%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO485^6 : 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 : n001.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 09:12:58 AM UTC 2026 % Result : Theorem 0.63s 0.88s % Output : Proof 0.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO485^6 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n001.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Wed Jun 3 00:17:20 EDT 2026 % 0.15/0.34 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.63/0.88 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.63/0.88 % SZS status Theorem % 0.63/0.88 % SZS output start Proof % 0.63/0.88 ( % 0.63/0.88 (declare-sort $$unsorted 0) % 0.63/0.88 (declare-sort tptp.mu 0) % 0.63/0.88 (declare-const tptp.rel_s5 (-> $$unsorted $$unsorted Bool)) % 0.63/0.88 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.63/0.88 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.63/0.88 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.63/0.88 (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)))))) % 0.63/0.88 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.63/0.88 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.63/0.88 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.63/0.88 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.63/0.88 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.63/0.88 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.63/0.88 (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))))))) % 0.63/0.88 (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))))))) % 0.63/0.88 (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)))))) % 0.63/0.88 (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)))))) % 0.63/0.88 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.63/0.88 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.63/0.88 (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)))))) % 0.63/0.88 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.63/0.88 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.63/0.88 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.63/0.88 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.63/0.88 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.63/0.88 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.63/0.88 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.63/0.88 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.63/0.88 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.63/0.88 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.63/0.88 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.63/0.88 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.63/0.88 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.63/0.88 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.63/0.88 (define tptp.mbox_s5 () (let ((_let_1 (@var "V" $$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)))))))) % 0.63/0.88 (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))))) % 0.63/0.88 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.63/0.88 (define @t2 () (@var "Y" tptp.mu)) % 0.63/0.88 (define @t3 () (@var "X" tptp.mu)) % 0.63/0.88 (define @t4 () (@list @t2 @t1)) % 0.63/0.88 (define @t5 () (lambda @t4 (_ (_ (_ tptp.meq_ind @t3) @t2) @t1))) % 0.63/0.88 (define @t6 () (@list @t3 @t1)) % 0.63/0.88 (define @t7 () (lambda @t6 (_ (_ tptp.mdia_s5 (_ tptp.mexists_ind @t5)) @t1))) % 0.63/0.88 (define @t8 () (not (_ tptp.mvalid (_ tptp.mforall_ind @t7)))) % 0.63/0.88 (define @t9 () (= @t3 @t2)) % 0.63/0.88 (define @t10 () (@var "W" $$unsorted)) % 0.63/0.88 (define @t11 () (lambda (@list @t3 @t2 @t10) @t9)) % 0.63/0.88 (define @t12 () (@var "Y" (-> $$unsorted Bool))) % 0.63/0.88 (define @t13 () (@var "X" (-> $$unsorted Bool))) % 0.63/0.88 (define @t14 () (lambda (@list @t13 @t12 @t10) (= (_ @t13 @t10) (_ @t12 @t10)))) % 0.63/0.88 (define @t15 () (@var "Phi" (-> $$unsorted Bool))) % 0.63/0.88 (define @t16 () (_ @t15 @t10)) % 0.63/0.88 (define @t17 () (not @t16)) % 0.63/0.88 (define @t18 () (@list @t15 @t10)) % 0.63/0.88 (define @t19 () (lambda @t18 @t17)) % 0.63/0.88 (define @t20 () (@var "Psi" (-> $$unsorted Bool))) % 0.63/0.88 (define @t21 () (lambda (@list @t15 @t20 @t10) (or @t16 (_ @t20 @t10)))) % 0.63/0.88 (define @t22 () (_ tptp.mnot @t20)) % 0.63/0.88 (define @t23 () (_ tptp.mnot @t15)) % 0.63/0.88 (define @t24 () (_ tptp.mor @t23)) % 0.63/0.88 (define @t25 () (@list @t15 @t20 @t1)) % 0.63/0.88 (define @t26 () (lambda @t25 (_ (_ tptp.mnot (_ @t24 @t22)) @t1))) % 0.63/0.88 (define @t27 () (lambda @t25 (_ (_ @t24 @t20) @t1))) % 0.63/0.88 (define @t28 () (lambda @t25 (_ (_ (_ tptp.mor @t22) @t15) @t1))) % 0.63/0.88 (define @t29 () (lambda @t25 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t15) @t20)) (_ (_ tptp.mimplies @t20) @t15)) @t1))) % 0.63/0.88 (define @t30 () (lambda @t25 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t15) @t20)) @t1))) % 0.63/0.88 (define @t31 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.63/0.88 (define @t32 () (_ @t31 @t3)) % 0.63/0.88 (define @t33 () (_ @t32 @t10)) % 0.63/0.88 (define @t34 () (@list @t3)) % 0.63/0.88 (define @t35 () (forall @t34 @t33)) % 0.63/0.88 (define @t36 () (@list @t31 @t10)) % 0.63/0.88 (define @t37 () (lambda @t36 @t35)) % 0.63/0.88 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 0.63/0.88 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.63/0.88 (define @t40 () (_ @t39 @t38)) % 0.63/0.88 (define @t41 () (lambda (@list @t39 @t10) (forall (@list @t38) (_ @t40 @t10)))) % 0.63/0.88 (define @t42 () (lambda @t6 (_ (_ tptp.mnot @t32) @t1))) % 0.63/0.88 (define @t43 () (@list @t31 @t1)) % 0.63/0.88 (define @t44 () (lambda @t43 (_ (_ tptp.mnot (_ tptp.mforall_ind @t42)) @t1))) % 0.63/0.88 (define @t45 () (lambda (@list @t39 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t1) (_ (_ tptp.mnot @t40) @t1)))) @t1))) % 0.63/0.88 (define @t46 () (@list @t10)) % 0.63/0.88 (define @t47 () (lambda @t46 true)) % 0.63/0.88 (define @t48 () (@var "V" $$unsorted)) % 0.63/0.88 (define @t49 () (_ @t15 @t48)) % 0.63/0.88 (define @t50 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.63/0.88 (define @t51 () (@list @t48)) % 0.63/0.88 (define @t52 () (lambda (@list @t50 @t15 @t10) (forall @t51 (or (not (_ (_ @t50 @t10) @t48)) @t49)))) % 0.63/0.88 (define @t53 () (lambda (@list @t50 @t15 @t1) (_ (_ tptp.mnot (_ (_ tptp.mbox @t50) @t23)) @t1))) % 0.63/0.88 (define @t54 () (@var "S" $$unsorted)) % 0.63/0.88 (define @t55 () (_ @t50 @t54)) % 0.63/0.88 (define @t56 () (_ @t55 @t54)) % 0.63/0.88 (define @t57 () (@list @t54)) % 0.63/0.88 (define @t58 () (forall @t57 @t56)) % 0.63/0.88 (define @t59 () (@list @t50)) % 0.63/0.88 (define @t60 () (lambda @t59 @t58)) % 0.63/0.88 (define @t61 () (@var "T" $$unsorted)) % 0.63/0.88 (define @t62 () (_ @t50 @t61)) % 0.63/0.88 (define @t63 () (_ @t55 @t61)) % 0.63/0.88 (define @t64 () (lambda @t59 (forall (@list @t54 @t61) (=> @t63 (_ @t62 @t54))))) % 0.63/0.88 (define @t65 () (@list @t61)) % 0.63/0.88 (define @t66 () (lambda @t59 (forall @t57 (exists @t65 @t63)))) % 0.63/0.88 (define @t67 () (@var "U" $$unsorted)) % 0.63/0.88 (define @t68 () (_ @t55 @t67)) % 0.63/0.88 (define @t69 () (_ @t62 @t67)) % 0.63/0.88 (define @t70 () (@list @t54 @t61 @t67)) % 0.63/0.88 (define @t71 () (lambda @t59 (forall @t70 (=> (and @t63 @t69) @t68)))) % 0.63/0.88 (define @t72 () (and @t63 @t68)) % 0.63/0.88 (define @t73 () (lambda @t59 (forall @t70 (=> @t72 @t69)))) % 0.63/0.88 (define @t74 () (= @t61 @t67)) % 0.63/0.88 (define @t75 () (lambda @t59 (forall @t70 (=> @t72 @t74)))) % 0.63/0.88 (define @t76 () (@list @t67)) % 0.63/0.88 (define @t77 () (lambda @t59 (forall @t57 (exists @t65 (and @t63 (forall @t76 (=> @t68 @t74))))))) % 0.63/0.88 (define @t78 () (_ @t50 @t67)) % 0.63/0.88 (define @t79 () (_ @t78 @t61)) % 0.63/0.88 (define @t80 () (lambda @t59 (forall @t70 (=> @t63 (exists @t76 (and @t68 @t79)))))) % 0.63/0.88 (define @t81 () (lambda @t59 (forall @t70 (=> @t72 (or @t69 @t74 @t79))))) % 0.63/0.88 (define @t82 () (lambda @t59 (forall @t70 (=> @t72 (exists @t51 (and (_ @t62 @t48) (_ @t78 @t48))))))) % 0.63/0.88 (define @t83 () (forall @t46 @t16)) % 0.63/0.88 (define @t84 () (@list @t15)) % 0.63/0.88 (define @t85 () (lambda @t84 @t83)) % 0.63/0.88 (define @t86 () (lambda @t84 (forall @t46 @t17))) % 0.63/0.88 (define @t87 () (lambda @t84 (exists @t46 @t16))) % 0.63/0.88 (define @t88 () (lambda @t84 (exists @t46 @t17))) % 0.63/0.88 (define @t89 () (_ (_ tptp.rel_s5 @t10) @t48)) % 0.63/0.88 (define @t90 () (not @t89)) % 0.63/0.88 (define @t91 () (or @t90 @t49)) % 0.63/0.88 (define @t92 () (forall @t51 @t91)) % 0.63/0.88 (define @t93 () (lambda @t18 @t92)) % 0.63/0.88 (define @t94 () (@list @t15 @t1)) % 0.63/0.88 (define @t95 () (lambda @t94 (_ (_ tptp.mnot (_ tptp.mbox_s5 @t23)) @t1))) % 0.63/0.88 (define @t96 () (tptp.rel_s5 @t10 @t48)) % 0.63/0.88 (define @t97 () (not @t96)) % 0.63/0.88 (define @t98 () (not (forall @t51 @t97))) % 0.63/0.88 (define @t99 () (lambda @t46 @t98)) % 0.63/0.88 (define @t100 () (_ @t99 @t10)) % 0.63/0.88 (define @t101 () (forall @t46 @t100)) % 0.63/0.88 (define @t102 () (_ @t15 @t10)) % 0.63/0.88 (define @t103 () (lambda @t84 (forall @t46 @t102))) % 0.63/0.88 (define @t104 () (not (tptp.rel_s5 @t1 @t48))) % 0.63/0.88 (define @t105 () (not (forall @t51 @t104))) % 0.63/0.88 (define @t106 () (lambda @t6 @t105)) % 0.63/0.88 (define @t107 () (_ @t106 @t3 @t10)) % 0.63/0.88 (define @t108 () (forall @t34 @t107)) % 0.63/0.88 (define @t109 () (lambda @t46 @t108)) % 