)) % 0.29/0.60 (define @t117 () (forall @t115 @t111)) % 0.29/0.60 (define @t118 () (or @t109 @t117)) % 0.29/0.60 (define @t119 () (_ @t1 @t61 @t71)) % 0.29/0.60 (define @t120 () (_ @t1 @t61 @t65)) % 0.29/0.60 (define @t121 () (forall @t74 (or (not @t120) (not @t119) @t78))) % 0.29/0.60 (define @t122 () (_ (lambda @t8 @t121) @t1)) % 0.29/0.60 (define @t123 () (@list @t38 @t103 @t100)) % 0.29/0.60 (define @t124 () (forall @t123 @t106)) % 0.29/0.60 (define @t125 () (lambda @t48 @t124)) % 0.29/0.60 (define @t126 () (_ @t125 @t13)) % 0.29/0.60 (define @t127 () (forall @t48 @t126)) % 0.29/0.60 (define @t128 () (_ @t18 @t13)) % 0.29/0.60 (define @t129 () (lambda @t89 (forall @t48 @t128))) % 0.29/0.60 (define @t130 () (or @t102 @t101)) % 0.29/0.60 (define @t131 () (or @t105 @t104)) % 0.29/0.60 (define @t132 () (or @t131 @t130)) % 0.29/0.60 (define @t133 () (forall @t123 @t132)) % 0.29/0.60 (define @t134 () (forall (@list @t103 @t100) @t132)) % 0.29/0.60 (define @t135 () (forall (@list @t100) @t130)) % 0.29/0.60 (define @t136 () (@list @t50)) % 0.29/0.60 (define @t137 () (forall (@list @t103) @t131)) % 0.29/0.60 (define @t138 () (or @t137 @t135)) % 0.29/0.60 (define @t139 () (_ @t38 @t50)) % 0.29/0.60 (define @t140 () (_ @t1 @t13 @t50)) % 0.29/0.60 (define @t141 () (not @t140)) % 0.29/0.60 (define @t142 () (or (forall @t55 (or @t141 (not @t139))) (forall @t55 (or @t141 @t139)))) % 0.29/0.60 (define @t143 () (_ @t3 @t50)) % 0.29/0.60 (define @t144 () (not (_ @t1 @t2 @t50))) % 0.29/0.60 (define @t145 () (forall @t55 (or @t144 @t143))) % 0.29/0.60 (define @t146 () (forall @t55 (or @t144 (not @t143)))) % 0.29/0.60 (define @t147 () (or @t146 @t145)) % 0.29/0.60 (define @t148 () (lambda @t5 @t147)) % 0.29/0.60 (define @t149 () (_ @t148 @t38 @t13)) % 0.29/0.60 (define @t150 () (forall @t42 @t149)) % 0.29/0.60 (define @t151 () (lambda @t48 @t150)) % 0.29/0.60 (define @t152 () (_ @t39 @t38 @t13)) % 0.29/0.60 (define @t153 () (lambda @t44 (forall @t42 @t152))) % 0.29/0.60 (define @t154 () (@list @t2)) % 0.29/0.60 (define @t155 () (lambda @t48 (forall @t55 (or @t141 @t143)))) % 0.29/0.60 (define @t156 () (_ @t155 @t2)) % 0.29/0.60 (define @t157 () (or @t146 @t156)) % 0.29/0.60 (define @t158 () (lambda @t154 @t157)) % 0.29/0.60 (define @t159 () (_ @t23 @t2)) % 0.29/0.60 (define @t160 () (@list @t23 @t2)) % 0.29/0.60 (define @t161 () (_ @t18 @t50)) % 0.29/0.60 (define @t162 () (forall @t55 (or @t141 @t161))) % 0.29/0.60 (define @t163 () (lambda @t21 @t162)) % 0.29/0.60 (define @t164 () (_ (lambda @t57 @t162) @t1)) % 0.29/0.60 (define @t165 () (not @t146)) % 0.29/0.60 (define @t166 () (lambda @t154 @t165)) % 0.29/0.60 (define @t167 () (_ @t166 @t2)) % 0.29/0.60 (define @t168 () (not @t167)) % 0.29/0.60 (define @t169 () (or @t168 @t159)) % 0.29/0.60 (define @t170 () (lambda @t160 @t169)) % 0.29/0.60 (define @t171 () (or (not (_ @t18 @t2)) @t159)) % 0.29/0.60 (define @t172 () (lambda @t29 @t171)) % 0.29/0.60 (define @t173 () (not @t161)) % 0.29/0.60 (define @t174 () (not (forall @t55 (or @t144 @t173)))) % 0.29/0.60 (define @t175 () (lambda (@list @t18 @t2) @t174)) % 0.29/0.60 (define @t176 () (_ (lambda @t59 @t174) @t1)) % 0.29/0.60 (define @t177 () (lambda @t5 (_ (_ (_ @t172 (_ @t176 @t3)) (_ @t164 @t3)) @t2))) % 0.29/0.60 (define @t178 () (=> (_ @t129 (_ @t153 @t177)) @t122)) % 0.29/0.60 (define @t179 () (forall @t8 @t178)) % 0.29/0.60 (define @t180 () (not @t72)) % 0.29/0.60 (define @t181 () (not @t67)) % 0.29/0.60 (define @t182 () (or @t181 @t180 @t78)) % 0.29/0.60 (define @t183 () (forall @t55 (or @t141 @t173))) % 0.29/0.60 (define @t184 () (lambda @t48 @t183)) % 0.29/0.60 (define @t185 () (_ @t184 @t13)) % 0.29/0.60 (define @t186 () (not @t185)) % 0.29/0.60 (define @t187 () (lambda @t48 @t186)) % 0.29/0.60 (define @t188 () (not @t51)) % 0.29/0.60 (define @t189 () (or @t141 @t188)) % 0.29/0.60 (define @t190 () (lambda @t48 @t20)) % 0.29/0.60 (define @t191 () (_ @t190 @t50)) % 0.29/0.60 (define @t192 () (or @t141 @t191)) % 0.29/0.60 (define @t193 () (forall @t55 @t192)) % 0.29/0.60 (define @t194 () (lambda @t48 @t193)) % 0.29/0.60 (define @t195 () (or @t20 @t24)) % 0.29/0.60 (define @t196 () (lambda @t48 @t195)) % 0.29/0.60 (define @t197 () (@list @t23 @t13)) % 0.29/0.60 (define @t198 () (_ @t190 @t13)) % 0.29/0.60 (define @t199 () (or @t198 @t24)) % 0.29/0.60 (define @t200 () (lambda @t197 @t199)) % 0.29/0.60 (define @t201 () (forall @t113 @t110)) % 0.29/0.60 (define @t202 () (@quantifiers_skolemize @t201 0)) % 0.29/0.60 (define @t203 () (forall @t107 (or (not (_ @t202 @t13 @t103)) @t104 (not (_ @t202 @t13 @t100)) @t101))) % 0.29/0.60 (define @t204 () (@quantifiers_skolemize @t201 3)) % 0.29/0.60 (define @t205 () (@quantifiers_skolemize @t201 2)) % 0.29/0.60 (define @t206 () (= @t205 @t204)) % 0.29/0.60 (define @t207 () (@quantifiers_skolemize @t201 1)) % 0.29/0.60 (define @t208 () (_ @t202 @t207 @t204)) % 0.29/0.60 (define @t209 () (not @t208)) % 0.29/0.60 (define @t210 () (_ @t202 @t207 @t205)) % 0.29/0.60 (define @t211 () (not @t210)) % 0.29/0.60 (define @t212 () (not @t203)) % 0.29/0.60 (define @t213 () (or @t212 @t211 @t209 @t206)) % 0.29/0.60 (define @t214 () (@list true)) % 0.29/0.60 (define @t215 () (@list @t213)) % 0.29/0.60 (define @t216 () (or @t211 @t209 @t206)) % 0.29/0.60 (define @t217 () (not @t216)) % 0.29/0.60 (define @t218 () (@var "BOUND_VARIABLE_15920" $$unsorted)) % 0.29/0.60 (define @t219 () (lambda (@list @t218) (= @t218 @t205))) % 0.29/0.60 (define @t220 () (_ @t219 @t204)) % 0.29/0.60 (define @t221 () (_ @t219 @t205)) % 0.29/0.60 (define @t222 () (not @t221)) % 0.29/0.60 (define @t223 () (or @t211 @t222 @t209 @t220)) % 0.29/0.60 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.29/0.60 (assume @p2 @t10) % 0.29/0.60 (assume @p3 true) % 0.29/0.60 (step @p4 (= tptp.meq_ind @t14) :rule refl :args (@t14)) % 0.29/0.60 (step @p5 (= tptp.meq_prop @t17) :rule refl :args (@t17)) % 0.29/0.60 (step @p6 (= tptp.mnot @t22) :rule refl :args (@t22)) % 0.29/0.60 (step @p7 (= tptp.mor @t25) :rule refl :args (@t25)) % 0.29/0.60 (step @p8 (= tptp.mand @t30) :rule refl :args (@t30)) % 0.29/0.60 (step @p9 (= tptp.mimplies @t31) :rule refl :args (@t31)) % 0.29/0.60 (step @p10 (= tptp.mimplied @t32) :rule refl :args (@t32)) % 0.29/0.60 (step @p11 (= tptp.mequiv @t33) :rule refl :args (@t33)) % 0.29/0.60 (step @p12 (= tptp.mxor @t34) :rule refl :args (@t34)) % 