%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL707^1 : TPTP v9.3.1. Bugfixed v5.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n002.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 0.18s 0.50s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL707^1 : TPTP v9.3.1. Bugfixed v5.1.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.36 % Computer : n002.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Fri Sep 4 13:01:50 UTC 2026 % 0.13/0.36 % CPUTime : % 0.13/0.43 %----Proving TH0 % 0.18/0.50 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.18/0.50 % SZS status Theorem % 0.18/0.50 % SZS output start Proof % 0.18/0.50 ( % 0.18/0.50 (declare-sort $$unsorted 0) % 0.18/0.50 (declare-sort tptp.mu 0) % 0.18/0.50 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.18/0.50 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.18/0.50 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.18/0.50 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.18/0.50 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.18/0.50 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.18/0.50 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.18/0.50 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.18/0.50 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.18/0.50 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.18/0.50 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.18/0.50 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.18/0.50 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.18/0.50 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.18/0.50 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.18/0.50 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.18/0.50 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.18/0.50 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.18/0.50 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.18/0.50 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.18/0.50 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.18/0.50 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.18/0.50 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.18/0.51 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.18/0.51 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.18/0.51 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.18/0.51 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.18/0.51 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.51 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.51 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.51 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.51 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.18/0.51 (define @t2 () (@var "A" (-> $$unsorted Bool))) % 0.18/0.51 (define @t3 () (@var "B" (-> $$unsorted Bool))) % 0.18/0.51 (define @t4 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.18/0.51 (define @t5 () (_ tptp.mbox @t4)) % 0.18/0.51 (define @t6 () (@list @t3 @t1)) % 0.18/0.51 (define @t7 () (lambda @t6 (_ (_ (_ tptp.mor (_ @t5 (_ (_ tptp.mimplies (_ (_ tptp.mand @t2) (_ @t5 @t2))) @t3))) (_ @t5 (_ (_ tptp.mimplies (_ (_ tptp.mand @t3) (_ @t5 @t3))) @t2))) @t1))) % 0.18/0.51 (define @t8 () (@list @t2 @t1)) % 0.18/0.51 (define @t9 () (lambda @t8 (_ (_ tptp.mforall_prop @t7) @t1))) % 0.18/0.51 (define @t10 () (=> (_ tptp.mweakly_connected @t4) (_ tptp.mvalid (_ tptp.mforall_prop @t9)))) % 0.18/0.51 (define @t11 () (@list @t4)) % 0.18/0.51 (define @t12 () (forall @t11 @t10)) % 0.18/0.51 (define @t13 () (not @t12)) % 0.18/0.51 (define @t14 () (@var "Y" tptp.mu)) % 0.18/0.51 (define @t15 () (@var "X" tptp.mu)) % 0.18/0.51 (define @t16 () (@var "W" $$unsorted)) % 0.18/0.51 (define @t17 () (lambda (@list @t15 @t14 @t16) (= @t15 @t14))) % 0.18/0.51 (define @t18 () (@var "Y" (-> $$unsorted Bool))) % 0.18/0.51 (define @t19 () (@var "X" (-> $$unsorted Bool))) % 0.18/0.51 (define @t20 () (lambda (@list @t19 @t18 @t16) (= (_ @t19 @t16) (_ @t18 @t16)))) % 0.18/0.51 (define @t21 () (@var "Phi" (-> $$unsorted Bool))) % 0.18/0.51 (define @t22 () (_ @t21 @t16)) % 0.18/0.51 (define @t23 () (not @t22)) % 0.18/0.51 (define @t24 () (@list @t21 @t16)) % 0.18/0.51 (define @t25 () (lambda @t24 @t23)) % 0.18/0.51 (define @t26 () (@var "Psi" (-> $$unsorted Bool))) % 0.18/0.51 (define @t27 () (_ @t26 @t16)) % 0.18/0.51 (define @t28 () (lambda (@list @t21 @t26 @t16) (or @t22 @t27))) % 0.18/0.51 (define @t29 () (_ tptp.mnot @t26)) % 0.18/0.51 (define @t30 () (_ tptp.mnot @t21)) % 