%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL723^1 : 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 : 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 11:23:42 AM UTC 2026 % Result : Theorem 0.31s 0.70s % Output : Proof 0.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.05 % Problem : LCL723^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.41 % Computer : n002.cluster.edu % 0.15/0.41 % Model : x86_64 x86_64 % 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.41 % Memory : 8046.5625MB % 0.15/0.41 % OS : Linux 6.8.0-71-generic % 0.15/0.41 % CPULimit : 300 % 0.15/0.41 % WCLimit : 300 % 0.15/0.41 % DateTime : Sun Sep 6 01:44:21 UTC 2026 % 0.15/0.41 % CPUTime : % 0.26/0.53 %----Proving TH0 % 0.31/0.70 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.31/0.70 % SZS status Theorem % 0.31/0.70 % SZS output start Proof % 0.31/0.70 ( % 0.31/0.70 (declare-sort $$unsorted 0) % 0.31/0.70 (declare-sort tptp.mu 0) % 0.31/0.70 (declare-const tptp.rel_b (-> $$unsorted $$unsorted Bool)) % 0.31/0.70 (declare-const tptp.phi (-> $$unsorted Bool)) % 0.31/0.70 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.31/0.70 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.31/0.70 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.31/0.70 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.31/0.70 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.31/0.70 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.31/0.70 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.31/0.70 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.31/0.70 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.31/0.70 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.31/0.70 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.31/0.70 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.31/0.70 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.31/0.70 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.31/0.70 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.31/0.70 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.31/0.70 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.31/0.70 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.31/0.70 (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)))))))) % 0.31/0.70 (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)))))))) % 0.31/0.70 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.31/0.70 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.31/0.70 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.31/0.70 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.31/0.70 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.31/0.70 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.31/0.70 (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))))))))))))) % 0.31/0.70 (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)))))) % 0.31/0.70 (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))))))) % 0.31/0.70 (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)))))) % 0.31/0.70 (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))))))) % 0.31/0.70 (define tptp.mbox_b () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_b _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.31/0.70 (define tptp.mdia_b () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_b (_ tptp.mnot _let_2))) _let_1))))) % 0.31/0.70 (define @t1 () (and (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mbox_b tptp.phi)) tptp.phi)) (_ tptp.mvalid (_ (_ tptp.mimplies tptp.phi) (_ tptp.mbox_b (_ tptp.mdia_b tptp.phi)))))) % 0.31/0.70 (define @t2 () (not @t1)) % 0.31/0.70 (define @t3 () (@var "Y" tptp.mu)) % 0.31/0.70 (define @t4 () (@var "X" tptp.mu)) % 0.31/0.70 (define @t5 () (@var "W" $$unsorted)) % 0.31/0.70 (define @t6 () (lambda (@list @t4 @t3 @t5) (= @t4 @t3))) % 0.31/0.70 (define @t7 () (@var "Y" (-> $$unsorted Bool))) % 0.31/0.70 (define @t8 () (@var "X" (-> $$unsorted Bool))) % 0.31/0.70 (define @t9 () (lambda (@list @t8 @t7 @t5) (= (_ @t8 @t5) (_ @t7 @t5)))) % 0.31/0.70 (define @t10 () (@var "Phi" (-> $$unsorted Bool))) % 0.31/0.70 (define @t11 () (_ @t10 @t5)) % 0.31/0.70 (define @t12 () (not @t11)) % 0.31/0.70 (define @t13 () (@list @t10 @t5)) % 0.31/0.70 (define @t14 () (lambda @t13 @t12)) % 0.31/0.70 (define @t15 () (@var "Psi" (-> $$unsorted Bool))) % 0.31/0.70 (define @t16 () (_ @t15 @t5)) % 0.31/0.70 (define @t17 () (lambda (@list @t10 @t15 @t5) (or @t11 @t16))) % 0.31/0.70 (define @t18 () (@var "__flatten_var_0" $$unsorted)) % 0.31/0.70 (define @t19 () (_ tptp.mnot @t15)) % 0.31/0.70 (define @t20 () (_ tptp.mnot @t10)) % 0.31/0.70 (define @t21 () (_ tptp.mor @t20)) % 