%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL711^1 : 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 : n010.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:41 AM UTC 2026 % Result : Theorem 1.62s 1.94s % Output : Proof 1.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL711^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.13/0.38 % Computer : n010.cluster.edu % 0.13/0.38 % Model : x86_64 x86_64 % 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.38 % Memory : 8046.5625MB % 0.13/0.38 % OS : Linux 6.8.0-71-generic % 0.13/0.38 % CPULimit : 300 % 0.13/0.38 % WCLimit : 300 % 0.13/0.38 % DateTime : Fri Sep 4 23:11:23 UTC 2026 % 0.13/0.38 % CPUTime : % 0.21/0.46 %----Proving TH0 % 1.62/1.94 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.62/1.94 % SZS status Theorem % 1.62/1.94 % SZS output start Proof % 1.62/1.94 ( % 1.62/1.94 (declare-sort $$unsorted 0) % 1.62/1.94 (declare-sort tptp.mu 0) % 1.62/1.94 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 1.62/1.94 (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" $$unsorted)) (= _let_2 _let_1))))) % 1.62/1.94 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 1.62/1.94 (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)))))) % 1.62/1.94 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 1.62/1.94 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 1.62/1.94 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 1.62/1.94 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 1.62/1.94 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 1.62/1.94 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 1.62/1.94 (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))))))) % 1.62/1.94 (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))))))) % 1.62/1.94 (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)))))) % 1.62/1.94 (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)))))) % 1.62/1.94 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 1.62/1.94 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 1.62/1.94 (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)))))) % 1.62/1.94 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 1.62/1.94 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 1.62/1.94 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 1.62/1.94 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 1.62/1.94 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 1.62/1.94 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 1.62/1.94 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 1.62/1.94 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 1.62/1.94 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 1.62/1.94 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 1.62/1.94 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 1.62/1.94 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 1.62/1.94 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 1.62/1.94 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 1.62/1.94 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 1.62/1.94 (define @t2 () (@var "__flatten_var_0" $$unsorted)) % 1.62/1.94 (define @t3 () (@var "A" (-> $$unsorted Bool))) % 1.62/1.94 (define @t4 () (_ tptp.mbox @t1)) % 1.62/1.94 (define @t5 () (@list @t3 @t2)) % 1.62/1.94 (define @t6 () (lambda @t5 (_ (_ (_ tptp.mimplies (_ @t4 @t3)) (_ (_ tptp.mdia @t1) @t3)) @t2))) % 1.62/1.94 (define @t7 () (=> (_ tptp.mvalid (_ tptp.mforall_prop @t6)) (_ tptp.mserial @t1))) % 1.62/1.94 (define @t8 () (@list @t1)) % 1.62/1.94 (define @t9 () (forall @t8 @t7)) % 1.62/1.94 (define @t10 () (not @t9)) % 1.62/1.94 (define @t11 () (@var "Y" tptp.mu)) % 1.62/1.94 (define @t12 () (@var "X" tptp.mu)) % 1.62/1.94 (define @t13 () (@var "W" $$unsorted)) % 1.62/1.94 (define @t14 () (lambda (@list @t12 @t11 @t13) (= @t12 @t11))) % 1.62/1.94 (define @t15 () (@var "Y" (-> $$unsorted Bool))) % 1.62/1.94 (define @t16 () (@var "X" (-> $$unsorted Bool))) % 1.62/1.94 (define @t17 () (lambda (@list @t16 @t15 @t13) (= (_ @t16 @t13) (_ @t15 @t13)))) % 1.62/1.94 (define @t18 () (@var "Phi" (-> $$unsorted Bool))) % 1.62/1.94 (define @t19 () (_ @t18 @t13)) % 1.62/1.94 (define @t20 () (not @t19)) % 1.62/1.94 (define @t21 () (@list @t18 @t13)) % 1.62/1.94 (define @t22 () (lambda @t21 @t20)) % 1.62/1.94 (define @t23 () (@var "Psi" (-> $$unsorted Bool))) % 1.62/1.94 (define @t24 () (_ @t23 @t13)) % 1.62/1.94 (define @t25 () (lambda (@list @t18 @t23 @t13) (or @t19 @t24))) % 1.62/1.94 (define @t26 () (_ tptp.mnot @t23)) % 1.62/1.94 (define @t27 () (_ tptp.mnot @t18)) % 1.62/1.94 (define @t28 () (_ tptp.mor @t27)) % 1.62/1.94 (define @t29 () (@list @t18 @t23 @t2)) % 1.62/1.94 (define @t30 () (lambda @t29 (_ (_ tptp.mnot (_ @t28 @t26)) @t2))) % 1.62/1.94 (define @t31 () (lambda @t29 (_ (_ @t28 @t23) @t2))) % 1.62/1.94 (define @t32 () (lambda @t29 (_ (_ (_ tptp.mor @t26) @t18) @t2))) % 1.62/1.94 (define @t33 () (lambda @t29 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t18) @t23)) (_ (_ tptp.mimplies @t23) @t18)) @t2))) % 1.62/1.94 (define @t34 () (lambda @t29 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t18) @t23)) @t2))) % 1.62/1.94 (define @t35 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 1.62/1.94 (define @t36 () (_ @t35 @t12)) % 1.62/1.94 (define @t37 () (lambda (@list @t35 @t13) (forall (@list @t12) (_ @t36 @t13)))) % 1.62/1.94 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 1.62/1.94 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 1.62/1.94 (define @t40 () (_ @t39 @t38)) % 1.62/1.94 (define @t41 () (_ @t40 @t13)) % 1.62/1.94 (define @t42 () (@list @t38)) % 1.62/1.94 (define @t43 () (forall @t42 @t41)) % 1.62/1.94 (define @t44 () (@list @t39 @t13)) % 1.62/1.94 (define @t45 () (lambda @t44 @t43)) % 1.62/1.94 (define @t46 () (lambda (@list @t35 @t2) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t12 @t2) (_ (_ tptp.mnot @t36) @t2)))) @t2))) % 1.62/1.94 (define @t47 () (lambda (@list @t39 @t2) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t2) (_ (_ tptp.mnot @t40) @t2)))) @t2))) % 1.62/1.94 (define @t48 () (@list @t13)) % 1.62/1.94 (define @t49 () (lambda @t48 true)) % 1.62/1.94 (define @t50 () (@var "V" $$unsorted)) % 1.62/1.94 (define @t51 () (_ @t18 @t50)) % 1.62/1.94 (define @t52 () (_ (_ @t1 @t13) @t50)) % 1.62/1.94 (define @t53 () (not @t52)) % 1.62/1.94 (define @t54 () (or @t53 @t51)) % 1.62/1.94 (define @t55 () (@list @t50)) % 1.62/1.94 (define @t56 () (forall @t55 @t54)) % 1.62/1.94 (define @t57 () (@list @t1 @t18 @t13)) % 1.62/1.94 (define @t58 () (lambda @t57 @t56)) % 1.62/1.94 (define @t59 () (@list @t1 @t18 @t2)) % 1.62/1.94 (define @t60 () (lambda @t59 (_ (_ tptp.mnot (_ @t4 @t27)) @t2))) % 1.62/1.94 (define @t61 () (@var "S" $$unsorted)) % 1.62/1.94 (define @t62 () (_ @t1 @t61)) % 1.62/1.94 (define @t63 () (@list @t61)) % 1.62/1.94 (define @t64 () (lambda @t8 (forall @t63 (_ @t62 @t61)))) % 1.62/1.94 (define @t65 () (@var "T" $$unsorted)) % 1.62/1.94 (define @t66 () (_ @t1 @t65)) % 1.62/1.94 (define @t67 () (_ @t62 @t65)) % 1.62/1.94 (define @t68 () (lambda @t8 (forall (@list @t61 @t65) (=> @t67 (_ @t66 @t61))))) % 1.62/1.94 (define @t69 () (@list @t65)) % 1.62/1.94 (define @t70 () (exists @t69 @t67)) % 1.62/1.94 (define @t71 () (forall @t63 @t70)) % 1.62/1.94 (define @t72 () (lambda @t8 @t71)) % 1.62/1.94 (define @t73 () (@var "U" $$unsorted)) % 1.62/1.94 (define @t74 () (_ @t62 @t73)) % 1.62/1.94 (define @t75 () (_ @t66 @t73)) % 1.62/1.94 (define @t76 () (@list @t61 @t65 @t73)) % 1.62/1.94 (define @t77 () (lambda @t8 (forall @t76 (=> (and @t67 @t75) @t74)))) % 1.62/1.94 (define @t78 () (and @t67 @t74)) % 1.62/1.94 (define @t79 () (lambda @t8 (forall @t76 (=> @t78 @t75)))) % 1.62/1.94 (define @t80 () (= @t65 @t73)) % 1.62/1.94 (define @t81 () (lambda @t8 (forall @t76 (=> @t78 @t80)))) % 1.62/1.94 (define @t82 () (@list @t73)) % 1.62/1.94 (define @t83 () (lambda @t8 (forall @t63 (exists @t69 (and @t67 (forall @t82 (=> @t74 @t80))))))) % 1.62/1.94 (define @t84 () (_ @t1 @t73)) % 1.62/1.94 (define @t85 () (_ @t84 @t65)) % 1.62/1.94 (define @t86 () (lambda @t8 (forall @t76 (=> @t67 (exists @t82 (and @t74 @t85)))))) % 1.62/1.94 (define @t87 () (lambda @t8 (forall @t76 (=> @t78 (or @t75 @t80 @t85))))) % 1.62/1.94 (define @t88 () (lambda @t8 (forall @t76 (=> @t78 (exists @t55 (and (_ @t66 @t50) (_ @t84 @t50))))))) % 1.62/1.94 (define @t89 () (forall @t48 @t19)) % 1.62/1.94 (define @t90 () (@list @t18)) % 1.62/1.94 (define @t91 () (lambda @t90 @t89)) % 1.62/1.94 (define @t92 () (lambda @t90 (forall @t48 @t20))) % 1.62/1.94 (define @t93 () (lambda @t90 (exists @t48 @t19))) % 1.62/1.94 (define @t94 () (lambda @t90 (exists @t48 @t20))) % 1.62/1.94 (define @t95 () (@var "BOUND_VARIABLE_8402" $$unsorted)) % 1.62/1.94 (define @t96 () (not (forall @t69 (not (_ @t1 @t95 @t65))))) % 1.62/1.94 (define @t97 () (_ @t38 @t50)) % 1.62/1.94 (define @t98 () (not @t97)) % 1.62/1.94 (define @t99 () (_ @t1 @t13 @t50)) % 1.62/1.94 (define @t100 () (not @t99)) % 1.62/1.94 (define @t101 () (or (not (forall @t55 (or @t100 @t97))) (not (forall @t55 (or @t100 @t98))))) % 1.62/1.94 (define @t102 () (@list @t13 @t38)) % 1.62/1.94 (define @t103 () (forall @t102 @t101)) % 1.62/1.94 (define @t104 () (not @t103)) % 1.62/1.94 (define @t105 () (or @t104 @t96)) % 1.62/1.94 (define @t106 () (forall (@list @t1 @t95) @t105)) % 1.62/1.94 (define @t107 () (@list @t95)) % 1.62/1.94 (define @t108 () (forall @t107 @t105)) % 1.62/1.94 (define @t109 () (forall @t107 @t96)) % 1.62/1.94 (define @t110 () (or @t104 @t109)) % 1.62/1.94 (define @t111 () (_ @t1 @t61 @t65)) % 1.62/1.94 (define @t112 () (forall @t63 (not (forall @t69 (not @t111))))) % 1.62/1.94 (define @t113 () (_ (lambda @t8 @t112) @t1)) % 1.62/1.94 (define @t114 () (forall @t42 @t101)) % 1.62/1.94 (define @t115 () (lambda @t48 @t114)) % 1.62/1.94 (define @t116 () (_ @t115 @t13)) % 1.62/1.94 (define @t117 () (forall @t48 @t116)) % 1.62/1.94 (define @t118 () (_ @t18 @t13)) % 1.62/1.94 (define @t119 () (lambda @t90 (forall @t48 @t118))) % 1.62/1.94 (define @t120 () (_ @t3 @t50)) % 1.62/1.94 (define @t121 () (not (_ @t1 @t2 @t50))) % 1.62/1.94 (define @t122 () (not (forall @t55 (or @t121 (not @t120))))) % 1.62/1.94 (define @t123 () (forall @t55 (or @t121 @t120))) % 1.62/1.94 (define @t124 () (not @t123)) % 1.62/1.94 (define @t125 () (or @t124 @t122)) % 1.62/1.94 (define @t126 () (lambda @t5 @t125)) % 1.62/1.94 (define @t127 () (_ @t126 @t38 @t13)) % 1.62/1.94 (define @t128 () (forall @t42 @t127)) % 1.62/1.94 (define @t129 () (lambda @t48 @t128)) % 1.62/1.94 (define @t130 () (_ @t39 @t38 @t13)) % 1.62/1.94 (define @t131 () (lambda @t44 (forall @t42 @t130))) % 1.62/1.94 (define @t132 () (@list @t2)) % 1.62/1.94 (define @t133 () (lambda @t132 @t122)) % 1.62/1.94 (define @t134 () (_ @t133 @t2)) % 1.62/1.94 (define @t135 () (or @t124 @t134)) % 1.62/1.94 (define @t136 () (lambda @t132 @t135)) % 1.62/1.94 (define @t137 () (_ @t23 @t2)) % 1.62/1.94 (define @t138 () (@list @t23 @t2)) % 1.62/1.94 (define @t139 () (_ @t18 @t50)) % 1.62/1.94 (define @t140 () (not @t139)) % 1.62/1.94 (define @t141 () (not (forall @t55 (or @t121 @t140)))) % 1.62/1.94 (define @t142 () (lambda (@list @t18 @t2) @t141)) % 1.62/1.94 (define @t143 () (_ (lambda @t59 @t141) @t1)) % 1.62/1.94 (define @t144 () (lambda @t48 (forall @t55 (or @t100 @t120)))) % 1.62/1.94 (define @t145 () (_ @t144 @t2)) % 1.62/1.94 (define @t146 () (not @t145)) % 1.62/1.94 (define @t147 () (or @t146 @t137)) % 1.62/1.94 (define @t148 () (lambda @t138 @t147)) % 1.62/1.94 (define @t149 () (or (not (_ @t18 @t2)) @t137)) % 1.62/1.94 (define @t150 () (lambda @t29 @t149)) % 1.62/1.94 (define @t151 () (forall @t55 (or @t100 @t139))) % 1.62/1.94 (define @t152 () (lambda @t21 @t151)) % 1.62/1.94 (define @t153 () (_ (lambda @t57 @t151) @t1)) % 1.62/1.94 (define @t154 () (lambda @t5 (_ (_ (_ @t150 (_ @t153 @t3)) (_ @t143 @t3)) @t2))) % 1.62/1.94 (define @t155 () (=> (_ @t119 (_ @t131 @t154)) @t113)) % 1.62/1.94 (define @t156 () (forall @t8 @t155)) % 1.62/1.94 (define @t157 () (not @t67)) % 1.62/1.94 (define @t158 () (forall @t69 @t157)) % 1.62/1.94 (define @t159 () (not @t158)) % 1.62/1.94 (define @t160 () (forall @t55 (or @t100 @t140))) % 1.62/1.94 (define @t161 () (lambda @t48 @t160)) % 1.62/1.94 (define @t162 () (_ @t161 @t13)) % 1.62/1.94 (define @t163 () (not @t162)) % 1.62/1.94 (define @t164 () (lambda @t48 @t163)) % 1.62/1.94 (define @t165 () (not @t51)) % 1.62/1.94 (define @t166 () (or @t100 @t165)) % 1.62/1.94 (define @t167 () (lambda @t48 @t20)) % 1.62/1.94 (define @t168 () (_ @t167 @t50)) % 1.62/1.94 (define @t169 () (or @t100 @t168)) % 1.62/1.94 (define @t170 () (forall @t55 @t169)) % 1.62/1.94 (define @t171 () (lambda @t48 @t170)) % 1.62/1.94 (define @t172 () (or @t20 @t24)) % 1.62/1.94 (define @t173 () (lambda @t48 @t172)) % 1.62/1.94 (define @t174 () (@list @t23 @t13)) % 1.62/1.94 (define @t175 () (_ @t167 @t13)) % 1.62/1.94 (define @t176 () (or @t175 @t24)) % 1.62/1.94 (define @t177 () (lambda @t174 @t176)) % 1.62/1.94 (define @t178 () (@quantifiers_skolemize @t106 0)) % 1.62/1.94 (define @t179 () (not (_ @t178 @t13 @t50))) % 1.62/1.94 (define @t180 () (forall @t102 (or (not (forall @t55 (or @t179 @t97))) (not (forall @t55 (or @t179 @t98)))))) % 1.62/1.94 (define @t181 () (@quantifiers_skolemize @t106 1)) % 1.62/1.94 (define @t182 () (forall @t69 (not (_ @t178 @t181 @t65)))) % 1.62/1.94 (define @t183 () (not @t182)) % 1.62/1.94 (define @t184 () (not @t180)) % 1.62/1.94 (define @t185 () (or @t184 @t183)) % 1.62/1.94 (define @t186 () (@list true)) % 1.62/1.94 (define @t187 () (@list @t185)) % 1.62/1.94 (define @t188 () (not (_ @t178 @t181 @t50))) % 1.62/1.94 (define @t189 () (forall @t55 @t188)) % 1.62/1.94 (define @t190 () (not @t189)) % 1.62/1.94 (define @t191 () (lambda (@list (@var "BOUND_VARIABLE_15553" $$unsorted)) true)) % 1.62/1.94 (define @t192 () (_ @t191 @t50)) % 1.62/1.94 (define @t193 () (not @t192)) % 1.62/1.94 (define @t194 () (or @t188 @t193)) % 1.62/1.94 (define @t195 () (forall @t55 @t194)) % 1.62/1.94 (define @t196 () (not @t195)) % 1.62/1.94 (define @t197 () (or @t188 @t192)) % 1.62/1.94 (define @t198 () (forall @t55 @t197)) % 1.62/1.94 (define @t199 () (not @t198)) % 1.62/1.94 (define @t200 () (or @t199 @t196)) % 1.62/1.94 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 1.62/1.94 (assume @p2 @t10) % 1.62/1.94 (assume @p3 true) % 1.62/1.94 (step @p4 (= tptp.meq_ind @t14) :rule refl :args (@t14)) % 1.62/1.94 (step @p5 (= tptp.meq_prop @t17) :rule refl :args (@t17)) % 1.62/1.94 (step @p6 (= tptp.mnot @t22) :rule refl :args (@t22)) % 1.62/1.94 (step @p7 (= tptp.mor @t25) :rule refl :args (@t25)) % 1.62/1.94 (step @p8 (= tptp.mand @t30) :rule refl :args (@t30)) % 1.62/1.94 (step @p9 (= tptp.mimplies @t31) :rule refl :args (@t31)) % 1.62/1.94 (step @p10 (= tptp.mimplied @t32) :rule refl :args (@t32)) % 1.62/1.94 (step @p11 (= tptp.mequiv @t33) :rule refl :args (@t33)) % 1.62/1.94 (step @p12 (= tptp.mxor @t34) :rule refl :args (@t34)) % 1.62/1.94 (step @p13 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 1.62/1.94 (step @p14 (= tptp.mforall_prop @t45) :rule refl :args (@t45)) % 1.62/1.94 (step @p15 (= tptp.mexists_ind @t46) :rule refl :args (@t46)) % 1.62/1.94 (step @p16 (= tptp.mexists_prop @t47) :rule refl :args (@t47)) % 1.62/1.94 (step @p17 (= tptp.mtrue @t49) :rule refl :args (@t49)) % 1.62/1.94 (step @p18 (= tptp.mbox @t58) :rule refl :args (@t58)) % 1.62/1.94 (step @p19 (= tptp.mdia @t60) :rule refl :args (@t60)) % 1.62/1.94 (step @p20 (= tptp.mreflexive @t64) :rule refl :args (@t64)) % 1.62/1.94 (step @p21 (= tptp.msymmetric @t68) :rule refl :args (@t68)) % 1.62/1.94 (step @p22 (= tptp.mserial @t72) :rule refl :args (@t72)) % 1.62/1.94 (step @p23 (= tptp.mtransitive @t77) :rule refl :args (@t77)) % 1.62/1.94 (step @p24 (= tptp.meuclidean @t79) :rule refl :args (@t79)) % 1.62/1.94 (step @p25 (= tptp.mpartially_functional @t81) :rule refl :args (@t81)) % 1.62/1.94 (step @p26 (= tptp.mfunctional @t83) :rule refl :args (@t83)) % 1.62/1.94 (step @p27 (= tptp.mweakly_dense @t86) :rule refl :args (@t86)) % 1.62/1.94 (step @p28 (= tptp.mweakly_connected @t87) :rule refl :args (@t87)) % 1.62/1.94 (step @p29 (= tptp.mweakly_directed @t88) :rule refl :args (@t88)) % 1.62/1.94 (step @p30 (= tptp.mvalid @t91) :rule refl :args (@t91)) % 1.62/1.94 (step @p31 (= tptp.minvalid @t92) :rule refl :args (@t92)) % 1.62/1.94 (step @p32 (= tptp.msatisfiable @t93) :rule refl :args (@t93)) % 1.62/1.94 (step @p33 (= tptp.mcountersatisfiable @t94) :rule refl :args (@t94)) % 1.62/1.94 (step @p34 :rule quant-merge-prenex :args ((= (forall @t8 @t108) @t106))) % 1.62/1.94 (step @p35 :rule alpha_equiv :args (@t109 (@list @t95) (@list @t61))) % 1.62/1.94 (step @p36 :rule refl :args (@t104)) % 1.62/1.94 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t110)) % 1.62/1.94 (step @p38 :rule quant-miniscope-or :args ((= @t108 @t110))) % 1.62/1.94 (step @p39 :rule trans :premises (@p38 @p37)) % 1.62/1.94 (step @p40 :rule symm :premises (@p39)) % 1.62/1.94 (step @p41 :rule cong :premises (@p40) :args ((forall @t8 (or @t104 @t112)))) % 1.62/1.94 (step @p42 :rule trans :premises (@p41 @p34)) % 1.62/1.94 (step @p43 :rule bool-impl-elim :args (@t103 @t112)) % 1.62/1.94 (step @p44 :rule cong :premises (@p43) :args ((forall @t8 (=> @t103 @t112)))) % 1.62/1.94 (step @p45 :rule trans :premises (@p44 @p42)) % 1.62/1.94 (step @p46 :rule beta-reduce :args ((= @t113 @t112))) % 1.62/1.94 (step @p47 :rule quant-merge-prenex :args ((= (forall @t48 @t114) @t103))) % 1.62/1.94 (step @p48 :rule beta-reduce :args ((= @t116 @t114))) % 1.62/1.94 (step @p49 :rule cong :premises (@p48) :args (@t117)) % 1.62/1.94 (step @p50 :rule trans :premises (@p49 @p47)) % 1.62/1.94 (step @p51 :rule beta-reduce :args ((= (_ @t119 @t115) @t117))) % 1.62/1.94 (step @p52 :rule trans :premises (@p51 @p50)) % 1.62/1.94 (step @p53 :rule beta-reduce :args ((= @t127 @t101))) % 1.62/1.94 (step @p54 :rule cong :premises (@p53) :args (@t128)) % 1.62/1.94 (step @p55 :rule cong :premises (@p54) :args (@t129)) % 1.62/1.94 (step @p56 :rule beta-reduce :args ((= (_ @t131 @t126) @t129))) % 1.62/1.94 (step @p57 :rule trans :premises (@p56 @p55)) % 1.62/1.94 (step @p58 :rule beta-reduce :args ((= (_ (lambda @t132 @t125) @t2) @t125))) % 1.62/1.94 (step @p59 :rule refl :args (@t2)) % 1.62/1.94 (step @p60 :rule beta-reduce :args ((= @t134 @t122))) % 1.62/1.94 (step @p61 :rule refl :args (@t124)) % 1.62/1.94 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t135)) % 1.62/1.94 (step @p63 :rule cong :premises (@p62) :args (@t136)) % 1.62/1.94 (step @p64 :rule beta-reduce :args ((= (_ (lambda @t138 (or @t124 @t137)) @t133) @t136))) % 1.62/1.94 (step @p65 :rule trans :premises (@p64 @p63)) % 1.62/1.94 (step @p66 :rule beta-reduce :args ((= (_ @t142 @t3) @t133))) % 1.62/1.94 (step @p67 :rule refl :args (@t3)) % 1.62/1.94 (step @p68 :rule beta-reduce :args ((= @t143 @t142))) % 1.62/1.94 (step @p69 :rule ho_cong :premises (@p68 @p67)) % 1.62/1.94 (step @p70 :rule trans :premises (@p69 @p66)) % 1.62/1.94 (step @p71 :rule refl :args (@t137)) % 1.62/1.94 (step @p72 :rule beta-reduce :args ((= @t145 @t123))) % 1.62/1.94 (step @p73 :rule cong :premises (@p72) :args (@t146)) % 1.62/1.94 (step @p74 :rule nary_cong :premises (@p73 @p71) :args (@t147)) % 1.62/1.94 (step @p75 :rule cong :premises (@p74) :args (@t148)) % 1.62/1.94 (step @p76 :rule beta-reduce :args ((= (_ @t150 @t144) @t148))) % 1.62/1.94 (step @p77 :rule trans :premises (@p76 @p75)) % 1.62/1.94 (step @p78 :rule beta-reduce :args ((= (_ @t152 @t3) @t144))) % 1.62/1.94 (step @p79 :rule beta-reduce :args ((= @t153 @t152))) % 1.62/1.94 (step @p80 :rule ho_cong :premises (@p79 @p67)) % 1.62/1.94 (step @p81 :rule trans :premises (@p80 @p78)) % 1.62/1.94 (step @p82 :rule refl :args (@t150)) % 1.62/1.94 (step @p83 :rule ho_cong :premises (@p82 @p81)) % 1.62/1.94 (step @p84 :rule trans :premises (@p83 @p77)) % 1.62/1.94 (step @p85 :rule ho_cong :premises (@p84 @p70)) % 1.62/1.94 (step @p86 :rule trans :premises (@p85 @p65)) % 1.62/1.94 (step @p87 :rule ho_cong :premises (@p86 @p59)) % 1.62/1.94 (step @p88 :rule trans :premises (@p87 @p58)) % 1.62/1.94 (step @p89 :rule cong :premises (@p88) :args (@t154)) % 1.62/1.94 (step @p90 :rule refl :args (@t131)) % 1.62/1.94 (step @p91 :rule ho_cong :premises (@p90 @p89)) % 1.62/1.94 (step @p92 :rule trans :premises (@p91 @p57)) % 1.62/1.94 (step @p93 :rule refl :args (@t119)) % 1.62/1.94 (step @p94 :rule ho_cong :premises (@p93 @p92)) % 1.62/1.94 (step @p95 :rule trans :premises (@p94 @p52)) % 1.62/1.94 (step @p96 :rule cong :premises (@p95 @p46) :args (@t155)) % 1.62/1.94 (step @p97 :rule cong :premises (@p96) :args (@t156)) % 1.62/1.94 (step @p98 :rule trans :premises (@p97 @p45)) % 1.62/1.94 (step @p99 :rule cong :premises (@p98) :args ((not @t156))) % 1.62/1.94 (step @p100 :rule refl :args (@t1)) % 1.62/1.94 (step @p101 :rule refl :args (@t111)) % 1.62/1.94 (step @p102 :rule refl :args (@t67)) % 1.62/1.94 (step @p103 :rule cong :premises (@p102 @p101) :args ((= @t67 @t111))) % 1.62/1.94 (step @p104 :rule symm :premises (@p103)) % 1.62/1.94 (step @p105 :rule eq_resolve :premises (@p102 @p104)) % 1.62/1.94 (step @p106 :rule cong :premises (@p105) :args (@t157)) % 1.62/1.94 (step @p107 :rule cong :premises (@p106) :args (@t158)) % 1.62/1.94 (step @p108 :rule cong :premises (@p107) :args (@t159)) % 1.62/1.94 (step @p109 :rule exists-elim :args ((= @t70 @t159))) % 1.62/1.94 (step @p110 :rule trans :premises (@p109 @p108)) % 1.62/1.94 (step @p111 :rule cong :premises (@p110) :args (@t71)) % 1.62/1.94 (step @p112 :rule cong :premises (@p111) :args (@t72)) % 1.62/1.94 (step @p113 :rule trans :premises (@p22 @p112)) % 1.62/1.94 (step @p114 :rule ho_cong :premises (@p113 @p100)) % 1.62/1.94 (step @p115 :rule beta-reduce :args ((= (_ (lambda @t48 (not @t160)) @t2) @t141))) % 1.62/1.94 (step @p116 :rule beta-reduce :args ((= @t162 @t160))) % 1.62/1.94 (step @p117 :rule cong :premises (@p116) :args (@t163)) % 1.62/1.94 (step @p118 :rule cong :premises (@p117) :args (@t164)) % 1.62/1.94 (step @p119 :rule beta-reduce :args ((= (_ @t22 @t161) @t164))) % 1.62/1.94 (step @p120 :rule trans :premises (@p119 @p118)) % 1.62/1.94 (step @p121 :rule refl :args (@t139)) % 1.62/1.94 (step @p122 :rule refl :args (@t51)) % 1.62/1.94 (step @p123 :rule cong :premises (@p122 @p121) :args ((= @t51 @t139))) % 1.62/1.94 (step @p124 :rule symm :premises (@p123)) % 1.62/1.94 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 1.62/1.94 (step @p126 :rule cong :premises (@p125) :args (@t165)) % 1.62/1.94 (step @p127 :rule refl :args (@t100)) % 1.62/1.94 (step @p128 :rule nary_cong :premises (@p127 @p126) :args (@t166)) % 1.62/1.94 (step @p129 :rule cong :premises (@p128) :args ((forall @t55 @t166))) % 1.62/1.94 (step @p130 :rule beta-reduce :args ((= @t168 @t165))) % 1.62/1.94 (step @p131 :rule refl :args (@t100)) % 1.62/1.94 (step @p132 :rule nary_cong :premises (@p131 @p130) :args (@t169)) % 1.62/1.94 (step @p133 :rule cong :premises (@p132) :args (@t170)) % 1.62/1.94 (step @p134 :rule trans :premises (@p133 @p129)) % 1.62/1.94 (step @p135 :rule cong :premises (@p134) :args (@t171)) % 1.62/1.94 (step @p136 :rule beta-reduce :args ((= (_ @t152 @t167) @t171))) % 1.62/1.94 (step @p137 :rule trans :premises (@p136 @p135)) % 1.62/1.94 (step @p138 :rule beta-reduce :args ((= (_ @t22 @t18) @t167))) % 1.62/1.94 (step @p139 :rule ho_cong :premises (@p79 @p138)) % 1.62/1.94 (step @p140 :rule trans :premises (@p139 @p137)) % 1.62/1.94 (step @p141 :rule refl :args (@t22)) % 1.62/1.94 (step @p142 :rule ho_cong :premises (@p141 @p140)) % 1.62/1.94 (step @p143 :rule trans :premises (@p142 @p120)) % 1.62/1.94 (step @p144 :rule ho_cong :premises (@p143 @p59)) % 1.62/1.94 (step @p145 :rule trans :premises (@p144 @p115)) % 1.62/1.94 (step @p146 :rule refl :args (@t18)) % 1.62/1.94 (step @p147 :rule