0.18/0.51 (define @t31 () (_ tptp.mor @t30)) % 0.18/0.51 (define @t32 () (@list @t21 @t26 @t1)) % 0.18/0.51 (define @t33 () (lambda @t32 (_ (_ tptp.mnot (_ @t31 @t29)) @t1))) % 0.18/0.51 (define @t34 () (lambda @t32 (_ (_ @t31 @t26) @t1))) % 0.18/0.51 (define @t35 () (lambda @t32 (_ (_ (_ tptp.mor @t29) @t21) @t1))) % 0.18/0.51 (define @t36 () (lambda @t32 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t21) @t26)) (_ (_ tptp.mimplies @t26) @t21)) @t1))) % 0.18/0.51 (define @t37 () (lambda @t32 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t21) @t26)) @t1))) % 0.18/0.51 (define @t38 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.18/0.51 (define @t39 () (_ @t38 @t15)) % 0.18/0.51 (define @t40 () (lambda (@list @t38 @t16) (forall (@list @t15) (_ @t39 @t16)))) % 0.18/0.51 (define @t41 () (@var "P" (-> $$unsorted Bool))) % 0.18/0.51 (define @t42 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.18/0.51 (define @t43 () (_ @t42 @t41)) % 0.18/0.51 (define @t44 () (_ @t43 @t16)) % 0.18/0.51 (define @t45 () (@list @t41)) % 0.18/0.51 (define @t46 () (forall @t45 @t44)) % 0.18/0.51 (define @t47 () (@list @t42 @t16)) % 0.18/0.51 (define @t48 () (lambda @t47 @t46)) % 0.18/0.51 (define @t49 () (lambda (@list @t38 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t15 @t1) (_ (_ tptp.mnot @t39) @t1)))) @t1))) % 0.18/0.51 (define @t50 () (lambda (@list @t42 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t41 @t1) (_ (_ tptp.mnot @t43) @t1)))) @t1))) % 0.18/0.51 (define @t51 () (@list @t16)) % 0.18/0.51 (define @t52 () (lambda @t51 true)) % 0.18/0.51 (define @t53 () (@var "V" $$unsorted)) % 0.18/0.51 (define @t54 () (_ @t21 @t53)) % 0.18/0.51 (define @t55 () (_ (_ @t4 @t16) @t53)) % 0.18/0.51 (define @t56 () (not @t55)) % 0.18/0.51 (define @t57 () (or @t56 @t54)) % 0.18/0.51 (define @t58 () (@list @t53)) % 0.18/0.51 (define @t59 () (forall @t58 @t57)) % 0.18/0.51 (define @t60 () (@list @t4 @t21 @t16)) % 0.18/0.51 (define @t61 () (lambda @t60 @t59)) % 0.18/0.51 (define @t62 () (lambda (@list @t4 @t21 @t1) (_ (_ tptp.mnot (_ @t5 @t30)) @t1))) % 0.18/0.51 (define @t63 () (@var "S" $$unsorted)) % 0.18/0.51 (define @t64 () (_ @t4 @t63)) % 0.18/0.51 (define @t65 () (@list @t63)) % 0.18/0.51 (define @t66 () (lambda @t11 (forall @t65 (_ @t64 @t63)))) % 0.18/0.51 (define @t67 () (@var "T" $$unsorted)) % 0.18/0.51 (define @t68 () (_ @t4 @t67)) % 0.18/0.51 (define @t69 () (_ @t64 @t67)) % 0.18/0.51 (define @t70 () (lambda @t11 (forall (@list @t63 @t67) (=> @t69 (_ @t68 @t63))))) % 0.18/0.51 (define @t71 () (@list @t67)) % 0.18/0.51 (define @t72 () (lambda @t11 (forall @t65 (exists @t71 @t69)))) % 0.18/0.51 (define @t73 () (@var "U" $$unsorted)) % 0.18/0.51 (define @t74 () (_ @t64 @t73)) % 0.18/0.51 (define @t75 () (_ @t68 @t73)) % 0.18/0.51 (define @t76 () (@list @t63 @t67 @t73)) % 0.18/0.51 (define @t77 () (lambda @t11 (forall @t76 (=> (and @t69 @t75) @t74)))) % 0.18/0.51 (define @t78 () (and @t69 @t74)) % 0.18/0.51 (define @t79 () (lambda @t11 (forall @t76 (=> @t78 @t75)))) % 0.18/0.51 (define @t80 () (= @t67 @t73)) % 0.18/0.51 (define @t81 () (lambda @t11 (forall @t76 (=> @t78 @t80)))) % 0.18/0.51 (define @t82 () (@list @t73)) % 0.18/0.51 (define @t83 () (lambda @t11 (forall @t65 (exists @t71 (and @t69 (forall @t82 (=> @t74 @t80))))))) % 0.18/0.51 (define @t84 () (_ @t4 @t73)) % 0.18/0.51 (define @t85 () (_ @t84 @t67)) % 0.18/0.51 (define @t86 () (lambda @t11 (forall @t76 (=> @t69 (exists @t82 (and @t74 @t85)))))) % 0.18/0.51 (define @t87 () (or @t75 @t80 @t85)) % 0.18/0.51 (define @t88 () (forall @t76 (=> @t78 @t87))) % 0.18/0.51 (define @t89 () (lambda @t11 @t88)) % 0.18/0.51 (define @t90 () (lambda @t11 (forall @t76 (=> @t78 (exists @t58 (and (_ @t68 @t53) (_ @t84 @t53))))))) % 0.18/0.51 (define @t91 () (forall @t51 @t22)) % 0.18/0.51 (define @t92 () (@list @t21)) % 0.18/0.51 (define @t93 () (lambda @t92 @t91)) % 0.18/0.51 (define @t94 () (lambda @t92 (forall @t51 @t23))) % 0.18/0.51 (define @t95 () (lambda @t92 (exists @t51 @t22))) % 0.18/0.51 (define @t96 () (lambda @t92 (exists @t51 @t23))) % 0.18/0.51 (define @t97 () (@var "BOUND_VARIABLE_8486" $$unsorted)) % 0.18/0.51 (define @t98 () (@var "BOUND_VARIABLE_8627" (-> $$unsorted Bool))) % 0.18/0.51 (define @t99 () (@var "BOUND_VARIABLE_8631" $$unsorted)) % 0.18/0.51 (define @t100 () (@list @t97)) % 0.18/0.51 (define @t101 () (not (forall @t100 (or (not (_ @t4 @t99 @t97)) (_ @t98 @t97))))) % 0.18/0.51 (define @t102 () (not (_ @t98 @t99))) % 