0.63/0.88 (define @t110 () (_ @t31 @t3 @t10)) % 0.63/0.88 (define @t111 () (lambda @t36 (forall @t34 @t110))) % 0.63/0.88 (define @t112 () (@list @t1)) % 0.63/0.88 (define @t113 () (@var "BOUND_VARIABLE_8348" $$unsorted)) % 0.63/0.88 (define @t114 () (lambda (@list @t113) true)) % 0.63/0.88 (define @t115 () (_ @t114 @t48)) % 0.63/0.88 (define @t116 () (not @t115)) % 0.63/0.88 (define @t117 () (or @t104 @t116)) % 0.63/0.88 (define @t118 () (forall @t51 @t117)) % 0.63/0.88 (define @t119 () (not @t118)) % 0.63/0.88 (define @t120 () (lambda @t112 @t119)) % 0.63/0.88 (define @t121 () (_ @t15 @t48)) % 0.63/0.88 (define @t122 () (not @t121)) % 0.63/0.88 (define @t123 () (not (forall @t51 (or @t104 @t122)))) % 0.63/0.88 (define @t124 () (lambda @t94 @t123)) % 0.63/0.88 (define @t125 () (not (= @t3 @t3))) % 0.63/0.88 (define @t126 () (@var "BOUND_VARIABLE_8438" tptp.mu)) % 0.63/0.88 (define @t127 () (= @t3 @t126)) % 0.63/0.88 (define @t128 () (not @t127)) % 0.63/0.88 (define @t129 () (@list @t126)) % 0.63/0.88 (define @t130 () (or @t128 @t128)) % 0.63/0.88 (define @t131 () (lambda @t4 @t9)) % 0.63/0.88 (define @t132 () (_ @t131 @t126 @t1)) % 0.63/0.88 (define @t133 () (not @t132)) % 0.63/0.88 (define @t134 () (forall @t129 @t133)) % 0.63/0.88 (define @t135 () (not @t134)) % 0.63/0.88 (define @t136 () (lambda @t112 @t135)) % 0.63/0.88 (define @t137 () (forall @t34 (not (_ @t31 @t3 @t1)))) % 0.63/0.88 (define @t138 () (not @t137)) % 0.63/0.88 (define @t139 () (lambda @t43 @t138)) % 0.63/0.88 (define @t140 () (lambda @t46 @t9)) % 0.63/0.88 (define @t141 () (lambda (@list @t2 @t10) @t9)) % 0.63/0.88 (define @t142 () (_ @t11 @t3)) % 0.63/0.88 (define @t143 () (lambda @t4 (_ (_ @t142 @t2) @t1))) % 0.63/0.88 (define @t144 () (lambda @t6 (_ (_ @t124 (_ @t139 @t143)) @t1))) % 0.63/0.88 (define @t145 () (forall @t34 (not @t110))) % 0.63/0.88 (define @t146 () (lambda @t46 @t145)) % 0.63/0.88 (define @t147 () (_ @t146 @t10)) % 0.63/0.88 (define @t148 () (not @t147)) % 0.63/0.88 (define @t149 () (lambda @t46 @t148)) % 0.63/0.88 (define @t150 () (not @t33)) % 0.63/0.88 (define @t151 () (not (_ @t32 @t1))) % 0.63/0.88 (define @t152 () (lambda @t6 @t151)) % 0.63/0.88 (define @t153 () (_ @t152 @t3 @t10)) % 0.63/0.88 (define @t154 () (forall @t34 @t153)) % 0.63/0.88 (define @t155 () (lambda @t46 @t154)) % 0.63/0.88 (define @t156 () (lambda @t46 @t150)) % 0.63/0.88 (define @t157 () (_ @t19 @t32)) % 0.63/0.88 (define @t158 () (forall @t51 (or @t97 @t122))) % 0.63/0.88 (define @t159 () (lambda @t46 @t158)) % 0.63/0.88 (define @t160 () (_ @t159 @t10)) % 0.63/0.88 (define @t161 () (not @t160)) % 0.63/0.88 (define @t162 () (lambda @t46 @t161)) % 0.63/0.88 (define @t163 () (not @t49)) % 0.63/0.88 (define @t164 () (or @t97 @t163)) % 0.63/0.88 (define @t165 () (lambda @t46 @t17)) % 0.63/0.88 (define @t166 () (_ @t165 @t48)) % 0.63/0.88 (define @t167 () (or @t97 @t166)) % 0.63/0.88 (define @t168 () (forall @t51 @t167)) % 0.63/0.88 (define @t169 () (lambda @t46 @t168)) % 0.63/0.88 (define @t170 () (lambda @t18 (forall @t51 (or @t97 @t121)))) % 0.63/0.88 (define @t171 () (forall @t46 @t98)) % 0.63/0.88 (define @t172 () (@quantifiers_skolemize @t171 0)) % 