ho_cong :premises (@p6 @p146)) % 1.62/1.94 (step @p148 :rule refl :args (@t99)) % 1.62/1.94 (step @p149 :rule refl :args (@t52)) % 1.62/1.94 (step @p150 :rule cong :premises (@p149 @p148) :args ((= @t52 @t99))) % 1.62/1.94 (step @p151 :rule symm :premises (@p150)) % 1.62/1.94 (step @p152 :rule eq_resolve :premises (@p149 @p151)) % 1.62/1.94 (step @p153 :rule cong :premises (@p152) :args (@t53)) % 1.62/1.94 (step @p154 :rule nary_cong :premises (@p153 @p125) :args (@t54)) % 1.62/1.94 (step @p155 :rule cong :premises (@p154) :args (@t56)) % 1.62/1.94 (step @p156 :rule cong :premises (@p155) :args (@t58)) % 1.62/1.94 (step @p157 :rule trans :premises (@p18 @p156)) % 1.62/1.94 (step @p158 :rule ho_cong :premises (@p157 @p100)) % 1.62/1.94 (step @p159 :rule ho_cong :premises (@p158 @p147)) % 1.62/1.94 (step @p160 :rule ho_cong :premises (@p6 @p159)) % 1.62/1.94 (step @p161 :rule ho_cong :premises (@p160 @p59)) % 1.62/1.94 (step @p162 :rule trans :premises (@p161 @p145)) % 1.62/1.94 (step @p163 :rule cong :premises (@p162) :args (@t60)) % 1.62/1.94 (step @p164 :rule trans :premises (@p19 @p163)) % 1.62/1.94 (step @p165 :rule ho_cong :premises (@p164 @p100)) % 1.62/1.94 (step @p166 :rule ho_cong :premises (@p165 @p67)) % 1.62/1.94 (step @p167 :rule ho_cong :premises (@p158 @p67)) % 1.62/1.94 (step @p168 :rule beta-reduce :args ((= (_ @t173 @t2) @t149))) % 1.62/1.94 (step @p169 :rule beta-reduce :args ((= (_ (lambda @t174 @t172) @t23) @t173))) % 1.62/1.94 (step @p170 :rule refl :args (@t23)) % 1.62/1.94 (step @p171 :rule refl :args (@t24)) % 1.62/1.94 (step @p172 :rule beta-reduce :args ((= @t175 @t20))) % 1.62/1.94 (step @p173 :rule nary_cong :premises (@p172 @p171) :args (@t176)) % 1.62/1.94 (step @p174 :rule cong :premises (@p173) :args (@t177)) % 1.62/1.94 (step @p175 :rule beta-reduce :args ((= (_ @t25 @t167) @t177))) % 1.62/1.94 (step @p176 :rule trans :premises (@p175 @p174)) % 1.62/1.94 (step @p177 :rule refl :args (@t25)) % 1.62/1.94 (step @p178 :rule ho_cong :premises (@p177 @p138)) % 1.62/1.94 (step @p179 :rule trans :premises (@p178 @p176)) % 1.62/1.94 (step @p180 :rule ho_cong :premises (@p179 @p170)) % 1.62/1.94 (step @p181 :rule trans :premises (@p180 @p169)) % 1.62/1.94 (step @p182 :rule ho_cong :premises (@p181 @p59)) % 1.62/1.94 (step @p183 :rule trans :premises (@p182 @p168)) % 1.62/1.94 (step @p184 :rule ho_cong :premises (@p7 @p147)) % 1.62/1.94 (step @p185 :rule ho_cong :premises (@p184 @p170)) % 1.62/1.94 (step @p186 :rule ho_cong :premises (@p185 @p59)) % 1.62/1.94 (step @p187 :rule trans :premises (@p186 @p183)) % 1.62/1.94 (step @p188 :rule cong :premises (@p187) :args (@t31)) % 1.62/1.94 (step @p189 :rule trans :premises (@p9 @p188)) % 1.62/1.94 (step @p190 :rule ho_cong :premises (@p189 @p167)) % 1.62/1.94 (step @p191 :rule ho_cong :premises (@p190 @p166)) % 1.62/1.94 (step @p192 :rule ho_cong :premises (@p191 @p59)) % 1.62/1.94 (step @p193 :rule cong :premises (@p192) :args (@t6)) % 1.62/1.94 (step @p194 :rule refl :args (@t130)) % 1.62/1.94 (step @p195 :rule refl :args (@t41)) % 1.62/1.94 (step @p196 :rule cong :premises (@p195 @p194) :args ((= @t41 @t130))) % 1.62/1.94 (step @p197 :rule symm :premises (@p196)) % 1.62/1.94 (step @p198 :rule eq_resolve :premises (@p195 @p197)) % 1.62/1.94 (step @p199 :rule cong :premises (@p198) :args (@t43)) % 1.62/1.94 (step @p200 :rule cong :premises (@p199) :args (@t45)) % 1.62/1.94 (step @p201 :rule trans :premises (@p14 @p200)) % 1.62/1.94 (step @p202 :rule ho_cong :premises (@p201 @p193)) % 1.62/1.94 (step @p203 :rule refl :args (@t118)) % 1.62/1.94 (step @p204 :rule refl :args (@t19)) % 1.62/1.94 (step @p205 :rule cong :premises (@p204 @p203) :args ((= @t19 @t118))) % 1.62/1.94 (step @p206 :rule symm :premises (@p205)) % 1.62/1.94 (step @p207 :rule eq_resolve :premises (@p204 @p206)) % 1.62/1.94 (step @p208 :rule cong :premises (@p207) :args (@t89)) % 1.62/1.94 (step @p209 :rule cong :premises (@p208) :args (@t91)) % 1.62/1.95 (step @p210 :rule