0.18/0.51 (define @t103 () (@var "BOUND_VARIABLE_8625" (-> $$unsorted Bool))) % 0.18/0.51 (define @t104 () (_ @t103 @t99)) % 0.18/0.51 (define @t105 () (@var "BOUND_VARIABLE_8623" $$unsorted)) % 0.18/0.51 (define @t106 () (not (_ @t4 @t105 @t99))) % 0.18/0.51 (define @t107 () (@var "BOUND_VARIABLE_8412" $$unsorted)) % 0.18/0.51 (define @t108 () (@var "BOUND_VARIABLE_8629" $$unsorted)) % 0.18/0.51 (define @t109 () (@list @t107)) % 0.18/0.51 (define @t110 () (not (forall @t109 (or (not (_ @t4 @t108 @t107)) (_ @t103 @t107))))) % 0.18/0.51 (define @t111 () (not (_ @t103 @t108))) % 0.18/0.51 (define @t112 () (_ @t98 @t108)) % 0.18/0.51 (define @t113 () (not (_ @t4 @t105 @t108))) % 0.18/0.51 (define @t114 () (_ @t4 @t73 @t67)) % 0.18/0.51 (define @t115 () (_ @t4 @t67 @t73)) % 0.18/0.51 (define @t116 () (_ @t4 @t63 @t73)) % 0.18/0.51 (define @t117 () (_ @t4 @t63 @t67)) % 0.18/0.51 (define @t118 () (forall @t76 (or (not @t117) (not @t116) @t115 @t80 @t114))) % 0.18/0.51 (define @t119 () (not @t118)) % 0.18/0.51 (define @t120 () (or @t119 @t113 @t112 @t111 @t110 @t106 @t104 @t102 @t101)) % 0.18/0.51 (define @t121 () (or @t113 @t112 @t111 @t110 @t106 @t104 @t102 @t101)) % 0.18/0.51 (define @t122 () (or @t119 @t121)) % 0.18/0.51 (define @t123 () (@list @t4 @t105 @t103 @t98 @t108 @t99)) % 0.18/0.51 (define @t124 () (forall @t123 @t122)) % 0.18/0.51 (define @t125 () (@list @t105 @t103 @t98 @t108 @t99)) % 0.18/0.51 (define @t126 () (forall @t125 @t122)) % 0.18/0.51 (define @t127 () (forall @t125 @t121)) % 0.18/0.51 (define @t128 () (@var "BOUND_VARIABLE_8555" $$unsorted)) % 0.18/0.51 (define @t129 () (@var "BOUND_VARIABLE_8542" $$unsorted)) % 0.18/0.51 (define @t130 () (@var "BOUND_VARIABLE_8587" (-> $$unsorted Bool))) % 0.18/0.51 (define @t131 () (or @t119 @t127)) % 0.18/0.51 (define @t132 () (not (_ @t4 @t128 @t97))) % 0.18/0.51 (define @t133 () (not (forall @t100 (or @t132 (_ @t130 @t97))))) % 0.18/0.51 (define @t134 () (not (_ @t130 @t128))) % 0.18/0.51 (define @t135 () (_ @t41 @t128)) % 0.18/0.51 (define @t136 () (not (_ @t4 @t16 @t128))) % 0.18/0.51 (define @t137 () (not (_ @t4 @t129 @t107))) % 0.18/0.51 (define @t138 () (_ @t41 @t129)) % 0.18/0.51 (define @t139 () (_ @t130 @t129)) % 0.18/0.51 (define @t140 () (not (_ @t4 @t16 @t129))) % 0.18/0.51 (define @t141 () (or @t140 @t139 (not @t138) (not (forall @t109 (or @t137 (_ @t41 @t107)))) @t136 @t135 @t134 @t133)) % 0.18/0.51 (define @t142 () (forall (@list @t16 @t41 @t130 @t129 @t128) @t141)) % 0.18/0.51 (define @t143 () (forall (@list @t41 @t130 @t129 @t128) @t141)) % 0.18/0.51 (define @t144 () (lambda @t51 @t143)) % 0.18/0.51 (define @t145 () (_ @t144 @t16)) % 0.18/0.51 (define @t146 () (forall @t51 @t145)) % 0.18/0.51 (define @t147 () (_ @t21 @t16)) % 0.18/0.51 (define @t148 () (lambda @t92 (forall @t51 @t147))) % 0.18/0.51 (define @t149 () (@list @t130 @t129 @t128)) % 0.18/0.51 (define @t150 () (forall @t149 @t141)) % 0.18/0.51 (define @t151 () (_ @t2 @t128)) % 0.18/0.51 (define @t152 () (not (_ @t4 @t1 @t128))) % 0.18/0.51 (define @t153 () (_ @t2 @t107)) % 0.18/0.51 (define @t154 () (not (forall @t109 (or @t137 @t153)))) % 0.18/0.51 (define @t155 () (not (_ @t2 @t129))) % 0.18/0.51 (define @t156 () (not (_ @t4 @t1 @t129))) % 0.18/0.51 (define @t157 () (_ @t41 @t97)) % 0.18/0.51 (define @t158 () (not (forall @t100 (or @t132 @t157)))) % 0.18/0.51 (define @t159 () (not @t135)) % 0.18/0.51 (define @t160 () (@list @t41 @t129 @t128)) % 0.18/0.51 (define @t161 () (forall @t160 (or @t156 @t138 @t155 @t154 @t152 @t151 @t159 @t158))) % 0.18/0.51 (define @t162 () (lambda @t8 @t161)) % 0.18/0.51 (define @t163 () (forall @t45 (_ @t162 @t41 @t16))) % 0.18/0.51 (define @t164 () (lambda @t51 @t163)) % 0.18/0.51 (define @t165 () (_ @t42 @t41 @t16)) % 0.18/0.51 (define @t166 () (lambda @t47 (forall @t45 @t165))) % 0.18/0.51 (define @t167 () (or @t140 @t138 @t155 @t154 @t136 @t151 @t159 @t158)) % 0.18/0.51 (define @t168 () (or @t136 @t151 @t159 @t158)) % 0.18/0.51 (define @t169 () (or @t140 @t138 @t155 @t154)) % 0.18/0.51 (define @t170 () (or @t169 @t168)) % 0.18/0.51 (define @t171 () (forall @t160 @t170)) % 0.18/0.51 (define @t172 () (forall (@list @t129 @t128) @t170)) % 0.18/0.51 (define @t173 () (forall (@list @t128) @t168)) % 0.18/0.51 (define @t174 () (@list @t53)) % 0.18/0.51 (define @t175 () (forall (@list @t129) @t169)) % 0.18/0.51 (define @t176 () (or @t175 @t173)) % 0.18/0.51 (define @t177 () (not (_ @t4 @t53 @t97))) % 0.18/0.51 (define @t178 () (_ @t41 @t53)) % 0.18/0.51 (define @t179 () (_ @t2 @t53)) % 0.18/0.51 (define @t180 () (_ @t4 @t16 @t53)) % 0.18/0.51 (define @t181 () (not @t180)) % 0.18/0.51 (define @t182 () (not (forall @t109 (or (not (_ @t4 @t53 @t107)) @t153)))) % 0.18/0.51 (define @t183 () (not @t179)) % 0.18/0.51 (define @t184 () (or (forall @t58 (or @t181 @t178 @t183 @t182)) (forall @t58 (or @t181 @t179 (not @t178) (not (forall @t100 (or @t177 @t157))))))) % 0.18/0.51 (define @t185 () (_ @t3 @t97)) % 0.18/0.51 (define @t186 () (not (forall @t100 (or @t177 @t185)))) % 0.18/0.51 (define @t187 () (_ @t3 @t53)) % 0.18/0.51 (define @t188 () (not @t187)) % 0.18/0.51 (define @t189 () (not (_ @t4 @t1 @t53))) % 0.18/0.51 (define @t190 () (or (forall @t58 (or @t189 @t187 @t183 @t182)) (forall @t58 (or @t189 @t179 @t188 @t186)))) % 0.18/0.51 (define @t191 () (lambda @t6 @t190)) % 0.18/0.51 (define @t192 () (_ @t191 @t41 @t16)) % 0.18/0.51 (define @t193 () (forall @t45 @t192)) % 0.18/0.51 (define @t194 () (lambda @t51 @t193)) % 0.18/0.51 (define @t195 () (forall @t58 (or @t181 @t179 @t188 @t186))) % 0.18/0.51 (define @t196 () (forall @t58 (or @t181 @t187 @t183 @t182))) % 0.18/0.51 (define @t197 () (lambda @t51 @t195)) % 0.18/0.51 (define @t198 () (_ @t197 @t16)) % 0.18/0.51 (define @t199 () (or @t196 @t198)) % 0.18/0.51 (define @t200 () (lambda @t51 @t199)) % 0.18/0.51 (define @t201 () (@list @t26 @t16)) % 0.18/0.51 (define @t202 () (_ @t3 @t53)) % 0.18/0.51 (define @t203 () (not @t202)) % 0.18/0.51 (define @t204 () (_ @t2 @t53)) % 0.18/0.51 (define @t205 () (or @t181 @t204 @t203 @t186)) % 0.18/0.51 (define @t206 () (or @t204 @t203 @t186)) % 0.18/0.51 (define @t207 () (_ @t3 @t1)) % 0.18/0.51 (define @t208 () (not @t207)) % 0.18/0.51 (define @t209 () (_ @t2 @t1)) % 0.18/0.51 (define @t210 () (@list @t1)) % 0.18/0.51 (define @t211 () (forall @t58 (or @t189 @t187))) % 0.18/0.51 (define @t212 () (not @t211)) % 0.18/0.51 (define @t213 () (or @t209 @t208 @t212)) % 0.18/0.51 (define @t214 () (lambda @t210 @t213)) % 0.18/0.51 (define @t215 () (or @t181 (_ @t214 @t53))) % 0.18/0.51 (define @t216 () (forall @t58 @t215)) % 0.18/0.51 (define @t217 () (lambda @t51 @t216)) % 0.18/0.51 (define @t218 () (_ @t21 @t53)) % 0.18/0.51 (define @t219 () (forall @t58 (or @t181 @t218))) % 0.18/0.51 (define @t220 () (lambda @t24 @t219)) % 0.18/0.51 (define @t221 () (_ @t26 @t1)) % 0.18/0.51 (define @t222 () (or @t221 @t208 @t212)) % 0.18/0.51 (define @t223 () (@list @t26 @t1)) % 0.18/0.51 (define @t224 () (or @t208 @t212)) % 0.18/0.51 (define @t225 () (not @t224)) % 0.18/0.51 (define @t226 () (lambda @t210 @t225)) % 0.18/0.51 (define @t227 () (_ @t226 @t1)) % 0.18/0.51 (define @t228 () (not @t227)) % 0.18/0.51 (define @t229 () (or @t228 @t221)) % 0.18/0.51 (define @t230 () (lambda @t223 @t229)) % 0.18/0.51 (define @t231 () (not (_ @t21 @t1))) % 0.18/0.51 (define @t232 () (or @t231 @t221)) % 0.18/0.51 (define @t233 () (lambda @t32 @t232)) % 0.18/0.51 (define @t234 () (lambda @t51 (forall @t58 (or @t181 @t187)))) % 0.18/0.51 (define @t235 () (_ @t234 @t1)) % 0.18/0.51 (define @t236 () (not @t235)) % 0.18/0.51 (define @t237 () (or @t208 @t236)) % 0.18/0.51 (define @t238 () (not @t237)) % 0.18/0.51 (define @t239 () (lambda @t210 @t238)) % 0.18/0.51 (define @t240 () (not @t221)) % 0.18/0.51 (define @t241 () (lambda @t223 (not (or @t208 @t240)))) % 0.18/0.51 (define @t242 () (_ (lambda @t60 @t219) @t4)) % 0.18/0.51 (define @t243 () (not (or @t231 @t240))) % 0.18/0.51 (define @t244 () (lambda @t32 @t243)) % 0.18/0.51 (define @t245 () (_ @t244 @t3)) % 0.18/0.51 (define @t246 () (lambda @t51 @t196)) % 0.18/0.51 (define @t247 () (_ @t246 @t16)) % 0.18/0.51 (define @t248 () (or @t247 @t27)) % 0.18/0.51 (define @t249 () (lambda @t201 @t248)) % 0.18/0.51 (define @t250 () (not @t204)) % 0.18/0.51 (define @t251 () (or @t181 @t202 @t250 @t182)) % 0.18/0.51 (define @t252 () (or @t202 @t250 @t182)) % 0.18/0.51 (define @t253 () (not @t209)) % 0.18/0.51 (define @t254 () (forall @t58 (or @t189 @t179))) % 0.18/0.51 (define @t255 () (not @t254)) % 0.18/0.51 (define @t256 () (or @t207 @t253 @t255)) % 0.18/0.51 (define @t257 () (lambda @t210 @t256)) % 0.18/0.51 (define @t258 () (or @t181 (_ @t257 @t53))) % 0.18/0.51 (define @t259 () (forall @t58 @t258)) % 0.18/0.51 (define @t260 () (lambda @t51 @t259)) % 0.18/0.51 (define @t261 () (or @t221 @t253 @t255)) % 0.18/0.51 (define @t262 () (or @t253 @t255)) % 0.18/0.51 (define @t263 () (not @t262)) % 0.18/0.51 (define @t264 () (lambda @t210 @t263)) % 0.18/0.51 (define @t265 () (_ @t264 @t1)) % 0.18/0.51 (define @t266 () (not @t265)) % 0.18/0.51 (define @t267 () (or @t266 @t221)) % 0.18/0.51 (define @t268 () (lambda @t223 @t267)) % 0.18/0.51 (define @t269 () (lambda @t51 (forall @t58 (or @t181 @t179)))) % 0.18/0.51 (define @t270 () (_ @t269 @t1)) % 0.18/0.51 (define @t271 () (not @t270)) % 0.18/0.51 (define @t272 () (or @t253 @t271)) % 0.18/0.51 (define @t273 () (not @t272)) % 0.18/0.51 (define @t274 () (lambda @t210 @t273)) % 0.18/0.51 (define @t275 () (lambda @t223 (not (or @t253 @t240)))) % 0.18/0.51 (define @t276 () (_ @t244 @t2)) % 0.18/0.51 (define @t277 () (lambda @t6 (_ (_ (_ @t28 (_ @t242 (_ (_ @t233 (_ @t276 (_ @t242 @t2))) @t3))) (_ @t242 (_ (_ @t233 (_ @t245 (_ @t242 @t3))) @t2))) @t1))) % 0.18/0.51 (define @t278 () (lambda @t8 (_ (_ @t166 @t277) @t1))) % 0.18/0.51 (define @t279 () (_ (lambda @t11 @t118) @t4)) % 0.18/0.51 (define @t280 () (=> @t279 (_ @t148 (_ @t166 @t278)))) % 0.18/0.51 (define @t281 () (forall @t11 @t280)) % 0.18/0.51 (define @t282 () (not @t27)) % 0.18/0.51 (define @t283 () (or @t23 @t282)) % 0.18/0.51 (define @t284 () (lambda @t51 @t283)) % 0.18/0.51 (define @t285 () (_ @t284 @t16)) % 0.18/0.51 (define @t286 () (not @t285)) % 0.18/0.51 (define @t287 () (lambda @t51 @t286)) % 0.18/0.51 (define @t288 () (lambda @t51 @t282)) % 0.18/0.51 (define @t289 () (_ @t288 @t16)) % 0.18/0.51 (define @t290 () (or @t23 @t289)) % 0.18/0.51 (define @t291 () (lambda @t51 @t290)) % 0.18/0.51 (define @t292 () (or @t23 @t27)) % 0.18/0.51 (define @t293 () (lambda @t201 @t292)) % 0.18/0.51 (define @t294 () (lambda @t51 @t23)) % 0.18/0.51 (define @t295 () (_ @t294 @t16)) % 0.18/0.51 (define @t296 () (or @t295 @t27)) % 0.18/0.51 (define @t297 () (lambda @t201 @t296)) % 0.18/0.51 (define @t298 () (lambda @t51 @t292)) % 0.18/0.51 (define @t299 () (not @t74)) % 0.18/0.51 (define @t300 () (not @t69)) % 0.18/0.51 (define @t301 () (or @t300 @t299 @t75 @t80 @t85)) % 0.18/0.51 (define @t302 () (forall @t123 @t120)) % 0.18/0.51 (define @t303 () (@quantifiers_skolemize @t302 3)) % 0.18/0.51 (define @t304 () (@quantifiers_skolemize @t302 5)) % 0.18/0.51 (define @t305 () (@quantifiers_skolemize @t302 0)) % 0.18/0.51 (define @t306 () (forall @t100 (or (not (_ @t305 @t304 @t97)) (_ @t303 @t97)))) % 0.18/0.51 (define @t307 () (not @t306)) % 0.18/0.51 (define @t308 () (_ @t303 @t304)) % 0.18/0.51 (define @t309 () (not @t308)) % 0.18/0.51 (define @t310 () (@quantifiers_skolemize @t302 2)) % 0.18/0.51 (define @t311 () (_ @t310 @t304)) % 0.18/0.51 (define @t312 () (@quantifiers_skolemize @t302 1)) % 0.18/0.51 (define @t313 () (_ @t305 @t312 @t304)) % 0.18/0.51 (define @t314 () (not @t313)) % 0.18/0.51 (define @t315 () (@quantifiers_skolemize @t302 4)) % 0.18/0.51 (define @t316 () (forall @t109 (or (not (_ @t305 @t315 @t107)) (_ @t310 @t107)))) % 0.18/0.51 (define @t317 () (not @t316)) % 0.18/0.51 (define @t318 () (_ @t303 @t315)) % 0.18/0.51 (define @t319 () (_ @t305 @t312 @t315)) % 0.18/0.51 (define @t320 () (not @t319)) % 0.18/0.51 (define @t321 () (forall @t76 (or (not (_ @t305 @t63 @t67)) (not (_ @t305 @t63 @t73)) (_ @t305 @t67 @t73) @t80 (_ @t305 @t73 @t67)))) % 0.18/0.51 (define @t322 () (not @t321)) % 0.18/0.51 (define @t323 () (or @t322 @t320 @t318 (not (_ @t310 @t315)) @t317 @t314 @t311 @t309 @t307)) % 0.18/0.51 (define @t324 () (@list true)) % 0.18/0.51 (define @t325 () (@list @t323)) % 0.18/0.51 (define @t326 () (_ @t305 @t304 @t315)) % 0.18/0.51 (define @t327 () (not @t326)) % 0.18/0.51 (define @t328 () (or @t327 @t318)) % 0.18/0.51 (define @t329 () (@list true false)) % 0.18/0.51 (define @t330 () (_ @t305 @t315 @t304)) % 0.18/0.51 (define @t331 () (not @t330)) % 0.18/0.51 (define @t332 () (or @t331 @t311)) % 0.18/0.51 (define @t333 () (= @t315 @t304)) % 0.18/0.51 (define @t334 () (or @t320 @t314 @t330 @t333 @t326)) % 0.18/0.51 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.18/0.51 (assume @p2 @t13) % 0.18/0.51 (assume @p3 true) % 0.18/0.51 (step @p4 (= tptp.meq_ind @t17) :rule refl :args (@t17)) % 0.18/0.51 (step @p5 (= tptp.meq_prop @t20) :rule refl :args (@t20)) % 0.18/0.51 (step @p6 (= tptp.mnot @t25) :rule refl :args (@t25)) % 0.18/0.51 (step @p7 (= tptp.mor @t28) :rule refl :args (@t28)) % 0.18/0.51 (step @p8 (= tptp.mand @t33) :rule refl :args (@t33)) % 0.18/0.51 (step @p9 (= tptp.mimplies @t34) :rule refl :args (@t34)) % 0.18/0.51 (step @p10 (= tptp.mimplied @t35) :rule refl :args (@t35)) % 0.18/0.51 (step @p11 (= tptp.mequiv @t36) :rule refl :args (@t36)) % 0.18/0.51 (step @p12 (= tptp.mxor @t37) :rule refl :args (@t37)) % 0.18/0.51 (step @p13 (= tptp.mforall_ind @t40) :rule refl :args (@t40)) % 0.18/0.51 (step @p14 (= tptp.mforall_prop @t48) :rule refl :args (@t48)) % 0.18/0.51 (step @p15 (= tptp.mexists_ind @t49) :rule refl :args (@t49)) % 0.18/0.51 (step @p16 (= tptp.mexists_prop @t50) :rule refl :args (@t50)) % 0.18/0.51 (step @p17 (= tptp.mtrue @t52) :rule refl :args (@t52)) % 0.18/0.51 (step @p18 (= tptp.mbox @t61) :rule refl :args (@t61)) % 0.18/0.51 (step @p19 (= tptp.mdia @t62) :rule refl :args (@t62)) % 0.18/0.51 (step @p20 (= tptp.mreflexive @t66) :rule refl :args (@t66)) % 0.18/0.51 (step @p21 (= tptp.msymmetric @t70) :rule refl :args (@t70)) % 0.18/0.51 (step @p22 (= tptp.mserial @t72) :rule refl :args (@t72)) % 0.18/0.51 (step @p23 (= tptp.mtransitive @t77) :rule refl :args (@t77)) % 0.18/0.51 (step @p24 (= tptp.meuclidean @t79) :rule refl :args (@t79)) % 0.18/0.51 (step @p25 (= tptp.mpartially_functional @t81) :rule refl :args (@t81)) % 0.18/0.51 (step @p26 (= tptp.mfunctional @t83) :rule refl :args (@t83)) % 0.18/0.51 (step @p27 (= tptp.mweakly_dense @t86) :rule refl :args (@t86)) % 0.18/0.51 (step @p28 (= tptp.mweakly_connected @t89) :rule refl :args (@t89)) % 0.18/0.51 (step @p29 (= tptp.mweakly_directed @t90) :rule refl :args (@t90)) % 0.18/0.51 (step @p30 (= 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@p282 :rule beta-reduce :args ((= (_ @t28 @t294) @t297))) % 0.18/0.51 (step @p283 :rule trans :premises (@p282 @p281)) % 0.18/0.51 (step @p284 :rule beta-reduce :args ((= (_ @t25 @t21) @t294))) % 0.18/0.51 (step @p285 :rule ho_cong :premises (@p224 @p284)) % 0.18/0.51 (step @p286 :rule trans :premises (@p285 @p283)) % 0.18/0.51 (step @p287 :rule ho_cong :premises (@p286 @p278)) % 0.18/0.51 (step @p288 :rule trans :premises (@p287 @p277)) % 0.18/0.51 (step @p289 :rule refl :args (@t25)) % 0.18/0.51 (step @p290 :rule ho_cong :premises (@p289 @p288)) % 0.18/0.51 (step @p291 :rule trans :premises (@p290 @p271)) % 0.18/0.51 (step @p292 :rule ho_cong :premises (@p291 @p70)) % 0.18/0.51 (step @p293 :rule trans :premises (@p292 @p266)) % 0.18/0.51 (step @p294 :rule refl :args (@t26)) % 0.18/0.51 (step @p295 :rule ho_cong :premises (@p6 @p294)) % 0.18/0.51 (step @p296 :rule refl :args (@t21)) % 0.18/0.51 (step @p297 :rule ho_cong :premises (@p6 @p296)) % 0.18/0.51 (step @p298 :rule ho_cong :premises (@p7 @p297)) % 0.18/0.51 (step @p299 :rule ho_cong :premises (@p298 @p295)) % 0.18/0.51 (step @p300 :rule ho_cong :premises (@p6 @p299)) % 0.18/0.51 (step @p301 :rule ho_cong :premises (@p300 @p70)) % 0.18/0.51 (step @p302 :rule trans :premises (@p301 @p293)) % 0.18/0.51 (step @p303 :rule cong :premises (@p302) :args (@t33)) % 0.18/0.51 (step @p304 :rule trans :premises (@p8 @p303)) % 0.18/0.51 (step @p305 :rule ho_cong :premises (@p304 @p152)) % 0.18/0.51 (step @p306 :rule ho_cong :premises (@p305 @p265)) % 0.18/0.51 (step @p307 :rule beta-reduce :args ((= (_ @t298 @t1) @t232))) % 0.18/0.51 (step @p308 :rule beta-reduce :args ((= (_ @t293 @t26) @t298))) % 0.18/0.51 (step @p309 :rule ho_cong :premises (@p286 @p294)) % 0.18/0.51 (step @p310 :rule trans :premises (@p309 @p308)) % 0.18/0.51 (step @p311 :rule ho_cong :premises (@p310 @p70)) % 0.18/0.51 (step @p312 :rule trans :premises (@p311 @p307)) % 0.18/0.51 (step @p313 :rule ho_cong :premises (@p298 @p294)) % 0.18/0.51 (step @p314 :rule ho_cong :premises (@p313 @p70)) % 0.18/0.51 (step @p315 :rule trans :premises (@p314 @p312)) % 0.18/0.51 (step @p316 :rule cong :premises (@p315) :args (@t34)) % 0.18/0.51 (step @p317 :rule trans :premises (@p9 @p316)) % 0.18/0.51 (step @p318 :rule ho_cong :premises (@p317 @p306)) % 0.18/0.51 (step @p319 :rule ho_cong :premises (@p318 @p131)) % 0.18/0.51 (step @p320 :rule ho_cong :premises (@p264 @p319)) % 0.18/0.51 (step @p321 :rule ho_cong :premises (@p264 @p131)) % 0.18/0.51 (step @p322 :rule ho_cong :premises (@p304 @p131)) % 0.18/0.51 (step @p323 :rule ho_cong :premises (@p322 @p321)) % 0.18/0.51 (step @p324 :rule ho_cong :premises (@p317 @p323)) % 0.18/0.51 (step @p325 :rule ho_cong :premises (@p324 @p152)) % 0.18/0.51 (step @p326 :rule ho_cong :premises (@p264 @p325)) % 0.18/0.51 (step @p327 :rule ho_cong :premises (@p7 @p326)) % 0.18/0.51 (step @p328 :rule ho_cong :premises (@p327 @p320)) % 0.18/0.51 (step @p329 :rule ho_cong :premises (@p328 @p70)) % 0.18/0.51 (step @p330 :rule cong :premises (@p329) :args (@t7)) % 0.18/0.51 (step @p331 :rule refl :args (@t165)) % 