%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO476^6 : TPTP v9.2.1. Released v4.0.0. % 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 : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:12:57 AM UTC 2026 % Result : Theorem 0.35s 0.61s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO476^6 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n002.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 00:16:18 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.52 %----Proving TH0 % 0.35/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.35/0.61 % SZS status Theorem % 0.35/0.61 % SZS output start Proof % 0.35/0.61 ( % 0.35/0.61 (declare-sort $$unsorted 0) % 0.35/0.61 (declare-sort tptp.mu 0) % 0.35/0.61 (declare-const tptp.rel_s5 (-> $$unsorted $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.f (-> tptp.mu $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.35/0.61 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.35/0.61 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.35/0.61 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.35/0.61 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.35/0.61 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.35/0.61 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.35/0.61 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.35/0.61 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.35/0.61 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.35/0.61 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.35/0.61 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.35/0.61 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.35/0.61 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.35/0.61 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.35/0.61 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.35/0.61 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.35/0.61 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.35/0.61 (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)))))))) % 0.35/0.61 (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)))))))) % 0.35/0.61 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.35/0.61 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.35/0.61 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.35/0.61 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.35/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.35/0.61 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.35/0.61 (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))))))))))))) % 0.35/0.61 (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)))))) % 0.35/0.61 (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))))))) % 0.35/0.61 (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)))))) % 0.35/0.61 (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))))))) % 0.35/0.61 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s5 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.35/0.61 (define tptp.mdia_s5 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s5 (_ tptp.mnot _let_2))) _let_1))))) % 0.35/0.61 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.35/0.61 (define @t2 () (@var "X" tptp.mu)) % 0.35/0.61 (define @t3 () (_ tptp.f @t2)) % 0.35/0.61 (define @t4 () (@list @t2 @t1)) % 0.35/0.61 (define @t5 () (lambda @t4 (_ (_ tptp.mbox_s5 @t3) @t1))) % 0.35/0.61 (define @t6 () (lambda @t4 (_ @t3 @t1))) % 0.35/0.61 (define @t7 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mbox_s5 (_ tptp.mforall_ind @t6))) (_ tptp.mforall_ind @t5))))) % 0.35/0.61 (define @t8 () (@var "Y" tptp.mu)) % 0.35/0.61 (define @t9 () (@var "W" $$unsorted)) % 0.35/0.61 (define @t10 () (lambda (@list @t2 @t8 @t9) (= @t2 @t8))) % 0.35/0.61 (define @t11 () (@var "Y" (-> $$unsorted Bool))) % 0.35/0.61 (define @t12 () (@var "X" (-> $$unsorted Bool))) % 0.35/0.61 (define @t13 () (lambda (@list @t12 @t11 @t9) (= (_ @t12 @t9) (_ @t11 @t9)))) % 0.35/0.61 (define @t14 () (@var "Phi" (-> $$unsorted Bool))) % 0.35/0.61 (define @t15 () (_ @t14 @t9)) % 0.35/0.61 (define @t16 () (not @t15)) % 0.35/0.61 (define @t17 () (@list @t14 @t9)) % 0.35/0.61 (define @t18 () (lambda @t17 @t16)) % 0.35/0.61 (define @t19 () (@var "Psi" (-> $$unsorted Bool))) % 0.35/0.61 (define @t20 () (_ @t19 @t9)) % 0.35/0.61 (define @t21 () (lambda (@list @t14 @t19 @t9) (or @t15 @t20))) % 0.35/0.61 (define @t22 () (_ tptp.mnot @t19)) % 0.35/0.61 (define @t23 () (_ tptp.mnot @t14)) % 0.35/0.61 (define @t24 () (_ tptp.mor @t23)) % 0.35/0.61 (define @t25 () (@list @t14 @t19 @t1)) % 0.35/0.61 (define @t26 () (lambda @t25 (_ (_ tptp.mnot (_ @t24 @t22)) @t1))) % 0.35/0.61 (define @t27 () (lambda @t25 (_ (_ @t24 @t19) @t1))) % 0.35/0.61 (define @t28 () (lambda @t25 (_ (_ (_ tptp.mor @t22) @t14) @t1))) % 0.35/0.61 (define @t29 () (lambda @t25 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t14) @t19)) (_ (_ tptp.mimplies @t19) @t14)) @t1))) % 0.35/0.61 (define @t30 () (lambda @t25 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t14) @t19)) @t1))) % 0.35/0.61 (define @t31 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.35/0.61 (define @t32 () (_ @t31 @t2)) % 0.35/0.61 (define @t33 () (_ @t32 @t9)) % 0.35/0.61 (define @t34 () (@list @t2)) % 0.35/0.61 (define @t35 () (forall @t34 @t33)) % 0.35/0.61 (define @t36 () (@list @t31 @t9)) % 0.35/0.61 (define @t37 () (lambda @t36 @t35)) % 0.35/0.61 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 0.35/0.61 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.35/0.61 (define @t40 () (_ @t39 @t38)) % 0.35/0.61 (define @t41 () (lambda (@list @t39 @t9) (forall (@list @t38) (_ @t40 @t9)))) % 0.35/0.61 (define @t42 () (lambda (@list @t31 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda @t4 (_ (_ tptp.mnot @t32) @t1)))) @t1))) % 0.35/0.61 (define @t43 () (lambda (@list @t39 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t1) (_ (_ tptp.mnot @t40) @t1)))) @t1))) % 0.35/0.61 (define @t44 () (@list @t9)) % 0.35/0.61 (define @t45 () (lambda @t44 true)) % 0.35/0.61 (define @t46 () (@var "V" $$unsorted)) % 0.35/0.61 (define @t47 () (_ @t14 @t46)) % 0.35/0.61 (define @t48 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.35/0.61 (define @t49 () (@list @t46)) % 0.35/0.61 (define @t50 () (lambda (@list @t48 @t14 @t9) (forall @t49 (or (not (_ (_ @t48 @t9) @t46)) @t47)))) % 0.35/0.61 (define @t51 () (lambda (@list @t48 @t14 @t1) (_ (_ tptp.mnot (_ (_ tptp.mbox @t48) @t23)) @t1))) % 0.35/0.61 (define @t52 () (@var "S" $$unsorted)) % 0.35/0.61 (define @t53 () (_ @t48 @t52)) % 0.35/0.61 (define @t54 () (@list @t52)) % 0.35/0.61 (define @t55 () (@list @t48)) % 0.35/0.61 (define @t56 () (lambda @t55 (forall @t54 (_ @t53 @t52)))) % 0.35/0.61 (define @t57 () (@var "T" $$unsorted)) % 0.35/0.61 (define @t58 () (_ @t48 @t57)) % 0.35/0.61 (define @t59 () (_ @t53 @t57)) % 0.35/0.61 (define @t60 () (lambda @t55 (forall (@list @t52 @t57) (=> @t59 (_ @t58 @t52))))) % 0.35/0.61 (define @t61 () (@list @t57)) % 0.35/0.61 (define @t62 () (lambda @t55 (forall @t54 (exists @t61 @t59)))) % 0.35/0.61 (define @t63 () (@var "U" $$unsorted)) % 0.35/0.61 (define @t64 () (_ @t53 @t63)) % 0.35/0.61 (define @t65 () (_ @t58 @t63)) % 0.35/0.61 (define @t66 () (@list @t52 @t57 @t63)) % 0.35/0.61 (define @t67 () (lambda @t55 (forall @t66 (=> (and @t59 @t65) @t64)))) % 0.35/0.61 (define @t68 () (and @t59 @t64)) % 0.35/0.61 (define @t69 () (lambda @t55 (forall @t66 (=> @t68 @t65)))) % 0.35/0.61 (define @t70 () (= @t57 @t63)) % 0.35/0.61 (define @t71 () (lambda @t55 (forall @t66 (=> @t68 @t70)))) % 0.35/0.61 (define @t72 () (@list @t63)) % 0.35/0.61 (define @t73 () (lambda @t55 (forall @t54 (exists @t61 (and @t59 (forall @t72 (=> @t64 @t70))))))) % 0.35/0.61 (define @t74 () (_ @t48 @t63)) % 0.35/0.61 (define @t75 () (_ @t74 @t57)) % 0.35/0.61 (define @t76 () (lambda @t55 (forall @t66 (=> @t59 (exists @t72 (and @t64 @t75)))))) % 0.35/0.61 (define @t77 () (lambda @t55 (forall @t66 (=> @t68 (or @t65 @t70 @t75))))) % 0.35/0.61 (define @t78 () (lambda @t55 (forall @t66 (=> @t68 (exists @t49 (and (_ @t58 @t46) (_ @t74 @t46))))))) % 0.35/0.61 (define @t79 () (forall @t44 @t15)) % 0.35/0.61 (define @t80 () (@list @t14)) % 0.35/0.61 (define @t81 () (lambda @t80 @t79)) % 0.35/0.61 (define @t82 () (lambda @t80 (forall @t44 @t16))) % 0.35/0.61 (define @t83 () (lambda @t80 (exists @t44 @t15))) % 0.35/0.61 (define @t84 () (lambda @t80 (exists @t44 @t16))) % 0.35/0.61 (define @t85 () (_ (_ tptp.rel_s5 @t9) @t46)) % 0.35/0.61 (define @t86 () (not @t85)) % 0.35/0.61 (define @t87 () (or @t86 @t47)) % 0.35/0.61 (define @t88 () (forall @t49 @t87)) % 0.35/0.61 (define @t89 () (lambda @t17 @t88)) % 0.35/0.61 (define @t90 () (lambda (@list @t14 @t1) (_ (_ tptp.mnot (_ tptp.mbox_s5 @t23)) @t1))) % 0.35/0.61 (define @t91 () (@var "BOUND_VARIABLE_8501" $$unsorted)) % 0.35/0.61 (define @t92 () (@var "BOUND_VARIABLE_8499" tptp.mu)) % 0.35/0.61 (define @t93 () (tptp.f @t92 @t91)) % 0.35/0.61 (define @t94 () (not (tptp.rel_s5 @t9 @t91))) % 0.35/0.61 (define @t95 () (@var "BOUND_VARIABLE_8445" tptp.mu)) % 0.35/0.61 (define @t96 () (tptp.f @t95 @t46)) % 0.35/0.61 (define @t97 () (tptp.rel_s5 @t9 @t46)) % 0.35/0.61 (define @t98 () (not @t97)) % 0.35/0.61 (define @t99 () (or @t98 @t96)) % 0.35/0.61 (define @t100 () (@list @t46 @t95)) % 0.35/0.61 (define @t101 () (forall @t100 @t99)) % 0.35/0.61 (define @t102 () (not @t101)) % 0.35/0.61 (define @t103 () (or @t102 @t94 @t93)) % 0.35/0.61 (define @t104 () (or @t94 @t93)) % 0.35/0.61 (define @t105 () (or @t102 @t104)) % 0.35/0.61 (define @t106 () (@list @t9 @t92 @t91)) % 0.35/0.61 (define @t107 () (forall @t106 @t105)) % 0.35/0.61 (define @t108 () (@list @t92 @t91)) % 0.35/0.61 (define @t109 () (forall @t108 @t105)) % 0.35/0.61 (define @t110 () (forall @t108 @t104)) % 0.35/0.61 (define @t111 () (or @t102 @t110)) % 0.35/0.61 (define @t112 () (tptp.f @t2 @t46)) % 0.35/0.61 (define @t113 () (or @t98 @t112)) % 0.35/0.61 (define @t114 () (@list @t2 @t46)) % 0.35/0.61 (define @t115 () (forall @t114 @t113)) % 0.35/0.61 (define @t116 () (or @t102 @t115)) % 0.35/0.61 (define @t117 () (not (tptp.rel_s5 @t1 @t46))) % 0.35/0.61 (define @t118 () (or @t117 @t112)) % 0.35/0.61 (define @t119 () (forall @t114 @t118)) % 0.35/0.61 (define @t120 () (forall @t100 (or @t117 @t96))) % 0.35/0.61 (define @t121 () (not @t120)) % 0.35/0.61 (define @t122 () (@list @t1)) % 0.35/0.61 (define @t123 () (lambda @t122 (or @t121 @t119))) % 0.35/0.61 (define @t124 () (_ @t123 @t9)) % 0.35/0.61 (define @t125 () (forall @t44 @t124)) % 0.35/0.61 (define @t126 () (_ @t14 @t9)) % 0.35/0.61 (define @t127 () (lambda @t80 (forall @t44 @t126))) % 0.35/0.61 (define @t128 () (lambda @t44 @t115)) % 0.35/0.61 (define @t129 () (_ @t128 @t1)) % 0.35/0.61 (define @t130 () (or @t121 @t129)) % 0.35/0.61 (define @t131 () (lambda @t122 @t130)) % 0.35/0.61 (define @t132 () (_ @t19 @t1)) % 0.35/0.61 (define @t133 () (@list @t19 @t1)) % 0.35/0.61 (define @t134 () (forall @t49 @t113)) % 0.35/0.61 (define @t135 () (forall @t49 @t118)) % 0.35/0.61 (define @t136 () (lambda @t4 @t135)) % 0.35/0.61 (define @t137 () (_ @t136 @t2 @t9)) % 0.35/0.61 (define @t138 () (forall @t34 @t137)) % 0.35/0.61 (define @t139 () (lambda @t44 @t138)) % 0.35/0.61 (define @t140 () (_ @t31 @t2 @t9)) % 0.35/0.61 (define @t141 () (lambda @t36 (forall @t34 @t140))) % 0.35/0.61 (define @t142 () (_ @t3 @t46)) % 0.35/0.61 (define @t143 () (or @t98 @t142)) % 0.35/0.61 (define @t144 () (_ @t3 @t46)) % 0.35/0.61 (define @t145 () (or @t98 @t144)) % 0.35/0.61 (define @t146 () (forall @t49 @t145)) % 0.35/0.61 (define @t147 () (lambda @t44 @t146)) % 0.35/0.61 (define @t148 () (_ @t14 @t46)) % 0.35/0.61 (define @t149 () (lambda @t17 (forall @t49 (or @t98 @t148)))) % 0.35/0.61 (define @t150 () (_ @t149 @t3)) % 0.35/0.61 (define @t151 () (lambda @t4 (_ @t150 @t1))) % 0.35/0.61 (define @t152 () (lambda @t44 @t101)) % 0.35/0.61 (define @t153 () (_ @t152 @t1)) % 0.35/0.61 (define @t154 () (not @t153)) % 0.35/0.61 (define @t155 () (or @t154 @t132)) % 0.35/0.61 (define @t156 () (lambda @t133 @t155)) % 0.35/0.61 (define @t157 () (or (not (_ @t14 @t1)) @t132)) % 0.35/0.61 (define @t158 () (lambda @t25 @t157)) % 0.35/0.61 (define @t159 () (@list @t95)) % 0.35/0.61 (define @t160 () (forall @t159 @t99)) % 0.35/0.61 (define @t161 () (forall @t159 @t96)) % 0.35/0.61 (define @t162 () (or @t98 @t161)) % 0.35/0.61 (define @t163 () (forall @t34 @t112)) % 0.35/0.61 (define @t164 () (tptp.f @t2 @t9)) % 0.35/0.61 (define @t165 () (lambda @t44 (forall @t34 @t164))) % 0.35/0.61 (define @t166 () (_ @t165 @t46)) % 0.35/0.61 (define @t167 () (or @t98 @t166)) % 0.35/0.61 (define @t168 () (forall @t49 @t167)) % 0.35/0.61 (define @t169 () (lambda @t44 @t168)) % 0.35/0.61 (define @t170 () (_ @t3 @t9)) % 0.35/0.61 (define @t171 () (_ @t6 @t2 @t9)) % 0.35/0.61 (define @t172 () (forall @t34 @t171)) % 0.35/0.61 (define @t173 () (lambda @t44 @t172)) % 0.35/0.61 (define @t174 () (_ @t141 @t6)) % 0.35/0.61 (define @t175 () (or @t16 @t20)) % 0.35/0.61 (define @t176 () (lambda @t44 @t175)) % 0.35/0.61 (define @t177 () (@list @t19 @t9)) % 0.35/0.61 (define @t178 () (lambda @t44 @t16)) % 0.35/0.61 (define @t179 () (_ @t178 @t9)) % 0.35/0.61 (define @t180 () (or @t179 @t20)) % 0.35/0.61 (define @t181 () (lambda @t177 @t180)) % 0.35/0.61 (define @t182 () (forall @t106 @t103)) % 0.35/0.61 (define @t183 () (@quantifiers_skolemize @t182 0)) % 0.35/0.61 (define @t184 () (forall @t100 (or (not (tptp.rel_s5 @t183 @t46)) @t96))) % 0.35/0.61 (define @t185 () (@quantifiers_skolemize @t182 2)) % 0.35/0.61 (define @t186 () (@quantifiers_skolemize @t182 1)) % 0.35/0.61 (define @t187 () (tptp.f @t186 @t185)) % 0.35/0.61 (define @t188 () (tptp.rel_s5 @t183 @t185)) % 0.35/0.61 (define @t189 () (not @t188)) % 0.35/0.61 (define @t190 () (not @t184)) % 0.35/0.61 (define @t191 () (or @t190 @t189 @t187)) % 0.35/0.61 (define @t192 () (@list true)) % 0.35/0.61 (define @t193 () (@list @t191)) % 0.35/0.61 (define @t194 () (or @t189 @t187)) % 0.35/0.61 (define @t195 () (not @t194)) % 0.35/0.61 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.35/0.61 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.35/0.61 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.35/0.61 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.35/0.61 (assume @p5 @t7) % 0.35/0.61 (assume @p6 true) % 0.35/0.61 (step @p7 (= tptp.meq_ind @t10) :rule refl :args (@t10)) % 0.35/0.61 (step @p8 (= tptp.meq_prop @t13) :rule refl :args (@t13)) % 0.35/0.61 (step @p9 (= tptp.mnot @t18) :rule refl :args (@t18)) % 0.35/0.61 (step @p10 (= tptp.mor @t21) :rule refl :args (@t21)) % 0.35/0.61 (step @p11 (= tptp.mand @t26) :rule refl :args (@t26)) % 0.35/0.61 (step @p12 (= tptp.mimplies @t27) :rule refl :args (@t27)) % 0.35/0.61 (step @p13 (= tptp.mimplied @t28) :rule refl :args (@t28)) % 0.35/0.61 (step @p14 (= tptp.mequiv @t29) :rule