0.31/0.70 (define @t22 () (@list @t10 @t15 @t18)) % 0.31/0.70 (define @t23 () (lambda @t22 (_ (_ tptp.mnot (_ @t21 @t19)) @t18))) % 0.31/0.70 (define @t24 () (lambda @t22 (_ (_ @t21 @t15) @t18))) % 0.31/0.70 (define @t25 () (lambda @t22 (_ (_ (_ tptp.mor @t19) @t10) @t18))) % 0.31/0.70 (define @t26 () (lambda @t22 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t10) @t15)) (_ (_ tptp.mimplies @t15) @t10)) @t18))) % 0.31/0.70 (define @t27 () (lambda @t22 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t10) @t15)) @t18))) % 0.31/0.70 (define @t28 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.31/0.70 (define @t29 () (_ @t28 @t4)) % 0.31/0.70 (define @t30 () (lambda (@list @t28 @t5) (forall (@list @t4) (_ @t29 @t5)))) % 0.31/0.70 (define @t31 () (@var "P" (-> $$unsorted Bool))) % 0.31/0.70 (define @t32 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.31/0.70 (define @t33 () (_ @t32 @t31)) % 0.31/0.70 (define @t34 () (lambda (@list @t32 @t5) (forall (@list @t31) (_ @t33 @t5)))) % 0.31/0.70 (define @t35 () (lambda (@list @t28 @t18) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t4 @t18) (_ (_ tptp.mnot @t29) @t18)))) @t18))) % 0.31/0.70 (define @t36 () (lambda (@list @t32 @t18) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t31 @t18) (_ (_ tptp.mnot @t33) @t18)))) @t18))) % 0.31/0.70 (define @t37 () (@list @t5)) % 0.31/0.70 (define @t38 () (lambda @t37 true)) % 0.31/0.70 (define @t39 () (@var "V" $$unsorted)) % 0.31/0.70 (define @t40 () (_ @t10 @t39)) % 0.31/0.70 (define @t41 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.31/0.70 (define @t42 () (@list @t39)) % 0.31/0.70 (define @t43 () (lambda (@list @t41 @t10 @t5) (forall @t42 (or (not (_ (_ @t41 @t5) @t39)) @t40)))) % 0.31/0.70 (define @t44 () (lambda (@list @t41 @t10 @t18) (_ (_ tptp.mnot (_ (_ tptp.mbox @t41) @t20)) @t18))) % 0.31/0.70 (define @t45 () (@var "S" $$unsorted)) % 0.31/0.70 (define @t46 () (_ @t41 @t45)) % 0.31/0.70 (define @t47 () (_ @t46 @t45)) % 0.31/0.70 (define @t48 () (@list @t45)) % 0.31/0.70 (define @t49 () (forall @t48 @t47)) % 0.31/0.70 (define @t50 () (@list @t41)) % 0.31/0.70 (define @t51 () (lambda @t50 @t49)) % 0.31/0.70 (define @t52 () (@var "T" $$unsorted)) % 0.31/0.70 (define @t53 () (_ @t41 @t52)) % 0.31/0.70 (define @t54 () (_ @t53 @t45)) % 0.31/0.70 (define @t55 () (_ @t46 @t52)) % 0.31/0.70 (define @t56 () (@list @t45 @t52)) % 0.31/0.70 (define @t57 () (forall @t56 (=> @t55 @t54))) % 0.31/0.70 (define @t58 () (lambda @t50 @t57)) % 0.31/0.70 (define @t59 () (@list @t52)) % 0.31/0.70 (define @t60 () (lambda @t50 (forall @t48 (exists @t59 @t55)))) % 0.31/0.70 (define @t61 () (@var "U" $$unsorted)) % 0.31/0.70 (define @t62 () (_ @t46 @t61)) % 0.31/0.70 (define @t63 () (_ @t53 @t61)) % 0.31/0.70 (define @t64 () (@list @t45 @t52 @t61)) % 0.31/0.70 (define @t65 () (lambda @t50 (forall @t64 (=> (and @t55 @t63) @t62)))) % 0.31/0.70 (define @t66 () (and @t55 @t62)) % 0.31/0.70 (define @t67 () (lambda @t50 (forall @t64 (=> @t66 @t63)))) % 0.31/0.70 (define @t68 () (= @t52 @t61)) % 0.31/0.70 (define @t69 () (lambda @t50 (forall @t64 (=> @t66 @t68)))) % 0.31/0.70 (define @t70 () (@list @t61)) % 0.31/0.70 (define @t71 () (lambda @t50 (forall @t48 (exists @t59 (and @t55 (forall @t70 (=> @t62 @t68))))))) % 0.31/0.70 (define @t72 () (_ @t41 @t61)) % 0.31/0.70 (define @t73 () (_ @t72 @t52)) % 0.31/0.70 (define @t74 () (lambda @t50 (forall @t64 (=> @t55 (exists @t70 (and @t62 @t73)))))) % 0.31/0.70 (define @t75 () (lambda @t50 (forall @t64 (=> @t66 (or @t63 @t68 @t73))))) % 0.31/0.70 (define @t76 () (lambda @t50 (forall @t64 (=> @t66 (exists @t42 (and (_ @t53 @t39) (_ @t72 @t39))))))) % 0.31/0.70 (define @t77 () (forall @t37 @t11)) % 0.31/0.70 (define @t78 () (@list @t10)) % 0.31/0.70 (define @t79 () (lambda @t78 @t77)) % 0.31/0.70 (define @t80 () (lambda @t78 (forall @t37 @t12))) % 0.31/0.70 (define @t81 () (lambda @t78 (exists @t37 @t11))) % 0.31/0.70 (define @t82 () (lambda @t78 (exists @t37 @t12))) % 0.31/0.70 (define @t83 () (_ (_ tptp.rel_b @t5) @t39)) % 0.31/0.70 (define @t84 () (not @t83)) % 0.31/0.70 (define @t85 () (or @t84 @t40)) % 0.31/0.70 (define @t86 () (forall @t42 @t85)) % 0.31/0.70 (define @t87 () (lambda @t13 @t86)) % 0.31/0.70 (define @t88 () (@list @t10 @t18)) % 0.31/0.70 (define @t89 () (lambda @t88 (_ (_ tptp.mnot (_ tptp.mbox_b @t20)) @t18))) % 0.31/0.70 (define @t90 () (tptp.phi @t39)) % 0.31/0.70 (define @t91 () (tptp.phi @t5)) % 0.31/0.70 (define @t92 () (tptp.rel_b @t5 @t39)) % 0.31/0.70 (define @t93 () (not @t92)) % 0.31/0.70 (define @t94 () (forall @t42 (or @t93 @t90))) % 0.31/0.70 (define @t95 () (not @t94)) % 0.31/0.70 (define @t96 () (forall @t37 (or @t95 @t91))) % 0.31/0.70 (define @t97 () (@quantifiers_skolemize @t96 0)) % 0.31/0.70 (define @t98 () (forall @t42 (or (not (tptp.rel_b @t97 @t39)) @t90))) % 0.31/0.70 (define @t99 () (tptp.phi @t97)) % 0.31/0.70 (define @t100 () (not @t98)) % 0.31/0.70 (define @t101 () (or @t100 @t99)) % 0.31/0.70 (define @t102 () (@list @t97)) % 0.31/0.70 (define @t103 () (tptp.rel_b @t97 @t97)) % 0.31/0.70 (define @t104 () (not @t103)) % 0.31/0.70 (define @t105 () (or @t104 @t99)) % 0.31/0.70 (define @t106 () (_ @t41 @t45 @t45)) % 0.31/0.70 (define @t107 () (not @t101)) % 0.31/0.70 (define @t108 () (not @t96)) % 0.31/0.70 (define @t109 () (@list false)) % 0.31/0.70 (define @t110 () (@var "BOUND_VARIABLE_8461" $$unsorted)) % 0.31/0.70 (define @t111 () (not (tptp.phi @t110))) % 0.31/0.70 (define @t112 () (@var "BOUND_VARIABLE_8499" $$unsorted)) % 0.31/0.70 (define @t113 () (@list @t110)) % 0.31/0.70 (define @t114 () (not (forall @t113 (or (not (tptp.rel_b @t112 @t110)) @t111)))) % 0.31/0.70 (define @t115 () (not (tptp.rel_b @t5 @t112))) % 0.31/0.70 (define @t116 () (not @t91)) % 0.31/0.70 (define @t117 () (or @t116 @t115 @t114)) % 0.31/0.70 (define @t118 () (or @t115 @t114)) % 0.31/0.70 (define @t119 () (or @t116 @t118)) % 0.31/0.70 (define @t120 () (@list @t5 @t112)) % 0.31/0.70 (define @t121 () (forall @t120 @t119)) % 0.31/0.70 (define @t122 () (@list @t112)) % 0.31/0.70 (define @t123 () (forall @t122 @t119)) % 0.31/0.70 (define @t124 () (forall @t122 @t118)) % 0.31/0.70 (define @t125 () (@list @t39)) % 0.31/0.70 (define @t126 () (or @t116 @t124)) % 0.31/0.70 (define @t127 () (not (forall @t113 (or (not (tptp.rel_b @t39 @t110)) @t111)))) % 0.31/0.70 (define @t128 () (forall @t42 (or @t93 @t127))) % 0.31/0.70 (define @t129 () (_ tptp.phi @t5)) % 0.31/0.70 (define @t130 () (not @t129)) % 0.31/0.70 (define @t131 () (or @t130 @t128)) % 0.31/0.70 (define @t132 () (not (tptp.rel_b @t18 @t39))) % 0.31/0.70 (define @t133 () (forall @t42 (or @t132 @t127))) % 0.31/0.70 (define @t134 () (_ tptp.phi @t18)) % 0.31/0.70 (define @t135 () (not @t134)) % 0.31/0.70 (define @t136 () (@list @t18)) % 0.31/0.70 (define @t137 () (lambda @t136 (or @t135 @t133))) % 0.31/0.70 (define @t138 () (_ @t137 @t5)) % 0.31/0.70 (define @t139 () (forall @t37 @t138)) % 0.31/0.70 (define @t140 () (_ @t10 @t5)) % 0.31/0.70 (define @t141 () (lambda @t78 (forall @t37 @t140))) % 0.31/0.70 (define @t142 () (lambda @t37 @t128)) % 0.31/0.70 (define @t143 () (_ @t142 @t18)) % 0.31/0.70 (define @t144 () (or @t135 @t143)) % 0.31/0.70 (define @t145 () (lambda @t136 @t144)) % 0.31/0.70 (define @t146 () (_ @t15 @t18)) % 0.31/0.70 (define @t147 () (@list @t15 @t18)) % 0.31/0.70 (define @t148 () (lambda @t147 (or @t135 @t146))) % 0.31/0.70 (define @t149 () (forall @t42 (or @t132 (not @t90)))) % 0.31/0.70 (define @t150 () (not @t149)) % 0.31/0.70 (define @t151 () (lambda @t136 @t150)) % 0.31/0.70 (define @t152 () (or @t93 (_ @t151 @t39))) % 0.31/0.70 (define @t153 () (forall @t42 @t152)) % 0.31/0.70 (define @t154 () (lambda @t37 @t153)) % 0.31/0.70 (define @t155 () (_ @t10 @t39)) % 0.31/0.70 (define @t156 () (lambda @t13 (forall @t42 (or @t93 @t155)))) % 0.31/0.70 (define @t157 () (not @t155)) % 0.31/0.70 (define @t158 () (not (forall @t42 (or @t132 @t157)))) % 0.31/0.70 (define @t159 () (_ (lambda @t88 @t158) tptp.phi)) % 0.31/0.70 (define @t160 () (or (not (_ @t10 @t18)) @t146)) % 0.31/0.70 (define @t161 () (lambda @t22 @t160)) % 0.31/0.70 (define @t162 () (_ @t161 tptp.phi)) % 0.31/0.70 (define @t163 () (or @t95 @t129)) % 0.31/0.70 (define @t164 () (forall @t42 (or @t132 @t90))) % 0.31/0.70 (define @t165 () (not @t164)) % 0.31/0.70 (define @t166 () (lambda @t136 (or @t165 @t134))) % 0.31/0.70 (define @t167 () (_ @t166 @t5)) % 0.31/0.70 (define @t168 () (forall @t37 @t167)) % 0.31/0.70 (define @t169 () (lambda @t37 @t94)) % 0.31/0.70 (define @t170 () (_ @t169 @t18)) % 0.31/0.70 (define @t171 () (not @t170)) % 0.31/0.70 (define @t172 () (or @t171 @t146)) % 0.31/0.70 (define @t173 () (lambda @t147 @t172)) % 0.31/0.70 (define @t174 () (_ @t156 tptp.phi)) % 0.31/0.70 (define @t175 () (and (_ @t141 (_ (_ @t161 @t174) tptp.phi)) (_ @t141 (_ @t162 (_ @t156 @t159))))) % 0.31/0.70 (define @t176 () (forall @t42 (or @t93 @t157))) % 0.31/0.70 (define @t177 () (lambda @t37 @t176)) % 0.31/0.70 (define @t178 () (_ @t177 @t5)) % 0.31/0.70 (define @t179 () (not @t178)) % 0.31/0.70 (define @t180 () (lambda @t37 @t179)) % 0.31/0.70 (define @t181 () (not @t40)) % 0.31/0.70 (define @t182 () (or @t93 @t181)) % 0.31/0.70 (define @t183 () (lambda @t37 @t12)) % 0.31/0.70 (define @t184 () (_ @t183 @t39)) % 0.31/0.70 (define @t185 () (or @t93 @t184)) % 0.31/0.70 (define @t186 () (forall @t42 @t185)) % 0.31/0.70 (define @t187 () (lambda @t37 @t186)) % 0.31/0.70 (define @t188 () (or @t12 @t16)) % 0.31/0.70 (define @t189 () (lambda @t37 @t188)) % 0.31/0.70 (define @t190 () (@list @t15 @t5)) % 0.31/0.70 (define @t191 () (_ @t183 @t5)) % 0.31/0.70 (define @t192 () (or @t191 @t16)) % 0.31/0.70 (define @t193 () (lambda @t190 @t192)) % 0.31/0.70 (define @t194 () (forall @t120 @t117)) % 0.31/0.70 (define @t195 () (not @t194)) % 0.31/0.70 (define @t196 () (@quantifiers_skolemize @t194 1)) % 0.31/0.70 (define @t197 () (forall @t113 (or (not (tptp.rel_b @t196 @t110)) @t111))) % 0.31/0.70 (define @t198 () (not @t197)) % 0.31/0.70 (define @t199 () (@quantifiers_skolemize @t194 0)) % 0.31/0.70 (define @t200 () (tptp.rel_b @t199 @t196)) % 0.31/0.70 (define @t201 () (not @t200)) % 0.31/0.70 (define @t202 () (tptp.phi @t199)) % 0.31/0.70 (define @t203 () (not @t202)) % 0.31/0.70 (define @t204 () (or @t203 @t201 @t198)) % 0.31/0.70 (define @t205 () (not @t204)) % 0.31/0.70 (define @t206 () (@list true)) % 0.31/0.70 (define @t207 () (@list @t204)) % 0.31/0.70 (define @t208 () (tptp.rel_b @t196 @t199)) % 0.31/0.70 (define @t209 () (not @t208)) % 0.31/0.70 (define @t210 () (or @t209 @t203)) % 0.31/0.70 (define @t211 () (_ @t41 @t52 @t45)) % 0.31/0.70 (define @t212 () (_ @t41 @t45 @t52)) % 0.31/0.70 (define @t213 () (not @t55)) % 0.31/0.70 (define @t214 () (or @t213 @t54)) % 0.31/0.70 (define @t215 () (or @t201 @t208)) % 0.31/0.70 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.31/0.70 (assume @p2 (_ tptp.mreflexive tptp.rel_b)) % 0.31/0.70 (assume @p3 (_ tptp.msymmetric tptp.rel_b)) % 0.31/0.70 (assume @p4 @t2) % 0.31/0.70 (assume @p5 true) % 0.31/0.70 (step @p6 (= tptp.meq_ind @t6) :rule refl :args (@t6)) % 0.31/0.70 (step @p7 (= tptp.meq_prop @t9) :rule refl :args (@t9)) % 0.31/0.70 (step @p8 (= tptp.mnot @t14) :rule refl :args (@t14)) % 0.31/0.70 (step @p9 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.31/0.70 (step @p10 (= tptp.mand @t23) :rule refl :args (@t23)) % 0.31/0.70 (step @p11 (= tptp.mimplies @t24) :rule refl :args (@t24)) % 0.31/0.70 (step @p12 (= tptp.mimplied @t25) :rule refl :args (@t25)) % 0.31/0.70 (step @p13 (= tptp.mequiv @t26) :rule refl :args (@t26)) % 0.31/0.70 (step @p14 (= tptp.mxor @t27) :rule refl :args (@t27)) % 0.31/0.70 (step @p15 (= tptp.mforall_ind @t30) :rule refl :args (@t30)) % 0.31/0.70 (step @p16 (= tptp.mforall_prop @t34) :rule refl :args (@t34)) % 0.31/0.70 (step @p17 (= tptp.mexists_ind @t35) :rule refl :args (@t35)) % 0.31/0.70 (step @p18 (= tptp.mexists_prop @t36) :rule refl :args (@t36)) % 0.31/0.70 (step @p19 (= tptp.mtrue @t38) :rule refl :args (@t38)) % 0.31/0.70 (step @p20 (= tptp.mbox @t43) :rule refl :args (@t43)) % 0.31/0.70 (step @p21 (= tptp.mdia @t44) :rule refl :args (@t44)) % 0.31/0.70 (step @p22 (= tptp.mreflexive @t51) :rule refl :args (@t51)) % 0.31/0.70 (step @p23 (= tptp.msymmetric @t58) :rule refl :args (@t58)) % 0.31/0.70 (step @p24 (= tptp.mserial @t60) :rule refl :args (@t60)) % 0.31/0.70 (step @p25 (= tptp.mtransitive @t65) :rule refl :args (@t65)) % 0.31/0.70 (step @p26 (= tptp.meuclidean @t67) :rule refl :args (@t67)) % 0.31/0.70 (step @p27 (= tptp.mpartially_functional @t69) :rule refl :args (@t69)) % 0.31/0.70 (step @p28 (= tptp.mfunctional @t71) :rule refl :args (@t71)) % 0.31/0.70 (step @p29 (= tptp.mweakly_dense @t74) :rule refl :args (@t74)) % 0.31/0.70 (step @p30 (= tptp.mweakly_connected @t75) :rule refl :args (@t75)) % 0.31/0.70 (step @p31 (= tptp.mweakly_directed @t76) :rule refl :args (@t76)) % 0.31/0.70 (step @p32 (= tptp.mvalid @t79) :rule refl :args (@t79)) % 0.31/0.70 (step @p33 (= tptp.minvalid @t80) :rule refl :args (@t80)) % 0.31/0.70 (step @p34 (= tptp.msatisfiable @t81) :rule refl :args (@t81)) % 0.31/0.70 (step @p35 (= tptp.mcountersatisfiable @t82) :rule refl :args (@t82)) % 0.31/0.70 (step @p36 (= tptp.mbox_b @t87) :rule refl :args (@t87)) % 0.31/0.70 (step @p37 (= tptp.mdia_b @t89) :rule refl :args (@t89)) % 0.31/0.70 (step @p38 :rule bool-double-not-elim :args (@t98)) % 0.31/0.70 (step @p39 :rule refl :args (@t101)) % 0.31/0.70 (step @p40 :rule nary_cong :premises (@p39 @p38) :args ((or @t101 (not @t100)))) % 0.31/0.70 (step @p41 :rule cnf_or_neg :args (@t101 0)) % 0.31/0.70 (step @p42 :rule eq_resolve :premises (@p41 @p40)) % 0.31/0.70 (step @p43 :rule reordering :premises (@p42) :args ((or @t98 @t101))) % 0.31/0.70 (step @p44 :rule cnf_or_neg :args (@t101 1)) % 0.31/0.70 (assume-push @p318 @t98) % 0.31/0.70 (step @p46 :rule instantiate :premises (@p318) :args (@t102)) % 0.31/0.70 (step-pop @p319 :rule scope :premises (@p46)) % 0.31/0.70 (step @p47 :rule process_scope :premises (@p319) :args (@t105)) % 0.31/0.70 (step @p49 :rule implies_elim :premises (@p47)) % 0.31/0.70 (step @p50 :rule beta-reduce :args ((= (_ (lambda @t50 (forall @t48 @t106)) tptp.rel_b) (forall @t48 (tptp.rel_b @t45 @t45))))) % 0.31/0.70 (step @p51 :rule refl :args (tptp.rel_b)) % 0.31/0.70 (step @p52 :rule refl :args (@t106)) % 0.31/0.70 (step @p53 :rule refl :args (@t47)) % 0.31/0.70 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t47 @t106))) % 0.31/0.70 (step @p55 :rule symm :premises (@p54)) % 0.31/0.70 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.31/0.70 (step @p57 :rule cong :premises (@p56) :args (@t49)) % 0.31/0.70 (step @p58 :rule cong :premises (@p57) :args (@t51)) % 0.31/0.70 (step @p59 :rule trans :premises (@p22 @p58)) % 0.31/0.70 (step @p60 :rule ho_cong :premises (@p59 @p51)) % 0.31/0.70 (step @p61 :rule trans :premises (@p60 @p50)) % 0.31/0.70 (step @p62 :rule eq_resolve :premises (@p2 @p61)) % 0.31/0.70 (step @p63 :rule instantiate :premises (@p62) :args (@t102)) % 0.31/0.70 (step @p64 :rule cnf_or_pos :args (@t105)) % 0.31/0.70 (step @p65 :rule reordering :premises (@p64) :args ((or @t99 @t104 (not @t105)))) % 0.31/0.70 (step @p66 :rule chain_m_resolution :premises (@p65 @p63 @p49 @p44 @p43) :args (@t101 (@list false false true false) (@list @t103 @t105 @t99 @t98))) % 0.31/0.70 (step @p67 :rule refl :args (@t107)) % 0.31/0.70 (step @p68 :rule bool-double-not-elim :args (@t96)) % 0.31/0.70 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or (not @t108) @t107))) % 0.31/0.70 (assume-push @p320 @t108) % 0.31/0.70 (step @p71 :rule skolemize :premises (@p320)) % 0.31/0.70 (step-pop @p321 :rule scope :premises (@p71)) % 0.31/0.70 (step @p72 :rule process_scope :premises (@p321) :args (@t107)) % 0.31/0.70 (step @p74 :rule implies_elim :premises (@p72)) % 0.31/0.70 (step @p75 :rule eq_resolve :premises (@p74 @p69)) % 0.31/0.70 (step @p76 :rule chain_m_resolution :premises (@p75 @p66) :args (@t96 @t109 (@list @t101))) % 0.31/0.70 (step @p77 :rule aci_norm :args ((= @t119 @t117))) % 0.31/0.70 (step @p78 :rule cong :premises (@p77) :args (@t121)) % 0.31/0.70 (step @p79 :rule quant-merge-prenex :args ((= (forall @t37 @t123) @t121))) % 0.31/0.70 (step @p80 :rule alpha_equiv :args (@t124 (@list @t112) @t125)) % 0.31/0.70 (step @p81 :rule refl :args (@t116)) % 0.31/0.70 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t126)) % 0.31/0.70 (step @p83 :rule quant-miniscope-or :args ((= @t123 @t126))) % 0.31/0.70 (step @p84 :rule trans :premises (@p83 @p82)) % 0.31/0.70 (step @p85 :rule symm :premises (@p84)) % 0.31/0.70 (step @p86 :rule cong :premises (@p85) :args ((forall @t37 (or @t116 @t128)))) % 0.31/0.70 (step @p87 :rule trans :premises (@p86 @p79)) % 0.31/0.70 (step @p88 :rule trans :premises (@p87 @p78)) % 0.31/0.70 (step @p89 :rule refl :args (@t128)) % 0.31/0.70 (step @p90 :rule refl :args (@t91)) % 0.31/0.70 (step @p91 :rule refl :args (@t129)) % 0.31/0.70 (step @p92 :rule cong :premises (@p91 @p90) :args ((= @t129 @t91))) % 0.31/0.70 (step @p93 :rule symm :premises (@p92)) % 0.31/0.70 (step @p94 :rule eq_resolve :premises (@p91 @p93)) % 0.31/0.70 (step @p95 :rule cong :premises (@p94) :args (@t130)) % 0.31/0.70 (step @p96 :rule nary_cong :premises (@p95 @p89) :args (@t131)) % 0.31/0.70 (step @p97 :rule cong :premises (@p96) :args ((forall @t37 @t131))) % 0.31/0.70 (step @p98 :rule trans :premises (@p97 @p88)) % 0.31/0.70 (step @p99 :rule beta-reduce :args ((= @t138 @t131))) % 0.31/0.70 (step @p100 :rule cong :premises (@p99) :args (@t139)) % 0.31/0.70 (step @p101 :rule trans :premises (@p100 @p98)) % 0.31/0.70 (step @p102 :rule beta-reduce :args ((= (_ @t141 @t137) @t139))) % 0.31/0.70 (step @p103 :rule trans :premises (@p102 @p101)) % 0.31/0.70 (step @p104 :rule beta-reduce :args ((= @t143 @t133))) % 0.31/0.70 (step @p105 :rule refl :args (@t135)) % 0.31/0.70 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t144)) % 0.31/0.70 (step @p107 :rule cong :premises (@p106) :args (@t145)) % 0.31/0.70 (step @p108 :rule beta-reduce :args ((= (_ @t148 @t142) @t145))) % 0.31/0.70 (step @p109 :rule trans :premises (@p108 @p107)) % 0.31/0.70 (step @p110 :rule beta-reduce :args ((= (_ (lambda @t136 (not (forall @t113 (or (not (tptp.rel_b @t18 @t110)) @t111)))) @t39) @t127))) % 0.31/0.70 (step @p111 :rule refl :args (@t39)) % 0.31/0.70 (step @p112 :rule alpha_equiv :args (@t149 @t125 (@list @t110))) % 0.31/0.70 (step @p113 :rule cong :premises (@p112) :args (@t150)) % 0.31/0.70 (step @p114 :rule cong :premises (@p113) :args (@t151)) % 0.31/0.70 (step @p115 :rule ho_cong :premises (@p114 @p111)) % 0.31/0.70 (step @p116 :rule trans :premises (@p115 @p110)) % 0.31/0.70 (step @p117 :rule refl :args (@t93)) % 0.31/0.70 (step @p118 :rule nary_cong :premises (@p117 @p116) :args (@t152)) % 0.31/0.70 (step @p119 :rule cong :premises (@p118) :args (@t153)) % 0.31/0.70 (step @p120 :rule cong :premises (@p119) :args (@t154)) % 0.31/0.70 (step @p121 :rule beta-reduce :args ((= (_ @t156 @t151) @t154))) % 0.31/0.70 (step @p122 :rule trans :premises (@p121 @p120)) % 0.31/0.70 (step @p123 :rule beta-reduce :args ((= @t159 @t151))) % 0.31/0.70 (step @p124 :rule refl :args (@t156)) % 0.31/0.70 (step @p125 :rule ho_cong :premises (@p124 @p123)) % 0.31/0.70 (step @p126 :rule trans :premises (@p125 @p122)) % 0.31/0.70 (step @p127 :rule beta-reduce :args ((= @t162 @t148))) % 0.31/0.70 (step @p128 :rule ho_cong :premises (@p127 @p126)) % 0.31/0.70 (step @p129 :rule trans :premises (@p128 @p109)) % 0.31/0.70 (step @p130 :rule refl :args (@t141)) % 0.31/0.70 (step @p131 :rule ho_cong :premises (@p130 @p129)) % 0.31/0.70 (step @p132 :rule trans :premises (@p131 @p103)) % 0.31/0.70 (step @p133 :rule refl :args (@t95)) % 0.31/0.70 (step @p134 :rule nary_cong :premises (@p133 @p94) :args (@t163)) % 0.31/0.70 (step @p135 :rule cong :premises (@p134) :args ((forall @t37 @t163))) % 0.31/0.70 (step @p136 :rule beta-reduce :args ((= @t167 @t163))) % 0.31/0.70 (step @p137 :rule cong :premises (@p136) :args (@t168)) % 0.31/0.70 (step @p138 :rule trans :premises (@p137 @p135)) % 0.31/0.70 (step @p139 :rule beta-reduce :args ((= (_ @t141 @t166) @t168))) % 0.31/0.70 (step @p140 :rule trans :premises (@p139 @p138)) % 0.31/0.70 (step @p141 :rule beta-reduce :args ((= (_ (lambda @t147 (or @t165 @t146)) tptp.phi) @t166))) % 0.31/0.70 (step @p142 :rule refl :args (tptp.phi)) % 0.31/0.70 (step @p143 :rule refl :args (@t146)) % 0.31/0.70 (step @p144 :rule beta-reduce :args ((= @t170 @t164))) % 0.31/0.70 (step @p145 :rule cong :premises (@p144) :args (@t171)) % 0.31/0.70 (step @p146 :rule nary_cong :premises (@p145 @p143) :args (@t172)) % 0.31/0.70 (step @p147 :rule cong :premises (@p146) :args (@t173)) % 0.31/0.70 (step @p148 :rule beta-reduce :args ((= (_ @t161 @t169) @t173))) % 0.31/0.70 (step @p149 :rule trans :premises (@p148 @p147)) % 0.31/0.70 (step @p150 :rule beta-reduce :args ((= @t174 @t169))) % 0.31/0.70 (step @p151 :rule refl :args (@t161)) % 0.31/0.70 (step @p152 :rule ho_cong :premises (@p151 @p150)) % 0.31/0.70 (step @p153 :rule trans :premises (@p152 @p149)) % 0.31/0.70 (step @p154 :rule ho_cong :premises (@p153 @p142)) % 0.31/0.70 (step @p155 :rule trans :premises (@p154 @p141)) % 0.31/0.70 (step @p156 :rule ho_cong :premises (@p130 @p155)) % 0.31/0.70 (step @p157 :rule trans :premises (@p156 @p140)) % 0.31/0.70 (step @p158 :rule nary_cong :premises (@p157 @p132) :args (@t175)) % 0.31/0.70 (step @p159 :rule cong :premises (@p158) :args ((not @t175))) % 0.31/0.70 (step @p160 :rule beta-reduce :args ((= (_ (lambda @t37 (not @t176)) @t18) @t158))) % 0.31/0.70 (step @p161 :rule refl :args (@t18)) % 0.31/0.70 (step @p162 :rule beta-reduce :args ((= @t178 @t176))) % 0.31/0.70 (step @p163 :rule cong :premises (@p162) :args (@t179)) % 0.31/0.70 (step @p164 :rule cong :premises (@p163) :args (@t180)) % 0.31/0.70 (step @p165 :rule beta-reduce :args ((= (_ @t14 @t177) @t180))) % 0.31/0.70 (step @p166 :rule trans :premises (@p165 @p164)) % 0.31/0.70 (step @p167 :rule refl :args (@t155)) % 0.31/0.70 (step @p168 :rule refl :args (@t40)) % 0.31/0.70 (step @p169 :rule cong :premises (@p168 @p167) :args ((= @t40 @t155))) % 0.31/0.70 (step @p170 :rule symm :premises (@p169)) % 0.31/0.70 (step @p171 :rule eq_resolve :premises (@p168 @p170)) % 0.31/0.70 (step @p172 :rule cong :premises (@p171) :args (@t181)) % 0.31/0.70 (step @p173 :rule refl :args (@t93)) % 0.31/0.70 (step @p174 :rule nary_cong :premises (@p173 @p172) :args (@t182)) % 0.31/0.70 (step @p175 :rule cong :premises (@p174) :args ((forall @t42 @t182))) % 0.31/0.70 (step @p176 :rule beta-reduce :args ((= @t184 @t181))) % 0.31/0.70 (step @p177 :rule nary_cong :premises (@p117 @p176) :args (@t185)) % 0.31/0.70 (step @p178 :rule cong :premises (@p177) :args (@t186)) % 0.31/0.70 (step @p179 :rule trans :premises (@p178 @p175)) % 0.31/0.70 (step @p180 :rule cong :premises (@p179) :args (@t187)) % 0.31/0.70 (step @p181 :rule beta-reduce :args ((= (_ @t156 @t183) @t187))) % 0.31/0.70 (step @p182 :rule trans :premises (@p181 @p180)) % 0.31/0.70 (step @p183 :rule beta-reduce :args ((= (_ @t14 @t10) @t183))) % 0.31/0.70 (step @p184 :rule ho_cong :premises (@p124 @p183)) % 0.31/0.70 (step @p185 :rule trans :premises (@p184 @p182)) % 0.31/0.70 (step @p186 :rule refl :args (@t14)) % 0.31/0.70 (step @p187 :rule ho_cong :premises (@p186 @p185)) % 0.31/0.70 (step @p188 :rule trans :premises (@p187 @p166)) % 0.31/0.70 (step @p189 :rule ho_cong :premises (@p188 @p161)) % 0.31/0.70 (step @p190 :rule trans :premises (@p189 @p160)) % 0.31/0.70 (step @p191 :rule refl :args (@t10)) % 0.31/0.70 (step @p192 :rule ho_cong :premises (@p8 @p191)) % 0.31/0.70 (step @p193 :rule refl :args (@t92)) % 0.31/0.70 (step @p194 :rule refl :args (@t83)) % 0.31/0.70 (step @p195 :rule cong :premises (@p194 @p193) :args ((= @t83 @t92))) % 0.31/0.70 (step @p196 :rule symm :premises (@p195)) % 0.31/0.70 (step @p197 :rule eq_resolve :premises (@p194 @p196)) % 0.31/0.70 (step @p198 :rule cong :premises (@p197) :args (@t84)) % 0.31/0.70 (step @p199 :rule nary_cong :premises (@p198 @p171) :args (@t85)) % 0.31/0.70 (step @p200 :rule cong :premises (@p199) :args (@t86)) % 0.31/0.70 (step @p201 :rule cong :premises (@p200) :args (@t87)) % 0.31/0.70 (step @p202 :rule trans :premises (@p36 @p201)) % 0.31/0.70 (step @p203 :rule ho_cong :premises (@p202 @p192)) % 0.31/0.70 (step @p204 :rule ho_cong :premises (@p8 @p203)) % 0.31/0.70 (step @p205 :rule ho_cong :premises (@p204 @p161)) % 0.31/0.70 (step @p206 :rule trans :premises (@p205 @p190)) % 0.31/0.70 (step @p207 :rule cong :premises (@p206) :args (@t89)) % 0.31/0.70 (step @p208 :rule trans :premises (@p37 @p207)) % 0.31/0.70 (step @p209 :rule ho_cong :premises (@p208 @p142)) % 0.31/0.70 (step @p210 :rule ho_cong :premises (@p202 @p209)) % 0.31/0.70 (step @p211 :rule beta-reduce :args ((= (_ @t189 @t18) @t160))) % 0.31/0.70 (step @p212 :rule beta-reduce :args ((= (_ (lambda @t190 @t188) @t15) @t189))) % 0.31/0.70 (step @p213 :rule refl :args (@t15)) % 0.31/0.70 (step @p214 :rule refl :args (@t16)) % 0.31/0.70 (step @p215 :rule beta-reduce :args ((= @t191 @t12))) % 0.31/0.70 (step @p216 :rule nary_cong :premises (@p215 @p214) :args (@t192)) % 0.31/0.70 (step @p217 :rule cong :premises (@p216) :args (@t193)) % 0.31/0.70 (step @p218 :rule beta-reduce :args ((= (_ @t17 @t183) @t193))) % 0.31/0.70 (step @p219 :rule trans :premises (@p218 @p217)) % 0.31/0.70 (step @p220 :rule refl :args (@t17)) % 0.31/0.70 (step @p221 :rule ho_cong :premises (@p220 @p183)) % 0.31/0.70 (step @p222 :rule trans :premises (@p221 @p219)) % 0.31/0.70 (step @p223 :rule ho_cong :premises (@p222 @p213)) % 0.31/0.70 (step @p224 :rule trans :premises (@p223 @p212)) % 0.31/0.70 (step @p225 :rule ho_cong :premises (@p224 @p161)) % 0.31/0.70 (step @p226 :rule trans :premises (@p225 @p211)) % 0.31/0.70 (step @p227 :rule ho_cong :premises (@p9 @p192)) % 0.31/0.70 (step @p228 :rule ho_cong :premises (@p227 @p213)) % 0.31/0.70 (step @p229 :rule ho_cong :premises (@p228 @p161)) % 0.31/0.70 (step @p230 :rule trans :premises (@p229 @p226)) % 0.31/0.70 (step @p231 :rule cong :premises (@p230) :args (@t24)) % 0.31/0.70 (step @p232 :rule trans :premises (@p11 @p231)) % 0.31/0.70 (step @p233 :rule ho_cong :premises (@p232 @p142)) % 0.31/0.70 (step @p234 :rule ho_cong :premises (@p233 @p210)) % 0.31/0.70 (step @p235 :rule refl :args (@t140)) % 0.31/0.70 (step @p236 :rule refl :args (@t11)) % 0.31/0.70 (step @p237 :rule cong :premises (@p236 @p235) :args ((= @t11 @t140))) % 0.31/0.70 (step @p238 :rule symm :premises (@p237)) % 0.31/0.70 (step @p239 :rule eq_resolve :premises (@p236 @p238)) % 0.31/0.70 (step @p240 :rule cong :premises (@p239) :args (@t77)) % 0.31/0.70 (step @p241 :rule cong :premises (@p240) :args (@t79)) % 0.31/0.70 (step @p242 :rule trans :premises (@p32 @p241)) % 0.31/0.70 (step @p243 :rule ho_cong :premises (@p242 @p234)) % 0.31/0.70 (step @p244 :rule ho_cong :premises (@p202 @p142)) % 0.31/0.70 (step @p245 :rule ho_cong :premises (@p232 @p244)) % 0.31/0.70 (step @p246 :rule ho_cong :premises (@p245 @p142)) % 0.31/0.70 (step @p247 :rule ho_cong :premises (@p242 @p246)) % 0.31/0.70 (step @p248 :rule nary_cong :premises (@p247 @p243) :args (@t1)) % 0.31/0.70 (step @p249 :rule cong :premises (@p248) :args (@t2)) % 0.31/0.70 (step @p250 :rule trans :premises (@p249 @p159)) % 0.31/0.70 (step @p251 :rule eq_resolve :premises (@p4 @p250)) % 0.31/0.70 (step @p252 :rule not_and :premises (@p251)) % 0.31/0.70 (step @p253 :rule chain_m_resolution :premises (@p252 @p76) :args (@t195 @t109 (@list @t96))) % 0.31/0.70 (step @p254 :rule refl :args (@t205)) % 0.31/0.70 (step @p255 :rule bool-double-not-elim :args (@t194)) % 0.31/0.70 (step @p256 :rule nary_cong :premises (@p255 @p254) :args ((or (not @t195) @t205))) % 0.31/0.71 (assume-push @p322 @t195) % 0.31/0.71 (step @p258 :rule skolemize :premises (@p322)) % 0.31/0.71 (step-pop @p323 :rule scope :premises (@p258)) % 0.31/0.71 (step @p259 :rule process_scope :premises (@p323) :args (@t205)) % 0.31/0.71 (step @p261 :rule implies_elim :premises (@p259)) % 0.31/0.71 (step @p262 :rule eq_resolve :premises (@p261 @p256)) % 0.31/0.71 (step @p263 :rule chain_m_resolution :premises (@p262 @p253) :args (@t205 @t206 (@list @t194))) % 0.31/0.71 (step @p264 :rule bool-double-not-elim :args (@t202)) % 0.31/0.71 (step @p265 :rule refl :args (@t204)) % 0.31/0.71 (step @p266 :rule nary_cong :premises (@p265 @p264) :args ((or @t204 (not @t203)))) % 0.31/0.71 (step @p267 :rule cnf_or_neg :args (@t204 0)) % 0.31/0.71 (step @p268 :rule eq_resolve :premises (@p267 @p266)) % 0.31/0.71 (step @p269 :rule reordering :premises (@p268) :args ((or @t202 @t204))) % 0.31/0.71 (step @p270 :rule chain_m_resolution :premises (@p269 @p263) :args (@t202 @t206 @t207)) % 0.31/0.71 (step @p271 :rule bool-double-not-elim :args (@t197)) % 0.31/0.71 (step @p272 :rule nary_cong :premises (@p265 @p271) :args ((or @t204 (not @t198)))) % 0.31/0.71 (step @p273 :rule cnf_or_neg :args (@t204 2)) % 0.31/0.71 (step @p274 :rule eq_resolve :premises (@p273 @p272)) % 0.31/0.71 (step @p275 :rule reordering :premises (@p274) :args ((or @t197 @t204))) % 0.31/0.71 (step @p276 :rule chain_m_resolution :premises (@p275 @p263) :args (@t197 @t206 @t207)) % 0.31/0.71 (assume-push @p324 @t197) % 0.31/0.71 (step @p278 :rule instantiate :premises (@p324) :args ((@list @t199))) % 0.31/0.71 (step-pop @p325 :rule scope :premises (@p278)) % 0.31/0.71 (step @p279 :rule process_scope :premises (@p325) :args (@t210)) % 0.31/0.71 (step @p281 :rule implies_elim :premises (@p279)) % 0.31/0.71 (step @p282 :rule chain_m_resolution :premises (@p281 @p276) :args (@t210 @t109 (@list @t197))) % 0.31/0.71 (step @p283 :rule beta-reduce :args ((= (_ (lambda @t50 (forall @t56 (or (not @t212) @t211))) tptp.rel_b) (forall @t56 (or (not (tptp.rel_b @t45 @t52)) (tptp.rel_b @t52 @t45)))))) % 0.31/0.71 (step @p284 :rule refl :args (@t211)) % 0.31/0.71 (step @p285 :rule refl :args (@t54)) % 0.31/0.71 (step @p286 :rule cong :premises (@p285 @p284) :args ((= @t54 @t211))) % 0.31/0.71 (step @p287 :rule symm :premises (@p286)) % 0.31/0.71 (step @p288 :rule eq_resolve :premises (@p285 @p287)) % 0.31/0.71 (step @p289 :rule refl :args (@t212)) % 0.31/0.71 (step @p290 :rule refl :args (@t55)) % 0.31/0.71 (step @p291 :rule cong :premises (@p290 @p289) :args ((= @t55 @t212))) % 0.31/0.71 (step @p292 :rule symm :premises (@p291)) % 0.31/0.71 (step @p293 :rule eq_resolve :premises (@p290 @p292)) % 0.31/0.71 (step @p294 :rule cong :premises (@p293) :args (@t213)) % 0.31/0.71 (step @p295 :rule nary_cong :premises (@p294 @p288) :args (@t214)) % 0.31/0.71 (step @p296 :rule cong :premises (@p295) :args ((forall @t56 @t214))) % 0.31/0.71 (step @p297 :rule bool-impl-elim :args (@t55 @t54)) % 0.31/0.71 (step @p298 :rule cong :premises (@p297) :args (@t57)) % 0.31/0.71 (step @p299 :rule trans :premises (@p298 @p296)) % 0.31/0.71 (step @p300 :rule cong :premises (@p299) :args (@t58)) % 0.31/0.71 (step @p301 :rule trans :premises (@p23 @p300)) % 0.31/0.71 (step @p302 :rule ho_cong :premises (@p301 @p51)) % 0.31/0.71 (step @p303 :rule trans :premises (@p302 @p283)) % 0.31/0.71 (step @p304 :rule eq_resolve :premises (@p3 @p303)) % 0.31/0.71 (step @p305 :rule instantiate :premises (@p304) :args ((@list @t199 @t196))) % 0.31/0.71 (step @p306 :rule bool-double-not-elim :args (@t200)) % 0.31/0.71 (step @p307 :rule nary_cong :premises (@p265 @p306) :args ((or @t204 (not @t201)))) % 0.31/0.71 (step @p308 :rule cnf_or_neg :args (@t204 1)) % 0.31/0.71 (step @p309 :rule eq_resolve :premises (@p308 @p307)) % 0.31/0.71 (step @p310 :rule reordering :premises (@p309) :args ((or @t200 @t204))) % 0.31/0.71 (step @p311 :rule chain_m_resolution :premises (@p310 @p263) :args (@t200 @t206 @t207)) % 0.31/0.71 (step @p312 :rule cnf_or_pos :args (@t215)) % 0.31/0.71 (step @p313 :rule reordering :premises (@p312) :args ((or @t201 @t208 (not @t215)))) % 0.31/0.71 (step @p314 :rule chain_m_resolution :premises (@p313 @p311 @p305) :args (@t208 (@list false false) (@list @t200 @t215))) % 0.31/0.71 (step @p315 :rule cnf_or_pos :args (@t210)) % 0.31/0.71 (step @p316 :rule reordering :premises (@p315) :args ((or @t203 @t209 (not @t210)))) % 0.31/0.71 (step @p317 false :rule chain_m_resolution :premises (@p316 @p314 @p282 @p270) :args (false (@list false false false) (@list @t208 @t210 @t202))) % 0.31/0.71 ) % 0.31/0.71 % SZS output end Proof % 0.31/0.71 % cvc5 exiting %------------------------------------------------------------------------------