0.18/0.51 (step @p332 :rule refl :args (@t44)) % 0.18/0.51 (step @p333 :rule cong :premises (@p332 @p331) :args ((= @t44 @t165))) % 0.18/0.51 (step @p334 :rule symm :premises (@p333)) % 0.18/0.51 (step @p335 :rule eq_resolve :premises (@p332 @p334)) % 0.18/0.51 (step @p336 :rule cong :premises (@p335) :args (@t46)) % 0.18/0.51 (step @p337 :rule cong :premises (@p336) :args (@t48)) % 0.18/0.51 (step @p338 :rule trans :premises (@p14 @p337)) % 0.18/0.51 (step @p339 :rule ho_cong :premises (@p338 @p330)) % 0.18/0.51 (step @p340 :rule ho_cong :premises (@p339 @p70)) % 0.18/0.51 (step @p341 :rule cong :premises (@p340) :args (@t9)) % 0.18/0.51 (step @p342 :rule ho_cong :premises (@p338 @p341)) % 0.18/0.51 (step @p343 :rule refl :args (@t147)) % 0.18/0.51 (step @p344 :rule refl :args (@t22)) % 0.18/0.51 (step @p345 :rule cong :premises (@p344 @p343) :args ((= @t22 @t147))) % 0.18/0.51 (step @p346 :rule symm :premises (@p345)) % 0.18/0.51 (step @p347 :rule eq_resolve :premises (@p344 @p346)) % 0.18/0.51 (step @p348 :rule cong :premises (@p347) :args (@t91)) % 0.18/0.51 (step @p349 :rule cong :premises (@p348) :args (@t93)) % 0.18/0.51 (step @p350 :rule trans :premises (@p30 @p349)) % 0.18/0.51 (step @p351 :rule ho_cong :premises (@p350 @p342)) % 0.18/0.51 (step @p352 :rule refl :args (@t114)) % 0.18/0.51 (step @p353 :rule refl :args (@t85)) % 0.18/0.51 (step @p354 :rule cong :premises (@p353 @p352) :args ((= @t85 @t114))) % 0.18/0.51 (step @p355 :rule symm :premises (@p354)) % 0.18/0.51 (step @p356 :rule eq_resolve :premises (@p353 @p355)) % 0.18/0.51 (step @p357 :rule refl :args (@t80)) % 0.18/0.51 (step @p358 :rule refl :args (@t115)) % 0.18/0.51 (step @p359 :rule refl :args (@t75)) % 0.18/0.51 (step @p360 :rule cong :premises (@p359 @p358) :args ((= @t75 @t115))) % 0.18/0.51 (step @p361 :rule symm :premises (@p360)) % 0.18/0.51 (step @p362 :rule eq_resolve :premises (@p359 @p361)) % 0.18/0.51 (step @p363 :rule refl :args (@t116)) % 0.18/0.51 (step @p364 :rule refl :args (@t74)) % 0.18/0.51 (step @p365 :rule cong :premises (@p364 @p363) :args ((= @t74 @t116))) % 0.18/0.51 (step @p366 :rule symm :premises (@p365)) % 0.18/0.51 (step @p367 :rule eq_resolve :premises (@p364 @p366)) % 0.18/0.51 (step @p368 :rule cong :premises (@p367) :args (@t299)) % 0.18/0.51 (step @p369 :rule refl :args (@t117)) % 0.18/0.51 (step @p370 :rule refl :args (@t69)) % 0.18/0.51 (step @p371 :rule cong :premises (@p370 @p369) :args ((= @t69 @t117))) % 0.18/0.51 (step @p372 :rule symm :premises (@p371)) % 0.18/0.51 (step @p373 :rule eq_resolve :premises (@p370 @p372)) % 0.18/0.51 (step @p374 :rule cong :premises (@p373) :args (@t300)) % 0.18/0.51 (step @p375 :rule nary_cong :premises (@p374 @p368 @p362 @p357 @p356) :args (@t301)) % 0.18/0.51 (step @p376 :rule cong :premises (@p375) :args ((forall @t76 @t301))) % 0.18/0.51 (step @p377 :rule aci_norm :args ((= (or (or @t300 @t299) @t87) @t301))) % 0.18/0.51 (step @p378 :rule refl :args (@t87)) % 0.18/0.51 (step @p379 :rule bool-and-de-morgan :args (@t69 @t74 true)) % 0.18/0.51 (step @p380 :rule nary_cong :premises (@p379 @p378) :args ((or (not @t78) @t87))) % 0.18/0.51 (step @p381 :rule trans :premises (@p380 @p377)) % 0.18/0.51 (step @p382 :rule bool-impl-elim :args (@t78 @t87)) % 0.18/0.51 (step @p383 :rule trans :premises (@p382 @p381)) % 0.18/0.51 (step @p384 :rule cong :premises (@p383) :args (@t88)) % 0.18/0.51 (step @p385 :rule trans :premises (@p384 @p376)) % 0.18/0.51 (step @p386 :rule cong :premises (@p385) :args (@t89)) % 0.18/0.51 (step @p387 :rule trans :premises (@p28 @p386)) % 0.18/0.51 (step @p388 :rule ho_cong :premises (@p387 @p248)) % 0.18/0.51 (step @p389 :rule cong :premises (@p388 @p351) :args (@t10)) % 0.18/0.51 (step @p390 :rule cong :premises (@p389) :args (@t12)) % 0.18/0.51 (step @p391 :rule cong :premises (@p390) :args (@t13)) % 0.18/0.51 (step @p392 :rule trans :premises (@p391 @p247)) % 0.18/0.51 (step @p393 :rule eq_resolve :premises (@p2 @p392)) % 0.18/0.51 (step @p394 :rule skolemize :premises (@p393)) % 0.18/0.51 (step @p395 :rule cnf_or_neg :args (@t323 2)) % 0.18/0.51 (step @p396 :rule chain_m_resolution :premises (@p395 @p394) :args ((not @t318) @t324 @t325)) % 0.18/0.51 (step @p397 :rule false_intro :premises (@p396)) % 0.18/0.51 (step @p398 :rule bool-double-not-elim :args (@t321)) % 0.18/0.51 (step @p399 :rule refl :args (@t323)) % 0.18/0.51 (step @p400 :rule nary_cong :premises (@p399 @p398) :args ((or @t323 (not @t322)))) % 0.18/0.51 (step @p401 :rule