0.29/0.60 (step @p13 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 0.29/0.60 (step @p14 (= tptp.mforall_prop @t45) :rule refl :args (@t45)) % 0.29/0.60 (step @p15 (= tptp.mexists_ind @t46) :rule refl :args (@t46)) % 0.29/0.60 (step @p16 (= tptp.mexists_prop @t47) :rule refl :args (@t47)) % 0.29/0.60 (step @p17 (= tptp.mtrue @t49) :rule refl :args (@t49)) % 0.29/0.60 (step @p18 (= tptp.mbox @t58) :rule refl :args (@t58)) % 0.29/0.60 (step @p19 (= tptp.mdia @t60) :rule refl :args (@t60)) % 0.29/0.60 (step @p20 (= tptp.mreflexive @t64) :rule refl :args (@t64)) % 0.29/0.60 (step @p21 (= tptp.msymmetric @t68) :rule refl :args (@t68)) % 0.29/0.60 (step @p22 (= tptp.mserial @t70) :rule refl :args (@t70)) % 0.29/0.60 (step @p23 (= tptp.mtransitive @t75) :rule refl :args (@t75)) % 0.29/0.60 (step @p24 (= tptp.meuclidean @t77) :rule refl :args (@t77)) % 0.29/0.60 (step @p25 (= tptp.mpartially_functional @t80) :rule refl :args (@t80)) % 0.29/0.60 (step @p26 (= tptp.mfunctional @t82) :rule refl :args (@t82)) % 0.29/0.60 (step @p27 (= tptp.mweakly_dense @t85) :rule refl :args (@t85)) % 0.29/0.60 (step @p28 (= tptp.mweakly_connected @t86) :rule refl :args (@t86)) % 0.29/0.60 (step @p29 (= tptp.mweakly_directed @t87) :rule refl :args (@t87)) % 0.29/0.60 (step @p30 (= tptp.mvalid @t90) :rule refl :args (@t90)) % 0.29/0.60 (step @p31 (= tptp.minvalid @t91) :rule refl :args (@t91)) % 0.29/0.60 (step @p32 (= tptp.msatisfiable @t92) :rule refl :args (@t92)) % 0.29/0.60 (step @p33 (= tptp.mcountersatisfiable @t93) :rule refl :args (@t93)) % 0.29/0.60 (step @p34 :rule aci_norm :args ((= @t112 @t110))) % 0.29/0.60 (step @p35 :rule cong :premises (@p34) :args (@t114)) % 0.29/0.60 (step @p36 :rule quant-merge-prenex :args ((= (forall @t8 @t116) @t114))) % 0.29/0.60 (step @p37 :rule alpha_equiv :args (@t117 (@list @t97 @t95 @t94) (@list @t61 @t65 @t71))) % 0.29/0.60 (step @p38 :rule refl :args (@t109)) % 0.29/0.60 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t118)) % 0.29/0.60 (step @p40 :rule quant-miniscope-or :args ((= @t116 @t118))) % 0.29/0.60 (step @p41 :rule trans :premises (@p40 @p39)) % 0.29/0.60 (step @p42 :rule symm :premises (@p41)) % 0.29/0.60 (step @p43 :rule cong :premises (@p42) :args ((forall @t8 (or @t109 @t121)))) % 0.29/0.60 (step @p44 :rule trans :premises (@p43 @p36)) % 0.29/0.60 (step @p45 :rule trans :premises (@p44 @p35)) % 0.29/0.60 (step @p46 :rule bool-impl-elim :args (@t108 @t121)) % 0.29/0.60 (step @p47 :rule cong :premises (@p46) :args ((forall @t8 (=> @t108 @t121)))) % 0.29/0.60 (step @p48 :rule trans :premises (@p47 @p45)) % 0.29/0.60 (step @p49 :rule beta-reduce :args ((= @t122 @t121))) % 0.29/0.60 (step @p50 :rule quant-merge-prenex :args ((= (forall @t48 @t124) @t108))) % 0.29/0.60 (step @p51 :rule beta-reduce :args ((= @t126 @t124))) % 0.29/0.60 (step @p52 :rule cong :premises (@p51) :args (@t127)) % 0.29/0.60 (step @p53 :rule trans :premises (@p52 @p50)) % 0.29/0.60 (step @p54 :rule beta-reduce :args ((= (_ @t129 @t125) @t127))) % 0.29/0.60 (step @p55 :rule trans :premises (@p54 @p53)) % 0.29/0.60 (step @p56 :rule aci_norm :args ((= @t132 @t106))) % 0.29/0.60 (step @p57 :rule cong :premises (@p56) :args (@t133)) % 0.29/0.60 (step @p58 :rule quant-merge-prenex :args ((= (forall @t42 @t134) @t133))) % 0.29/0.60 (step @p59 :rule alpha_equiv :args (@t135 (@list @t100) @t136)) % 0.29/0.60 (step @p60 :rule alpha_equiv :args (@t137 (@list @t103) @t136)) % 0.29/0.60 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t138)) % 0.29/0.60 (step @p62 :rule quant-miniscope-or :args ((= @t134 @t138))) % 0.29/0.60 (step @p63 :rule trans :premises (@p62 @p61)) % 0.29/0.60 (step @p64 :rule symm :premises (@p63)) % 0.29/0.60 (step @p65 :rule cong :premises (@p64) :args ((forall @t42 @t142))) % 0.29/0.60 (step @p66 :rule trans :premises (@p65 @p58)) % 0.29/0.60 (step @p67 :rule trans :premises (@p66 @p57)) % 0.29/0.60 (step @p68 :rule beta-reduce :args ((= @t149 @t142))) % 0.29/0.60 (step @p69 :rule cong :premises (@p68) :args (@t150)) % 0.29/0.60 (step @p70 :rule trans :premises (@p69 @p67)) % 0.29/0.60 (step @p71 :rule cong :premises (@p70) :args (@t151)) % 0.29/0.60 (step @p72 :rule beta-reduce :args ((= (_ @t153 @t148) @t151))) % 0.29/0.60 (step @p73 :rule trans :premises (@p72 @p71)) % 0.29/0.60 (step @p74 :rule beta-reduce :args ((= (_ (lambda @t154 @t147) @t2) @t147))) % 0.29/0.60 (step @p75 :rule refl :args (@t2)) % 0.29/0.60 (step @p76 :rule beta-reduce :args ((= @t156 @t145))) % 0.29/0.60 (step @p77 :rule refl :args (@t146)) % 0.29/0.60 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t157)) % 0.29/0.60 (step @p79 :rule cong :premises (@p78) :args (@t158)) % 0.29/0.60 (step @p80 :rule beta-reduce :args ((= (_ (lambda @t160 (or @t146 @t159)) @t155) @t158))) % 0.29/0.60 (step @p81 :rule trans :premises (@p80 @p79)) % 0.29/0.60 (step @p82 :rule beta-reduce :args ((= (_ @t163 @t3) @t155))) % 0.29/0.60 (step @p83 :rule refl :args (@t3)) % 0.29/0.60 (step @p84 :rule beta-reduce :args ((= @t164 @t163))) % 0.29/0.60 (step @p85 :rule ho_cong :premises (@p84 @p83)) % 0.29/0.60 (step @p86 :rule trans :premises (@p85 @p82)) % 0.29/0.60 (step @p87 :rule refl :args (@t159)) % 0.29/0.60 (step @p88 :rule bool-double-not-elim :args (@t146)) % 0.29/0.60 (step @p89 :rule beta-reduce :args ((= @t167 @t165))) % 0.29/0.60 (step @p90 :rule cong :premises (@p89) :args (@t168)) % 0.29/0.60 (step @p91 :rule trans :premises (@p90 @p88)) % 0.29/0.60 (step @p92 :rule nary_cong :premises (@p91 @p87) :args (@t169)) % 0.29/0.60 (step @p93 :rule cong :premises (@p92) :args (@t170)) % 0.29/0.60 (step @p94 :rule beta-reduce :args ((= (_ @t172 @t166) @t170))) % 0.29/0.60 (step @p95 :rule trans :premises (@p94 @p93)) % 0.29/0.60 (step @p96 :rule beta-reduce :args ((= (_ @t175 @t3) @t166))) % 0.29/0.60 (step @p97 :rule beta-reduce :args ((= @t176 @t175))) % 0.29/0.60 (step @p98 :rule ho_cong :premises (@p97 @p83)) % 0.29/0.60 (step @p99 :rule trans :premises (@p98 @p96)) % 0.29/0.60 (step @p100 :rule refl :args (@t172)) % 0.29/0.60 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 0.29/0.60 (step @p102 :rule trans :premises (@p101 @p95)) % 0.29/0.60 (step @p103 :rule ho_cong :premises (@p102 @p86)) % 0.29/0.60 (step @p104 :rule trans :premises (@p103 @p81)) % 0.29/0.60 (step @p105 :rule ho_cong :premises (@p104 @p75)) % 0.29/0.60 (step @p106 :rule trans :premises (@p105 @p74)) % 0.29/0.60 (step @p107 :rule cong :premises (@p106) :args (@t177)) % 0.29/0.60 (step @p108 :rule refl :args (@t153)) % 0.29/0.60 (step @p109 :rule ho_cong :premises (@p108 @p107)) % 0.29/0.60 (step @p110 :rule trans :premises (@p109 @p73)) % 0.29/0.60 (step @p111 :rule refl :args (@t129)) % 0.29/0.60 (step @p112 :rule ho_cong :premises (@p111 @p110)) % 0.29/0.60 (step @p113 :rule trans :premises (@p112 @p55)) % 0.29/0.60 (step @p114 :rule cong :premises (@p113 @p49) :args (@t178)) % 0.29/0.60 (step @p115 :rule cong :premises (@p114) :args (@t179)) % 0.29/0.60 (step @p116 :rule trans :premises (@p115 @p48)) % 0.29/0.60 (step @p117 :rule cong :premises (@p116) :args ((not @t179))) % 0.29/0.60 (step @p118 :rule refl :args (@t1)) % 0.29/0.60 (step @p119 :rule refl :args (@t78)) % 0.29/0.60 (step @p120 :rule refl :args (@t119)) % 0.29/0.60 (step @p121 :rule refl :args (@t72)) % 0.29/0.60 (step @p122 :rule cong :premises (@p121 @p120) :args ((= @t72 @t119))) % 0.29/0.60 (step @p123 :rule symm :premises (@p122)) % 0.29/0.60 (step @p124 :rule eq_resolve :premises (@p121 @p123)) % 0.29/0.60 (step @p125 :rule cong :premises (@p124) :args (@t180)) % 0.29/0.60 (step @p126 :rule refl :args (@t120)) % 0.29/0.60 (step @p127 :rule refl :args (@t67)) % 0.29/0.60 (step @p128 :rule cong :premises (@p127 @p126) :args ((= @t67 @t120))) % 0.29/0.60 (step @p129 :rule symm :premises (@p128)) % 0.29/0.60 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 0.29/0.60 (step @p131 :rule cong :premises (@p130) :args (@t181)) % 0.29/0.60 (step @p132 :rule nary_cong :premises (@p131 @p125 @p119) :args (@t182)) % 0.29/0.60 (step @p133 :rule cong :premises (@p132) :args ((forall @t74 @t182))) % 0.29/0.60 (step @p134 :rule aci_norm :args ((= (or (or @t181 @t180) @t78) @t182))) % 0.29/0.60 (step @p135 :rule bool-and-de-morgan :args (@t67 @t72 true)) % 0.29/0.60 (step @p136 :rule nary_cong :premises (@p135 @p119) :args ((or (not @t76) @t78))) % 0.29/0.60 (step @p137 :rule trans :premises (@p136 @p134)) % 0.29/0.60 (step @p138 :rule bool-impl-elim :args (@t76 @t78)) % 0.29/0.60 (step @p139 :rule trans :premises (@p138 @p137)) % 0.29/0.60 (step @p140 :rule cong :premises (@p139) :args (@t79)) % 0.29/0.60 (step @p141 :rule trans :premises (@p140 @p133)) % 0.29/0.60 (step @p142 :rule cong :premises (@p141) :args (@t80)) % 0.29/0.60 (step @p143 :rule trans :premises (@p25 @p142)) % 0.29/0.60 (step @p144 :rule ho_cong :premises (@p143 @p118)) % 0.29/0.60 (step @p145 :rule refl :args (@t161)) % 0.29/0.60 (step @p146 :rule refl :args (@t51)) % 0.29/0.60 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t51 @t161))) % 0.29/0.61 (step @p148 :rule symm :premises (@p147)) % 0.29/0.61 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.29/0.61 (step @p150 :rule refl :args (@t140)) % 0.29/0.61 (step @p151 :rule refl :args (@t52)) % 0.29/0.61 (step @p152 :rule cong :premises (@p151 @p150) :args ((= @t52 @t140))) % 0.29/0.61 (step @p153 :rule symm :premises (@p152)) % 0.29/0.61 (step @p154 :rule eq_resolve :premises (@p151 @p153)) % 0.29/0.61 (step @p155 :rule cong :premises (@p154) :args (@t53)) % 0.29/0.61 (step @p156 :rule nary_cong :premises (@p155 @p149) :args (@t54)) % 0.29/0.61 (step @p157 :rule cong :premises (@p156) :args (@t56)) % 0.29/0.61 (step @p158 :rule cong :premises (@p157) :args (@t58)) % 0.29/0.61 (step @p159 :rule trans :premises (@p18 @p158)) % 0.29/0.61 (step @p160 :rule ho_cong :premises (@p159 @p118)) % 0.29/0.61 (step @p161 :rule ho_cong :premises (@p160 @p83)) % 0.29/0.61 (step @p162 :rule beta-reduce :args ((= (_ (lambda @t48 (not @t183)) @t2) @t174))) % 0.29/0.61 (step @p163 :rule beta-reduce :args ((= @t185 @t183))) % 0.29/0.61 (step @p164 :rule cong :premises (@p163) :args (@t186)) % 0.29/0.61 (step @p165 :rule cong :premises (@p164) :args (@t187)) % 0.29/0.61 (step @p166 :rule beta-reduce :args ((= (_ @t22 @t184) @t187))) % 0.29/0.61 (step @p167 :rule trans :premises (@p166 @p165)) % 0.29/0.61 (step @p168 :rule cong :premises (@p149) :args (@t188)) % 0.29/0.61 (step @p169 :rule refl :args (@t141)) % 0.29/0.61 (step @p170 :rule nary_cong :premises (@p169 @p168) :args (@t189)) % 0.29/0.61 (step @p171 :rule cong :premises (@p170) :args ((forall @t55 @t189))) % 0.29/0.61 (step @p172 :rule beta-reduce :args ((= @t191 @t188))) % 0.29/0.61 (step @p173 :rule refl :args (@t141)) % 0.29/0.61 (step @p174 :rule nary_cong :premises (@p173 @p172) :args (@t192)) % 0.29/0.61 (step @p175 :rule cong :premises (@p174) :args (@t193)) % 0.29/0.61 (step @p176 :rule trans :premises (@p175 @p171)) % 0.29/0.61 (step @p177 :rule cong :premises (@p176) :args (@t194)) % 0.29/0.61 (step @p178 :rule beta-reduce :args ((= (_ @t163 @t190) @t194))) % 0.29/0.61 (step @p179 :rule trans :premises (@p178 @p177)) % 0.29/0.61 (step @p180 :rule beta-reduce :args ((= (_ @t22 @t18) @t190))) % 0.29/0.61 (step @p181 :rule ho_cong :premises (@p84 @p180)) % 0.29/0.61 (step @p182 :rule trans :premises (@p181 @p179)) % 0.29/0.61 (step @p183 :rule refl :args (@t22)) % 0.29/0.61 (step @p184 :rule ho_cong :premises (@p183 @p182)) % 0.29/0.61 (step @p185 :rule trans :premises (@p184 @p167)) % 0.29/0.61 (step @p186 :rule ho_cong :premises (@p185 @p75)) % 0.29/0.61 (step @p187 :rule trans :premises (@p186 @p162)) % 0.29/0.61 (step @p188 :rule refl :args (@t18)) % 0.29/0.61 (step @p189 :rule ho_cong :premises (@p6 @p188)) % 0.29/0.61 (step @p190 :rule ho_cong :premises (@p160 @p189)) % 0.29/0.61 (step @p191 :rule ho_cong :premises (@p6 @p190)) % 0.29/0.61 (step @p192 :rule ho_cong :premises (@p191 @p75)) % 0.29/0.61 (step @p193 :rule trans :premises (@p192 @p187)) % 0.29/0.61 (step @p194 :rule cong :premises (@p193) :args (@t60)) % 0.29/0.61 (step @p195 :rule trans :premises (@p19 @p194)) % 0.29/0.61 (step @p196 :rule ho_cong :premises (@p195 @p118)) % 0.29/0.61 (step @p197 :rule ho_cong :premises (@p196 @p83)) % 0.29/0.61 (step @p198 :rule beta-reduce :args ((= (_ @t196 @t2) @t171))) % 0.29/0.61 (step @p199 :rule beta-reduce :args ((= (_ (lambda @t197 @t195) @t23) @t196))) % 0.29/0.61 (step @p200 :rule refl :args (@t23)) % 0.29/0.61 (step @p201 :rule refl :args (@t24)) % 0.29/0.61 (step @p202 :rule beta-reduce :args ((= @t198 @t20))) % 0.29/0.61 (step @p203 :rule nary_cong :premises (@p202 @p201) :args (@t199)) % 0.29/0.61 (step @p204 :rule cong :premises (@p203) :args (@t200)) % 