refl :args (@t29)) % 0.35/0.61 (step @p15 (= tptp.mxor @t30) :rule refl :args (@t30)) % 0.35/0.61 (step @p16 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 0.35/0.61 (step @p17 (= tptp.mforall_prop @t41) :rule refl :args (@t41)) % 0.35/0.61 (step @p18 (= tptp.mexists_ind @t42) :rule refl :args (@t42)) % 0.35/0.61 (step @p19 (= tptp.mexists_prop @t43) :rule refl :args (@t43)) % 0.35/0.61 (step @p20 (= tptp.mtrue @t45) :rule refl :args (@t45)) % 0.35/0.61 (step @p21 (= tptp.mbox @t50) :rule refl :args (@t50)) % 0.35/0.61 (step @p22 (= tptp.mdia @t51) :rule refl :args (@t51)) % 0.35/0.61 (step @p23 (= tptp.mreflexive @t56) :rule refl :args (@t56)) % 0.35/0.61 (step @p24 (= tptp.msymmetric @t60) :rule refl :args (@t60)) % 0.35/0.61 (step @p25 (= tptp.mserial @t62) :rule refl :args (@t62)) % 0.35/0.61 (step @p26 (= tptp.mtransitive @t67) :rule refl :args (@t67)) % 0.35/0.61 (step @p27 (= tptp.meuclidean @t69) :rule refl :args (@t69)) % 0.35/0.61 (step @p28 (= tptp.mpartially_functional @t71) :rule refl :args (@t71)) % 0.35/0.61 (step @p29 (= tptp.mfunctional @t73) :rule refl :args (@t73)) % 0.35/0.61 (step @p30 (= tptp.mweakly_dense @t76) :rule refl :args (@t76)) % 0.35/0.61 (step @p31 (= tptp.mweakly_connected @t77) :rule refl :args (@t77)) % 0.35/0.61 (step @p32 (= tptp.mweakly_directed @t78) :rule refl :args (@t78)) % 0.35/0.61 (step @p33 (= tptp.mvalid @t81) :rule refl :args (@t81)) % 0.35/0.61 (step @p34 (= tptp.minvalid @t82) :rule refl :args (@t82)) % 0.35/0.61 (step @p35 (= tptp.msatisfiable @t83) :rule refl :args (@t83)) % 0.35/0.61 (step @p36 (= tptp.mcountersatisfiable @t84) :rule refl :args (@t84)) % 0.35/0.61 (step @p37 (= tptp.mbox_s5 @t89) :rule refl :args (@t89)) % 0.35/0.61 (step @p38 (= tptp.mdia_s5 @t90) :rule refl :args (@t90)) % 0.35/0.61 (step @p39 :rule aci_norm :args ((= @t105 @t103))) % 0.35/0.61 (step @p40 :rule cong :premises (@p39) :args (@t107)) % 0.35/0.61 (step @p41 :rule quant-merge-prenex :args ((= (forall @t44 @t109) @t107))) % 0.35/0.61 (step @p42 :rule alpha_equiv :args (@t110 (@list @t92 @t91) (@list @t2 @t46))) % 0.35/0.61 (step @p43 :rule refl :args (@t102)) % 0.35/0.61 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t111)) % 0.35/0.61 (step @p45 :rule quant-miniscope-or :args ((= @t109 @t111))) % 0.35/0.61 (step @p46 :rule trans :premises (@p45 @p44)) % 0.35/0.61 (step @p47 :rule symm :premises (@p46)) % 0.35/0.61 (step @p48 :rule cong :premises (@p47) :args ((forall @t44 @t116))) % 0.35/0.61 (step @p49 :rule trans :premises (@p48 @p41)) % 0.35/0.61 (step @p50 :rule trans :premises (@p49 @p40)) % 0.35/0.61 (step @p51 :rule beta-reduce :args ((= @t124 @t116))) % 0.35/0.61 (step @p52 :rule cong :premises (@p51) :args (@t125)) % 0.35/0.61 (step @p53 :rule trans :premises (@p52 @p50)) % 0.35/0.61 (step @p54 :rule beta-reduce :args ((= (_ @t127 @t123) @t125))) % 0.35/0.61 (step @p55 :rule trans :premises (@p54 @p53)) % 0.35/0.61 (step @p56 :rule beta-reduce :args ((= @t129 @t119))) % 0.35/0.61 (step @p57 :rule refl :args (@t121)) % 0.35/0.61 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t130)) % 0.35/0.61 (step @p59 :rule cong :premises (@p58) :args (@t131)) % 0.35/0.61 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t133 (or @t121 @t132)) @t128) @t131))) % 0.35/0.61 (step @p61 :rule trans :premises (@p60 @p59)) % 0.35/0.61 (step @p62 :rule quant-merge-prenex :args ((= (forall @t34 @t134) @t115))) % 0.35/0.61 (step @p63 :rule beta-reduce :args ((= @t137 @t134))) % 0.35/0.61 (step @p64 :rule cong :premises (@p63) :args (@t138)) % 0.35/0.61 (step @p65 :rule trans :premises (@p64 @p62)) % 0.35/0.61 (step @p66 :rule cong :premises (@p65) :args (@t139)) % 0.35/0.61 (step @p67 :rule beta-reduce :args ((= (_ @t141 @t136) @t139))) % 0.35/0.61 (step @p68 :rule trans :premises (@p67 @p66)) % 0.35/0.61 (step @p69 :rule beta-reduce :args ((= (_ (lambda @t44 @t134) @t1) @t135))) % 0.35/0.61 (step @p70 :rule refl :args (@t1)) % 0.35/0.61 (step @p71 :rule refl :args (@t112)) % 0.35/0.61 (step @p72 :rule refl :args (@t142)) % 0.35/0.61 (step @p73 :rule cong :premises (@p72 @p71) :args ((= @t142 @t112))) % 0.35/0.61 (step @p74 :rule symm :premises (@p73)) % 0.35/0.61 (step @p75 :rule eq_resolve :premises (@p72 @p74)) % 0.35/0.61 (step @p76 :rule refl :args (@t98)) % 0.35/0.61 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t143)) % 0.35/0.61 (step @p78 :rule cong :premises (@p77) :args ((forall @t49 @t143))) % 0.35/0.61 (step @p79 :rule refl :args (@t144)) % 0.35/0.61 (step @p80 :rule refl :args (@t98)) % 0.35/0.61 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t145)) % 0.35/0.61 (step @p82 :rule cong :premises (@p81) :args (@t146)) % 0.35/0.61 (step @p83 :rule trans :premises (@p82 @p78)) % 0.35/0.61 (step @p84 :rule cong :premises (@p83) :args (@t147)) % 0.35/0.61 (step @p85 :rule beta-reduce :args ((= @t150 @t147))) % 0.35/0.61 (step @p86 :rule trans :premises (@p85 @p84)) % 0.35/0.61 (step @p87 :rule ho_cong :premises (@p86 @p70)) % 0.35/0.61 (step @p88 :rule trans :premises (@p87 @p69)) % 0.35/0.61 (step @p89 :rule cong :premises (@p88) :args (@t151)) % 0.35/0.61 (step @p90 :rule refl :args (@t141)) % 0.35/0.61 (step @p91 :rule ho_cong :premises (@p90 @p89)) % 0.35/0.61 (step @p92 :rule trans :premises (@p91 @p68)) % 0.35/0.61 (step @p93 :rule refl :args (@t132)) % 0.35/0.61 (step @p94 :rule beta-reduce :args ((= @t153 @t120))) % 0.35/0.61 (step @p95 :rule cong :premises (@p94) :args (@t154)) % 0.35/0.61 (step @p96 :rule nary_cong :premises (@p95 @p93) :args (@t155)) % 0.35/0.61 (step @p97 :rule cong :premises (@p96) :args (@t156)) % 0.35/0.61 (step @p98 :rule beta-reduce :args ((= (_ @t158 @t152) @t156))) % 0.35/0.61 (step @p99 :rule trans :premises (@p98 @p97)) % 0.35/0.61 (step @p100 :rule quant-merge-prenex :args ((= (forall @t49 @t160) @t101))) % 0.35/0.61 (step @p101 :rule alpha_equiv :args (@t161 (@list @t95) (@list @t2))) % 0.35/0.61 (step @p102 :rule nary_cong :premises (@p76 @p101) :args (@t162)) % 0.35/0.61 (step @p103 :rule quant-miniscope-or :args ((= @t160 @t162))) % 0.35/0.61 (step @p104 :rule trans :premises (@p103 @p102)) % 0.35/0.61 (step @p105 :rule symm :premises (@p104)) % 0.35/0.61 (step @p106 :rule cong :premises (@p105) :args ((forall @t49 (or @t98 @t163)))) % 0.35/0.61 (step @p107 :rule trans :premises (@p106 @p100)) % 0.35/0.61 (step @p108 :rule beta-reduce :args ((= @t166 @t163))) % 0.35/0.61 (step @p109 :rule nary_cong :premises (@p80 @p108) :args (@t167)) % 0.35/0.61 (step @p110 :rule cong :premises (@p109) :args (@t168)) % 0.35/0.61 (step @p111 :rule trans :premises (@p110 @p107)) % 0.35/0.61 (step @p112 :rule cong :premises (@p111) :args (@t169)) % 0.35/0.61 (step @p113 :rule beta-reduce :args ((= (_ @t149 @t165) @t169))) % 0.35/0.61 (step @p114 :rule trans :premises (@p113 @p112)) % 0.35/0.61 (step @p115 :rule refl :args (@t164)) % 0.35/0.61 (step @p116 :rule refl :args (@t170)) % 0.35/0.61 (step @p117 :rule cong :premises (@p116 @p115) :args ((= @t170 @t164))) % 0.35/0.61 (step @p118 :rule symm :premises (@p117)) % 0.35/0.61 (step @p119 :rule eq_resolve :premises (@p116 @p118)) % 0.35/0.61 (step @p120 :rule cong :premises (@p119) :args ((forall @t34 @t170))) % 0.35/0.61 (step @p121 :rule beta-reduce :args ((= @t171 @t170))) % 0.35/0.61 (step @p122 :rule cong :premises (@p121) :args (@t172)) % 0.35/0.61 (step @p123 :rule trans :premises (@p122 @p120)) % 0.35/0.61 (step @p124 :rule cong :premises (@p123) :args (@t173)) % 0.35/0.61 (step @p125 :rule beta-reduce :args ((= @t174 @t173))) % 0.35/0.61 (step @p126 :rule trans :premises (@p125 @p124)) % 0.35/0.61 (step @p127 :rule refl :args (@t149)) % 0.35/0.61 (step @p128 :rule ho_cong :premises (@p127 @p126)) % 0.35/0.61 (step @p129 :rule trans :premises (@p128 @p114)) % 0.35/0.61 (step @p130 :rule refl :args (@t158)) % 0.35/0.61 (step @p131 :rule ho_cong :premises (@p130 @p129)) % 0.35/0.61 (step @p132 :rule trans :premises (@p131 @p99)) % 0.35/0.61 (step @p133 :rule ho_cong :premises (@p132 @p92)) % 0.35/0.61 (step @p134 :rule trans :premises (@p133 @p61)) % 0.35/0.61 (step @p135 :rule refl :args (@t127)) % 0.35/0.61 (step @p136 :rule ho_cong :premises (@p135 @p134)) % 0.35/0.61 (step @p137 :rule trans :premises (@p136 @p55)) % 0.35/0.61 (step @p138 :rule cong :premises (@p137) :args ((not (_ @t127 (_ (_ @t158 (_ @t149 @t174)) (_ @t141 @t151)))))) % 0.35/0.61 (step @p139 :rule refl :args (@t3)) % 0.35/0.61 (step @p140 :rule refl :args (@t148)) % 0.35/0.61 (step @p141 :rule refl :args (@t47)) % 0.35/0.61 (step @p142 :rule cong :premises (@p141 @p140) :args ((= @t47 @t148))) % 0.35/0.61 (step @p143 :rule symm :premises (@p142)) % 0.35/0.61 (step @p144 :rule eq_resolve :premises (@p141 @p143)) % 0.35/0.61 (step @p145 :rule refl :args (@t97)) % 0.35/0.61 (step @p146 :rule refl :args (@t85)) % 0.35/0.61 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t85 @t97))) % 0.35/0.61 (step @p148 :rule symm :premises (@p147)) % 0.35/0.61 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.35/0.61 (step @p150 :rule cong :premises (@p149) :args (@t86)) % 0.35/0.61 (step @p151 :rule nary_cong :premises (@p150 @p144) :args (@t87)) % 0.35/0.61 (step @p152 :rule cong :premises (@p151) :args (@t88)) % 0.35/0.61 (step @p153 :rule cong :premises (@p152) :args (@t89)) % 0.35/0.61 (step @p154 :rule trans :premises (@p37 @p153)) % 0.35/0.61 (step @p155 :rule ho_cong :premises (@p154 @p139)) % 0.35/0.61 (step @p156 :rule ho_cong :premises (@p155 @p70)) % 0.35/0.61 (step @p157 :rule cong :premises (@p156) :args (@t5)) % 0.35/0.61 (step @p158 :rule refl :args (@t140)) % 0.35/0.61 (step @p159 :rule refl :args (@t33)) % 0.35/0.61 (step @p160 :rule cong :premises (@p159 @p158) :args ((= @t33 @t140))) % 0.35/0.61 (step @p161 :rule symm :premises (@p160)) % 0.35/0.61 (step @p162 :rule eq_resolve :premises (@p159 @p161)) % 0.35/0.61 (step @p163 :rule cong :premises (@p162) :args (@t35)) % 0.35/0.61 (step @p164 :rule cong :premises (@p163) :args (@t37)) % 0.35/0.61 (step @p165 :rule trans :premises (@p16 @p164)) % 0.35/0.61 (step @p166 :rule ho_cong :premises (@p165 @p157)) % 0.35/0.61 (step @p167 :rule refl :args (@t6)) % 0.35/0.61 (step @p168 :rule ho_cong :premises (@p165 @p167)) % 0.35/0.61 (step @p169 :rule ho_cong :premises (@p154 @p168)) % 0.35/0.61 (step @p170 :rule beta-reduce :args ((= (_ @t176 @t1) @t157))) % 0.35/0.61 (step @p171 :rule beta-reduce :args ((= (_ (lambda @t177 @t175) @t19) @t176))) % 0.35/0.61 (step @p172 :rule refl :args (@t19)) % 0.35/0.61 (step @p173 :rule refl :args (@t20)) % 0.35/0.61 (step @p174 :rule beta-reduce :args ((= @t179 @t16))) % 0.35/0.61 (step @p175 :rule nary_cong :premises (@p174 @p173) :args (@t180)) % 0.35/0.61 (step @p176 :rule cong :premises (@p175) :args (@t181)) % 0.35/0.61 (step @p177 :rule beta-reduce :args ((= (_ @t21 @t178) @t181))) % 0.35/0.61 (step @p178 :rule trans :premises (@p177 @p176)) % 0.35/0.61 (step @p179 :rule beta-reduce :args ((= (_ @t18 @t14) @t178))) % 0.35/0.61 (step @p180 :rule refl :args (@t21)) % 0.35/0.61 (step @p181 :rule ho_cong :premises (@p180 @p179)) % 0.35/0.61 (step @p182 :rule trans :premises (@p181 @p178)) % 0.35/0.61 (step @p183 :rule ho_cong :premises (@p182 @p172)) % 0.35/0.61 (step @p184 :rule trans :premises (@p183 @p171)) % 0.35/0.61 (step @p185 :rule ho_cong :premises (@p184 @p70)) % 0.35/0.61 (step @p186 :rule trans :premises (@p185 @p170)) % 0.35/0.61 (step @p187 :rule refl :args (@t14)) % 0.35/0.61 (step @p188 :rule ho_cong :premises (@p9 @p187)) % 0.35/0.61 (step @p189 :rule ho_cong :premises (@p10 @p188)) % 0.35/0.61 (step @p190 :rule ho_cong :premises (@p189 @p172)) % 0.35/0.61 (step @p191 :rule ho_cong :premises (@p190 @p70)) % 0.35/0.61 (step @p192 :rule trans :premises (@p191 @p186)) % 0.35/0.61 (step @p193 :rule cong :premises (@p192) :args (@t27)) % 0.35/0.61 (step @p194 :rule trans :premises (@p12 @p193)) % 0.35/0.61 (step @p195 :rule ho_cong :premises (@p194 @p169)) % 0.35/0.61 (step @p196 :rule ho_cong :premises (@p195 @p166)) % 0.35/0.61 (step @p197 :rule refl :args (@t126)) % 0.35/0.61 (step @p198 :rule refl :args (@t15)) % 0.35/0.61 (step @p199 :rule cong :premises (@p198 @p197) :args ((= @t15 @t126))) % 0.35/0.61 (step @p200 :rule symm :premises (@p199)) % 0.35/0.61 (step @p201 :rule eq_resolve :premises (@p198 @p200)) % 0.35/0.62 (step @p202 :rule cong :premises (@p201) :args (@t79)) % 0.35/0.62 (step @p203 :rule cong :premises (@p202) :args (@t81)) % 0.35/0.62 (step @p204 :rule trans :premises (@p33 @p203)) % 0.35/0.62 (step @p205 :rule ho_cong :premises (@p204 @p196)) % 0.35/0.62 (step @p206 :rule cong :premises (@p205) :args (@t7)) % 0.35/0.62 (step @p207 :rule trans :premises (@p206 @p138)) % 0.35/0.62 (step @p208 :rule eq_resolve :premises (@p5 @p207)) % 0.35/0.62 (step @p209 :rule skolemize :premises (@p208)) % 0.35/0.62 (step @p210 :rule bool-double-not-elim :args (@t184)) % 0.35/0.62 (step @p211 :rule refl :args (@t191)) % 0.35/0.62 (step @p212 :rule nary_cong :premises (@p211 @p210) :args ((or @t191 (not @t190)))) % 0.35/0.62 (step @p213 :rule cnf_or_neg :args (@t191 0)) % 0.35/0.62 (step @p214 :rule eq_resolve :premises (@p213 @p212)) % 0.35/0.62 (step @p215 :rule reordering :premises (@p214) :args ((or @t184 @t191))) % 0.35/0.62 (step @p216 :rule chain_m_resolution :premises (@p215 @p209) :args (@t184 @t192 @t193)) % 0.35/0.62 (step @p217 :rule cnf_or_neg :args (@t191 2)) % 0.35/0.62 (step @p218 :rule chain_m_resolution :premises (@p217 @p209) :args ((not @t187) @t192 @t193)) % 0.35/0.62 (step @p219 :rule bool-double-not-elim :args (@t188)) % 0.35/0.62 (step @p220 :rule nary_cong :premises (@p211 @p219) :args ((or @t191 (not @t189)))) % 0.35/0.62 (step @p221 :rule cnf_or_neg :args (@t191 1)) % 0.35/0.62 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 0.35/0.62 (step @p223 :rule reordering :premises (@p222) :args ((or @t188 @t191))) % 0.35/0.62 (step @p224 :rule chain_m_resolution :premises (@p223 @p209) :args (@t188 @t192 @t193)) % 0.35/0.62 (step @p225 :rule cnf_or_pos :args (@t194)) % 0.35/0.62 (step @p226 :rule reordering :premises (@p225) :args ((or @t189 @t187 @t195))) % 0.35/0.62 (step @p227 :rule chain_m_resolution :premises (@p226 @p224 @p218) :args (@t195 (@list false true) (@list @t188 @t187))) % 0.35/0.62 (assume-push @p234 @t184) % 0.35/0.62 (step @p229 :rule instantiate :premises (@p216) :args ((@list @t185 @t186))) % 0.35/0.62 (step-pop @p235 :rule scope :premises (@p229)) % 0.35/0.62 (step @p230 :rule process_scope :premises (@p235) :args (@t194)) % 0.35/0.62 (step @p232 :rule implies_elim :premises (@p230)) % 0.35/0.62 (step @p233 false :rule chain_m_resolution :premises (@p232 @p227 @p216) :args (false (@list true false) (@list @t194 @t184))) % 0.35/0.62 ) % 0.35/0.62 % SZS output end Proof % 0.35/0.62 % cvc5 exiting %------------------------------------------------------------------------------