cnf_or_neg :args (@t323 0)) % 0.18/0.51 (step @p402 :rule eq_resolve :premises (@p401 @p400)) % 0.18/0.51 (step @p403 :rule reordering :premises (@p402) :args ((or @t321 @t323))) % 0.18/0.51 (step @p404 :rule chain_m_resolution :premises (@p403 @p394) :args (@t321 @t324 @t325)) % 0.18/0.51 (step @p405 :rule instantiate :premises (@p404) :args ((@list @t312 @t315 @t304))) % 0.18/0.51 (step @p406 :rule bool-double-not-elim :args (@t306)) % 0.18/0.51 (step @p407 :rule nary_cong :premises (@p399 @p406) :args ((or @t323 (not @t307)))) % 0.18/0.51 (step @p408 :rule cnf_or_neg :args (@t323 8)) % 0.18/0.51 (step @p409 :rule eq_resolve :premises (@p408 @p407)) % 0.18/0.51 (step @p410 :rule reordering :premises (@p409) :args ((or @t306 @t323))) % 0.18/0.51 (step @p411 :rule chain_m_resolution :premises (@p410 @p394) :args (@t306 @t324 @t325)) % 0.18/0.51 (step @p412 :rule instantiate :premises (@p411) :args ((@list @t315))) % 0.18/0.51 (step @p413 :rule cnf_or_pos :args (@t328)) % 0.18/0.51 (step @p414 :rule reordering :premises (@p413) :args ((or @t318 @t327 (not @t328)))) % 0.18/0.51 (step @p415 :rule chain_m_resolution :premises (@p414 @p396 @p412) :args (@t327 @t329 (@list @t318 @t328))) % 0.18/0.51 (step @p416 :rule bool-double-not-elim :args (@t316)) % 0.18/0.51 (step @p417 :rule nary_cong :premises (@p399 @p416) :args ((or @t323 (not @t317)))) % 0.18/0.51 (step @p418 :rule cnf_or_neg :args (@t323 4)) % 0.18/0.51 (step @p419 :rule eq_resolve :premises (@p418 @p417)) % 0.18/0.51 (step @p420 :rule reordering :premises (@p419) :args ((or @t316 @t323))) % 0.18/0.51 (step @p421 :rule chain_m_resolution :premises (@p420 @p394) :args (@t316 @t324 @t325)) % 0.18/0.51 (step @p422 :rule instantiate :premises (@p421) :args ((@list @t304))) % 0.18/0.51 (step @p423 :rule cnf_or_neg :args (@t323 6)) % 0.18/0.51 (step @p424 :rule chain_m_resolution :premises (@p423 @p394) :args ((not @t311) @t324 @t325)) % 0.18/0.51 (step @p425 :rule cnf_or_pos :args (@t332)) % 0.18/0.51 (step @p426 :rule reordering :premises (@p425) :args ((or @t311 @t331 (not @t332)))) % 0.18/0.51 (step @p427 :rule chain_m_resolution :premises (@p426 @p424 @p422) :args (@t331 @t329 (@list @t311 @t332))) % 0.18/0.51 (step @p428 :rule bool-double-not-elim :args (@t313)) % 0.18/0.51 (step @p429 :rule nary_cong :premises (@p399 @p428) :args ((or @t323 (not @t314)))) % 0.18/0.51 (step @p430 :rule cnf_or_neg :args (@t323 5)) % 0.18/0.51 (step @p431 :rule eq_resolve :premises (@p430 @p429)) % 0.18/0.51 (step @p432 :rule reordering :premises (@p431) :args ((or @t313 @t323))) % 0.18/0.51 (step @p433 :rule chain_m_resolution :premises (@p432 @p394) :args (@t313 @t324 @t325)) % 0.18/0.51 (step @p434 :rule bool-double-not-elim :args (@t319)) % 0.18/0.51 (step @p435 :rule nary_cong :premises (@p399 @p434) :args ((or @t323 (not @t320)))) % 0.18/0.51 (step @p436 :rule cnf_or_neg :args (@t323 1)) % 0.18/0.51 (step @p437 :rule eq_resolve :premises (@p436 @p435)) % 0.18/0.51 (step @p438 :rule reordering :premises (@p437) :args ((or @t319 @t323))) % 0.18/0.51 (step @p439 :rule chain_m_resolution :premises (@p438 @p394) :args (@t319 @t324 @t325)) % 0.18/0.51 (step @p440 :rule cnf_or_pos :args (@t334)) % 0.18/0.51 (step @p441 :rule reordering :premises (@p440) :args ((or @t320 @t314 @t330 @t333 @t326 (not @t334)))) % 0.18/0.51 (step @p442 :rule chain_m_resolution :premises (@p441 @p439 @p433 @p427 @p415 @p405) :args (@t333 (@list false false true true false) (@list @t319 @t313 @t330 @t326 @t334))) % 0.18/0.51 (step @p443 :rule symm :premises (@p442)) % 0.18/0.51 (step @p444 :rule cong :premises (@p443) :args (@t308)) % 0.18/0.51 (step @p445 :rule bool-double-not-elim :args (@t308)) % 0.18/0.51 (step @p446 :rule nary_cong :premises (@p399 @p445) :args ((or @t323 (not @t309)))) % 0.18/0.51 (step @p447 :rule cnf_or_neg :args (@t323 7)) % 0.18/0.51 (step @p448 :rule eq_resolve :premises (@p447 @p446)) % 0.18/0.51 (step @p449 :rule reordering :premises (@p448) :args ((or @t308 @t323))) % 0.18/0.51 (step @p450 :rule chain_m_resolution :premises (@p449 @p394) :args (@t308 @t324 @t325)) % 0.18/0.51 (step @p451 :rule true_intro :premises (@p450)) % 0.18/0.51 (step @p452 :rule symm :premises (@p451)) % 0.18/0.51 (step @p453 :rule trans :premises (@p452 @p444 @p397)) % 0.18/0.51 (step @p454 false :rule eq_resolve :premises (@p453 @p34)) % 0.18/0.51 ) % 0.18/0.51 % SZS output end Proof % 0.18/0.51 % cvc5 exiting %------------------------------------------------------------------------------