0.29/0.61 (step @p205 :rule beta-reduce :args ((= (_ @t25 @t190) @t200))) % 0.29/0.61 (step @p206 :rule trans :premises (@p205 @p204)) % 0.29/0.61 (step @p207 :rule refl :args (@t25)) % 0.29/0.61 (step @p208 :rule ho_cong :premises (@p207 @p180)) % 0.29/0.61 (step @p209 :rule trans :premises (@p208 @p206)) % 0.29/0.61 (step @p210 :rule ho_cong :premises (@p209 @p200)) % 0.29/0.61 (step @p211 :rule trans :premises (@p210 @p199)) % 0.29/0.61 (step @p212 :rule ho_cong :premises (@p211 @p75)) % 0.29/0.61 (step @p213 :rule trans :premises (@p212 @p198)) % 0.29/0.61 (step @p214 :rule ho_cong :premises (@p7 @p189)) % 0.29/0.61 (step @p215 :rule ho_cong :premises (@p214 @p200)) % 0.29/0.61 (step @p216 :rule ho_cong :premises (@p215 @p75)) % 0.29/0.61 (step @p217 :rule trans :premises (@p216 @p213)) % 0.29/0.61 (step @p218 :rule cong :premises (@p217) :args (@t31)) % 0.29/0.61 (step @p219 :rule trans :premises (@p9 @p218)) % 0.29/0.61 (step @p220 :rule ho_cong :premises (@p219 @p197)) % 0.29/0.61 (step @p221 :rule ho_cong :premises (@p220 @p161)) % 0.29/0.61 (step @p222 :rule ho_cong :premises (@p221 @p75)) % 0.29/0.61 (step @p223 :rule cong :premises (@p222) :args (@t6)) % 0.29/0.61 (step @p224 :rule refl :args (@t152)) % 0.29/0.61 (step @p225 :rule refl :args (@t41)) % 0.29/0.61 (step @p226 :rule cong :premises (@p225 @p224) :args ((= @t41 @t152))) % 0.29/0.61 (step @p227 :rule symm :premises (@p226)) % 0.29/0.61 (step @p228 :rule eq_resolve :premises (@p225 @p227)) % 0.29/0.61 (step @p229 :rule cong :premises (@p228) :args (@t43)) % 0.29/0.61 (step @p230 :rule cong :premises (@p229) :args (@t45)) % 0.29/0.61 (step @p231 :rule trans :premises (@p14 @p230)) % 0.29/0.61 (step @p232 :rule ho_cong :premises (@p231 @p223)) % 0.29/0.61 (step @p233 :rule refl :args (@t128)) % 0.29/0.61 (step @p234 :rule refl :args (@t19)) % 0.29/0.61 (step @p235 :rule cong :premises (@p234 @p233) :args ((= @t19 @t128))) % 0.29/0.61 (step @p236 :rule symm :premises (@p235)) % 0.29/0.61 (step @p237 :rule eq_resolve :premises (@p234 @p236)) % 0.29/0.61 (step @p238 :rule cong :premises (@p237) :args (@t88)) % 0.29/0.61 (step @p239 :rule cong :premises (@p238) :args (@t90)) % 0.29/0.61 (step @p240 :rule trans :premises (@p30 @p239)) % 0.29/0.61 (step @p241 :rule ho_cong :premises (@p240 @p232)) % 0.29/0.61 (step @p242 :rule cong :premises (@p241 @p144) :args (@t7)) % 0.29/0.61 (step @p243 :rule cong :premises (@p242) :args (@t9)) % 0.29/0.61 (step @p244 :rule cong :premises (@p243) :args (@t10)) % 0.29/0.61 (step @p245 :rule trans :premises (@p244 @p117)) % 0.29/0.61 (step @p246 :rule eq_resolve :premises (@p2 @p245)) % 0.29/0.61 (step @p247 :rule skolemize :premises (@p246)) % 0.29/0.61 (step @p248 :rule bool-double-not-elim :args (@t203)) % 0.29/0.61 (step @p249 :rule refl :args (@t213)) % 0.29/0.61 (step @p250 :rule nary_cong :premises (@p249 @p248) :args ((or @t213 (not @t212)))) % 0.29/0.61 (step @p251 :rule cnf_or_neg :args (@t213 0)) % 0.29/0.61 (step @p252 :rule eq_resolve :premises (@p251 @p250)) % 0.29/0.61 (step @p253 :rule reordering :premises (@p252) :args ((or @t203 @t213))) % 0.29/0.61 (step @p254 :rule chain_m_resolution :premises (@p253 @p247) :args (@t203 @t214 @t215)) % 0.29/0.61 (step @p255 :rule cnf_or_neg :args (@t213 3)) % 0.29/0.61 (step @p256 :rule chain_m_resolution :premises (@p255 @p247) :args ((not @t206) @t214 @t215)) % 0.29/0.61 (step @p257 :rule bool-double-not-elim :args (@t208)) % 0.29/0.61 (step @p258 :rule nary_cong :premises (@p249 @p257) :args ((or @t213 (not @t209)))) % 0.29/0.61 (step @p259 :rule cnf_or_neg :args (@t213 2)) % 0.29/0.61 (step @p260 :rule eq_resolve :premises (@p259 @p258)) % 0.29/0.61 (step @p261 :rule reordering :premises (@p260) :args ((or @t208 @t213))) % 0.29/0.61 (step @p262 :rule chain_m_resolution :premises (@p261 @p247) :args (@t208 @t214 @t215)) % 0.29/0.61 (step @p263 :rule bool-double-not-elim :args (@t210)) % 0.29/0.61 (step @p264 :rule nary_cong :premises (@p249 @p263) :args ((or @t213 (not @t211)))) % 0.29/0.61 (step @p265 :rule cnf_or_neg :args (@t213 1)) % 0.29/0.61 (step @p266 :rule eq_resolve :premises (@p265 @p264)) % 0.29/0.61 (step @p267 :rule reordering :premises (@p266) :args ((or @t210 @t213))) % 0.29/0.61 (step @p268 :rule chain_m_resolution :premises (@p267 @p247) :args (@t210 @t214 @t215)) % 0.29/0.61 (step @p269 :rule cnf_or_pos :args (@t216)) % 0.29/0.61 (step @p270 :rule reordering :premises (@p269) :args ((or @t211 @t209 @t206 @t217))) % 0.29/0.61 (step @p271 :rule chain_m_resolution :premises (@p270 @p268 @p262 @p256) :args (@t217 (@list false false true) (@list @t210 @t208 @t206))) % 0.29/0.61 (step @p272 :rule aci_norm :args ((= (or @t211 false @t209 @t206) @t216))) % 0.29/0.61 (step @p273 :rule eq-symm :args (@t204 @t205)) % 0.29/0.61 (step @p274 :rule beta-reduce :args ((= @t220 (= @t204 @t205)))) % 0.29/0.61 (step @p275 :rule trans :premises (@p274 @p273)) % 0.29/0.61 (step @p276 :rule refl :args (@t209)) % 0.29/0.61 (step @p277 :rule evaluate :args ((not true))) % 0.29/0.61 (step @p278 :rule eq-refl :args (@t205)) % 0.29/0.61 (step @p279 :rule beta-reduce :args ((= @t221 (= @t205 @t205)))) % 0.29/0.61 (step @p280 :rule trans :premises (@p279 @p278)) % 0.29/0.61 (step @p281 :rule cong :premises (@p280) :args (@t222)) % 0.29/0.61 (step @p282 :rule trans :premises (@p281 @p277)) % 0.29/0.61 (step @p283 :rule refl :args (@t211)) % 0.29/0.61 (step @p284 :rule nary_cong :premises (@p283 @p282 @p276 @p275) :args (@t223)) % 0.29/0.61 (step @p285 :rule trans :premises (@p284 @p272)) % 0.29/0.61 (step @p286 :rule refl :args (@t203)) % 0.29/0.61 (step @p287 :rule cong :premises (@p286 @p285) :args ((=> @t203 @t223))) % 0.29/0.61 (assume-push @p295 @t203) % 0.29/0.61 (step @p289 :rule instantiate :premises (@p254) :args ((@list @t207 @t219 @t205 @t204))) % 0.29/0.61 (step-pop @p296 :rule scope :premises (@p289)) % 0.29/0.61 (step @p290 :rule process_scope :premises (@p296) :args (@t223)) % 0.29/0.61 (step @p292 :rule eq_resolve :premises (@p290 @p287)) % 0.29/0.61 (step @p293 :rule implies_elim :premises (@p292)) % 0.29/0.61 (step @p294 false :rule chain_m_resolution :premises (@p293 @p271 @p254) :args (false (@list true false) (@list @t216 @t203))) % 0.29/0.61 ) % 0.29/0.61 % SZS output end Proof % 0.29/0.61 % cvc5 exiting %------------------------------------------------------------------------------