trans :premises (@p30 @p209)) % 1.62/1.95 (step @p211 :rule ho_cong :premises (@p210 @p202)) % 1.62/1.95 (step @p212 :rule cong :premises (@p211 @p114) :args (@t7)) % 1.62/1.95 (step @p213 :rule cong :premises (@p212) :args (@t9)) % 1.62/1.95 (step @p214 :rule cong :premises (@p213) :args (@t10)) % 1.62/1.95 (step @p215 :rule trans :premises (@p214 @p99)) % 1.62/1.95 (step @p216 :rule eq_resolve :premises (@p2 @p215)) % 1.62/1.95 (step @p217 :rule skolemize :premises (@p216)) % 1.62/1.95 (step @p218 :rule bool-double-not-elim :args (@t180)) % 1.62/1.95 (step @p219 :rule refl :args (@t185)) % 1.62/1.95 (step @p220 :rule nary_cong :premises (@p219 @p218) :args ((or @t185 (not @t184)))) % 1.62/1.95 (step @p221 :rule cnf_or_neg :args (@t185 0)) % 1.62/1.95 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 1.62/1.95 (step @p223 :rule reordering :premises (@p222) :args ((or @t180 @t185))) % 1.62/1.95 (step @p224 :rule chain_m_resolution :premises (@p223 @p217) :args (@t180 @t186 @t187)) % 1.62/1.95 (step @p225 :rule bool-double-not-elim :args (@t182)) % 1.62/1.95 (step @p226 :rule nary_cong :premises (@p219 @p225) :args ((or @t185 (not @t183)))) % 1.62/1.95 (step @p227 :rule cnf_or_neg :args (@t185 1)) % 1.62/1.95 (step @p228 :rule eq_resolve :premises (@p227 @p226)) % 1.62/1.95 (step @p229 :rule reordering :premises (@p228) :args ((or @t182 @t185))) % 1.62/1.95 (step @p230 :rule chain_m_resolution :premises (@p229 @p217) :args (@t182 @t186 @t187)) % 1.62/1.95 (step @p231 :rule alpha_equiv :args (@t182 (@list @t65) (@list @t50))) % 1.62/1.95 (step @p232 :rule equiv_elim1 :premises (@p231)) % 1.62/1.95 (step @p233 :rule chain_m_resolution :premises (@p232 @p230) :args (@t189 (@list false) (@list @t182))) % 1.62/1.95 (step @p234 :rule aci_norm :args ((= (or false @t190) @t190))) % 1.62/1.95 (step @p235 :rule aci_norm :args ((= (or @t188 false) @t188))) % 1.62/1.95 (step @p236 :rule evaluate :args ((not true))) % 1.62/1.95 (step @p237 :rule beta-reduce :args ((= @t192 true))) % 1.62/1.95 (step @p238 :rule cong :premises (@p237) :args (@t193)) % 1.62/1.95 (step @p239 :rule trans :premises (@p238 @p236)) % 1.62/1.95 (step @p240 :rule refl :args (@t188)) % 1.62/1.95 (step @p241 :rule nary_cong :premises (@p240 @p239) :args (@t194)) % 1.62/1.95 (step @p242 :rule trans :premises (@p241 @p235)) % 1.62/1.95 (step @p243 :rule cong :premises (@p242) :args (@t195)) % 1.62/1.95 (step @p244 :rule cong :premises (@p243) :args (@t196)) % 1.62/1.95 (step @p245 :rule quant-unused-vars :args ((= (forall @t55 true) true))) % 1.62/1.95 (step @p246 :rule absorb :args ((= (or @t188 true) true))) % 1.62/1.95 (step @p247 :rule nary_cong :premises (@p240 @p237) :args (@t197)) % 1.62/1.95 (step @p248 :rule trans :premises (@p247 @p246)) % 1.62/1.95 (step @p249 :rule cong :premises (@p248) :args (@t198)) % 1.62/1.95 (step @p250 :rule trans :premises (@p249 @p245)) % 1.62/1.95 (step @p251 :rule cong :premises (@p250) :args (@t199)) % 1.62/1.95 (step @p252 :rule trans :premises (@p251 @p236)) % 1.62/1.95 (step @p253 :rule nary_cong :premises (@p252 @p244) :args (@t200)) % 1.62/1.95 (step @p254 :rule trans :premises (@p253 @p234)) % 1.62/1.95 (step @p255 :rule refl :args (@t180)) % 1.62/1.95 (step @p256 :rule cong :premises (@p255 @p254) :args ((=> @t180 @t200))) % 1.62/1.95 (assume-push @p264 @t180) % 1.62/1.95 (step @p258 :rule instantiate :premises (@p224) :args ((@list @t181 @t191))) % 1.62/1.95 (step-pop @p265 :rule scope :premises (@p258)) % 1.62/1.95 (step @p259 :rule process_scope :premises (@p265) :args (@t200)) % 1.62/1.95 (step @p261 :rule eq_resolve :premises (@p259 @p256)) % 1.62/1.95 (step @p262 :rule implies_elim :premises (@p261)) % 1.62/1.95 (step @p263 false :rule chain_m_resolution :premises (@p262 @p233 @p224) :args (false (@list false false) (@list @t189 @t180))) % 1.62/1.95 ) % 1.62/1.95 % SZS output end Proof % 1.62/1.95 % cvc5 exiting %------------------------------------------------------------------------------