0.63/0.88 (define @t173 () (forall @t51 (not (tptp.rel_s5 @t172 @t48)))) % 0.63/0.88 (define @t174 () (not @t171)) % 0.63/0.88 (define @t175 () (not (not @t173))) % 0.63/0.88 (define @t176 () (_ @t50 @t54 @t54)) % 0.63/0.88 (define @t177 () (@list @t172)) % 0.63/0.88 (define @t178 () (tptp.rel_s5 @t172 @t172)) % 0.63/0.88 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.63/0.88 (assume @p2 (_ tptp.mreflexive tptp.rel_s5)) % 0.63/0.88 (assume @p3 (_ tptp.mtransitive tptp.rel_s5)) % 0.63/0.88 (assume @p4 (_ tptp.msymmetric tptp.rel_s5)) % 0.63/0.88 (assume @p5 @t8) % 0.63/0.88 (assume @p6 true) % 0.63/0.88 (step @p7 (= tptp.meq_ind @t11) :rule refl :args (@t11)) % 0.63/0.88 (step @p8 (= tptp.meq_prop @t14) :rule refl :args (@t14)) % 0.63/0.88 (step @p9 (= tptp.mnot @t19) :rule refl :args (@t19)) % 0.63/0.88 (step @p10 (= tptp.mor @t21) :rule refl :args (@t21)) % 0.63/0.88 (step @p11 (= tptp.mand @t26) :rule refl :args (@t26)) % 0.63/0.88 (step @p12 (= tptp.mimplies @t27) :rule refl :args (@t27)) % 0.63/0.88 (step @p13 (= tptp.mimplied @t28) :rule refl :args (@t28)) % 0.63/0.88 (step @p14 (= tptp.mequiv @t29) :rule refl :args (@t29)) % 0.63/0.88 (step @p15 (= tptp.mxor @t30) :rule refl :args (@t30)) % 0.63/0.88 (step @p16 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 0.63/0.88 (step @p17 (= tptp.mforall_prop @t41) :rule refl :args (@t41)) % 0.63/0.88 (step @p18 (= tptp.mexists_ind @t44) :rule refl :args (@t44)) % 0.63/0.88 (step @p19 (= tptp.mexists_prop @t45) :rule refl :args (@t45)) % 0.63/0.88 (step @p20 (= tptp.mtrue @t47) :rule refl :args (@t47)) % 0.63/0.88 (step @p21 (= tptp.mbox @t52) :rule refl :args (@t52)) % 0.63/0.88 (step @p22 (= tptp.mdia @t53) :rule refl :args (@t53)) % 0.63/0.88 (step @p23 (= tptp.mreflexive @t60) :rule refl :args (@t60)) % 0.63/0.88 (step @p24 (= tptp.msymmetric @t64) :rule refl :args (@t64)) % 0.63/0.88 (step @p25 (= tptp.mserial @t66) :rule refl :args (@t66)) % 0.63/0.88 (step @p26 (= tptp.mtransitive @t71) :rule refl :args (@t71)) % 0.63/0.88 (step @p27 (= tptp.meuclidean @t73) :rule refl :args (@t73)) % 0.63/0.88 (step @p28 (= tptp.mpartially_functional @t75) :rule refl :args (@t75)) % 0.63/0.88 (step @p29 (= tptp.mfunctional @t77) :rule refl :args (@t77)) % 0.63/0.88 (step @p30 (= tptp.mweakly_dense @t80) :rule refl :args (@t80)) % 0.63/0.88 (step @p31 (= tptp.mweakly_connected @t81) :rule refl :args (@t81)) % 0.63/0.88 (step @p32 (= tptp.mweakly_directed @t82) :rule refl :args (@t82)) % 0.63/0.88 (step @p33 (= tptp.mvalid @t85) :rule refl :args (@t85)) % 0.63/0.88 (step @p34 (= tptp.minvalid @t86) :rule refl :args (@t86)) % 0.63/0.88 (step @p35 (= tptp.msatisfiable @t87) :rule refl :args (@t87)) % 0.63/0.88 (step @p36 (= tptp.mcountersatisfiable @t88) :rule refl :args (@t88)) % 0.63/0.88 (step @p37 (= tptp.mbox_s5 @t93) :rule refl :args (@t93)) % 0.63/0.88 (step @p38 (= tptp.mdia_s5 @t95) :rule refl :args (@t95)) % 0.63/0.88 (step @p39 :rule beta-reduce :args ((= @t100 @t98))) % 0.63/0.88 (step @p40 :rule cong :premises (@p39) :args (@t101)) % 0.63/0.88 (step @p41 :rule beta-reduce :args ((= (_ @t103 @t99) @t101))) % 0.63/0.88 (step @p42 :rule trans :premises (@p41 @p40)) % 0.63/0.88 (step @p43 :rule quant-unused-vars :args ((= (forall @t34 @t98) @t98))) % 0.63/0.88 (step @p44 :rule beta-reduce :args ((= @t107 @t98))) % 0.63/0.88 (step @p45 :rule cong :premises (@p44) :args (@t108)) % 0.63/0.88 (step @p46 :rule trans :premises (@p45 @p43)) % 0.63/0.88 (step @p47 :rule cong :premises (@p46) :args (@t109)) % 0.63/0.88 (step @p48 :rule beta-reduce :args ((= (_ @t111 @t106) @t109))) % 0.63/0.88 (step @p49 :rule trans :premises (@p48 @p47)) % 0.63/0.88 (step @p50 :rule beta-reduce :args ((= (_ (lambda @t112 @t105) @t1) @t105))) % 0.63/0.88 (step @p51 :rule refl :args (@t1)) % 0.63/0.88 (step @p52 :rule aci_norm :args ((= (or @t104 false) @t104))) % 0.63/0.88 (step @p53 :rule evaluate :args ((not true))) % 0.63/0.88 (step @p54 :rule beta-reduce :args ((= @t115 true))) % 0.63/0.88 (step @p55 :rule cong :premises (@p54) :args (@t116)) % 0.63/0.88 (step @p56 :rule trans :premises (@p55 @p53)) % 0.63/0.88 (step @p57 :rule refl :args (@t104)) % 0.63/0.88 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t117)) % 0.63/0.88 (step @p59 :rule trans :premises (@p58 @p52)) % 0.63/0.88 (step @p60 :rule cong :premises (@p59) :args (@t118)) % 0.63/0.88 (step @p61 :rule cong :premises (@p60) :args (@t119)) % 0.63/0.88 (step @p62 :rule cong :premises (@p61) :args (@t120)) % 0.63/0.88 (step @p63 :rule beta-reduce :args ((= (_ @t124 @t114) @t120))) % 0.63/0.88 (step @p64 :rule trans :premises (@p63 @p62)) % 0.63/0.88 (step @p65 :rule refl :args (@t114)) % 0.63/0.88 (step @p66 :rule symm :premises (@p65)) % 0.63/0.88 (step @p67 :rule alpha_equiv :args ((lambda @t112 true) (@list @t1) (@list @t113))) % 0.63/0.88 (step @p68 :rule trans :premises (@p67 @p66)) % 0.63/0.88 (step @p69 :rule evaluate :args ((not false))) % 0.63/0.88 (step @p70 :rule eq-refl :args (@t3)) % 0.63/0.88 (step @p71 :rule cong :premises (@p70) :args (@t125)) % 0.63/0.88 (step @p72 :rule trans :premises (@p71 @p53)) % 0.63/0.88 (step @p73 :rule quant-var-elim-eq :args ((= (forall @t129 (or (not (= @t126 @t3)) @t128)) @t125))) % 0.63/0.88 (step @p74 :rule refl :args (@t128)) % 0.63/0.88 (step @p75 :rule eq-symm :args (@t3 @t126)) % 0.63/0.88 (step @p76 :rule cong :premises (@p75) :args (@t128)) % 0.63/0.88 (step @p77 :rule nary_cong :premises (@p76 @p74) :args (@t130)) % 0.63/0.88 (step @p78 :rule aci_norm :args ((= @t128 @t130))) % 0.63/0.88 (step @p79 :rule trans :premises (@p78 @p77)) % 0.63/0.88 (step @p80 :rule cong :premises (@p79) :args ((forall @t129 @t128))) % 0.63/0.88 (step @p81 :rule trans :premises (@p80 @p73)) % 0.63/0.88 (step @p82 :rule trans :premises (@p81 @p72)) % 0.63/0.88 (step @p83 :rule beta-reduce :args ((= @t132 @t127))) % 0.63/0.88 (step @p84 :rule cong :premises (@p83) :args (@t133)) % 0.63/0.88 (step @p85 :rule cong :premises (@p84) :args (@t134)) % 0.63/0.88 (step @p86 :rule trans :premises (@p85 @p82)) % 0.63/0.88 (step @p87 :rule cong :premises (@p86) :args (@t135)) % 0.63/0.88 (step @p88 :rule trans :premises (@p87 @p69)) % 0.63/0.88 (step @p89 :rule cong :premises (@p88) :args (@t136)) % 0.63/0.88 (step @p90 :rule trans :premises (@p89 @p68)) % 0.63/0.88 (step @p91 :rule beta-reduce :args ((= (_ (lambda @t43 (not (forall @t129 (not (_ @t31 @t126 @t1))))) @t131) @t136))) % 0.63/0.88 (step @p92 :rule trans :premises (@p91 @p90)) % 0.63/0.88 (step @p93 :rule refl :args (@t131)) % 0.63/0.88 (step @p94 :rule alpha_equiv :args (@t137 (@list @t3) (@list @t126))) % 0.63/0.88 (step @p95 :rule cong :premises (@p94) :args (@t138)) % 0.63/0.88 (step @p96 :rule cong :premises (@p95) :args (@t139)) % 0.63/0.88 (step @p97 :rule ho_cong :premises (@p96 @p93)) % 0.63/0.88 (step @p98 :rule trans :premises (@p97 @p92)) % 0.63/0.88 (step @p99 :rule beta-reduce :args ((= (_ @t140 @t1) @t9))) % 0.63/0.88 (step @p100 :rule beta-reduce :args ((= (_ @t141 @t2) @t140))) % 0.63/0.88 (step @p101 :rule refl :args (@t2)) % 0.63/0.88 (step @p102 :rule beta-reduce :args ((= @t142 @t141))) % 0.63/0.88 (step @p103 :rule ho_cong :premises (@p102 @p101)) % 0.63/0.88 (step @p104 :rule trans :premises (@p103 @p100)) % 0.63/0.88 (step @p105 :rule ho_cong :premises (@p104 @p51)) % 0.63/0.88 (step @p106 :rule trans :premises (@p105 @p99)) % 0.63/0.88 (step @p107 :rule cong :premises (@p106) :args (@t143)) % 0.63/0.88 (step @p108 :rule refl :args (@t139)) % 0.63/0.88 (step @p109 :rule ho_cong :premises (@p108 @p107)) % 0.63/0.88 (step @p110 :rule trans :premises (@p109 @p98)) % 0.63/0.88 (step @p111 :rule refl :args (@t124)) % 0.63/0.88 (step @p112 :rule ho_cong :premises (@p111 @p110)) % 0.63/0.88 (step @p113 :rule trans :premises (@p112 @p64)) % 0.63/0.88 (step @p114 :rule ho_cong :premises (@p113 @p51)) % 0.63/0.88 (step @p115 :rule trans :premises (@p114 @p50)) % 0.63/0.88 (step @p116 :rule cong :premises (@p115) :args (@t144)) % 0.63/0.88 (step @p117 :rule refl :args (@t111)) % 0.63/0.88 (step @p118 :rule ho_cong :premises (@p117 @p116)) % 0.63/0.88 (step @p119 :rule trans :premises (@p118 @p49)) % 0.63/0.88 (step @p120 :rule refl :args (@t103)) % 0.63/0.88 (step @p121 :rule ho_cong :premises (@p120 @p119)) % 0.63/0.88 (step @p122 :rule trans :premises (@p121 @p42)) % 0.63/0.88 (step @p123 :rule cong :premises (@p122) :args ((not (_ @t103 (_ @t111 @t144))))) % 0.63/0.88 (step @p124 :rule refl :args (@t3)) % 0.63/0.88 (step @p125 :rule ho_cong :premises (@p7 @p124)) % 0.63/0.88 (step @p126 :rule ho_cong :premises (@p125 @p101)) % 0.63/0.88 (step @p127 :rule ho_cong :premises (@p126 @p51)) % 0.63/0.88 (step @p128 :rule cong :premises (@p127) :args (@t5)) % 0.63/0.88 (step @p129 :rule beta-reduce :args ((= (_ (lambda @t46 (not @t145)) @t1) @t138))) % 0.63/0.88 (step @p130 :rule beta-reduce :args ((= @t147 @t145))) % 0.63/0.88 (step @p131 :rule cong :premises (@p130) :args (@t148)) % 0.63/0.88 (step @p132 :rule cong :premises (@p131) :args (@t149)) % 0.63/0.88 (step @p133 :rule beta-reduce :args ((= (_ @t19 @t146) @t149))) % 0.63/0.88 (step @p134 :rule trans :premises (@p133 @p132)) % 0.63/0.88 (step @p135 :rule refl :args (@t110)) % 0.63/0.88 (step @p136 :rule refl :args (@t33)) % 0.63/0.88 (step @p137 :rule cong :premises (@p136 @p135) :args ((= @t33 @t110))) % 0.63/0.88 (step @p138 :rule symm :premises (@p137)) % 0.63/0.88 (step @p139 :rule eq_resolve :premises (@p136 @p138)) % 0.63/0.88 (step @p140 :rule cong :premises (@p139) :args (@t150)) % 0.63/0.88 (step @p141 :rule cong :premises (@p140) :args ((forall @t34 @t150))) % 0.63/0.88 (step @p142 :rule beta-reduce :args ((= @t153 @t150))) % 0.63/0.88 (step @p143 :rule cong :premises (@p142) :args (@t154)) % 0.63/0.88 (step @p144 :rule trans :premises (@p143 @p141)) % 0.63/0.88 (step @p145 :rule cong :premises (@p144) :args (@t155)) % 0.63/0.88 (step @p146 :rule beta-reduce :args ((= (_ @t111 @t152) @t155))) % 0.63/0.88 (step @p147 :rule trans :premises (@p146 @p145)) % 0.63/0.88 (step @p148 :rule beta-reduce :args ((= (_ @t156 @t1) @t151))) % 0.63/0.88 (step @p149 :rule beta-reduce :args ((= @t157 @t156))) % 0.63/0.88 (step @p150 :rule ho_cong :premises (@p149 @p51)) % 0.63/0.88 (step @p151 :rule trans :premises (@p150 @p148)) % 0.63/0.88 (step @p152 :rule cong :premises (@p151) :args ((lambda @t6 (_ @t157 @t1)))) % 0.63/0.88 (step @p153 :rule ho_cong :premises (@p117 @p152)) % 0.63/0.88 (step @p154 :rule trans :premises (@p153 @p147)) % 0.63/0.88 (step @p155 :rule refl :args (@t19)) % 0.63/0.88 (step @p156 :rule ho_cong :premises (@p155 @p154)) % 0.63/0.88 (step @p157 :rule trans :premises (@p156 @p134)) % 0.63/0.88 (step @p158 :rule ho_cong :premises (@p157 @p51)) % 0.63/0.88 (step @p159 :rule trans :premises (@p158 @p129)) % 0.63/0.88 (step @p160 :rule refl :args (@t32)) % 0.63/0.88 (step @p161 :rule ho_cong :premises (@p9 @p160)) % 0.63/0.88 (step @p162 :rule ho_cong :premises (@p161 @p51)) % 0.63/0.88 (step @p163 :rule cong :premises (@p162) :args (@t42)) % 0.63/0.88 (step @p164 :rule cong :premises (@p139) :args (@t35)) % 0.63/0.88 (step @p165 :rule cong :premises (@p164) :args (@t37)) % 0.63/0.88 (step @p166 :rule trans :premises (@p16 @p165)) % 0.63/0.88 (step @p167 :rule ho_cong :premises (@p166 @p163)) % 0.63/0.88 (step @p168 :rule ho_cong :premises (@p9 @p167)) % 0.63/0.88 (step @p169 :rule ho_cong :premises (@p168 @p51)) % 0.63/0.88 (step @p170 :rule trans :premises (@p169 @p159)) % 0.63/0.88 (step @p171 :rule cong :premises (@p170) :args (@t44)) % 0.63/0.88 (step @p172 :rule trans :premises (@p18 @p171)) % 0.63/0.88 (step @p173 :rule ho_cong :premises (@p172 @p128)) % 0.63/0.88 (step @p174 :rule beta-reduce :args ((= (_ (lambda @t46 (not @t158)) @t1) @t123))) % 0.63/0.88 (step @p175 :rule beta-reduce :args ((= @t160 @t158))) % 0.63/0.88 (step @p176 :rule cong :premises (@p175) :args (@t161)) % 0.63/0.88 (step @p177 :rule cong :premises (@p176) :args (@t162)) % 0.63/0.88 (step @p178 :rule beta-reduce :args ((= (_ @t19 @t159) @t162))) % 0.63/0.88 (step @p179 :rule trans :premises (@p178 @p177)) % 0.63/0.88 (step @p180 :rule refl :args (@t121)) % 0.63/0.88 (step @p181 :rule refl :args (@t49)) % 0.63/0.88 (step @p182 :rule cong :premises (@p181 @p180) :args ((= @t49 @t121))) % 0.63/0.88 (step @p183 :rule symm :premises (@p182)) % 0.63/0.88 (step @p184 :rule eq_resolve :premises (@p181 @p183)) % 0.63/0.88 (step @p185 :rule cong :premises (@p184) :args (@t163)) % 0.63/0.88 (step @p186 :rule refl :args (@t97)) % 0.63/0.88 (step @p187 :rule nary_cong :premises (@p186 @p185) :args (@t164)) % 0.63/0.88 (step @p188 :rule cong :premises (@p187) :args ((forall @t51 @t164))) % 0.63/0.88 (step @p189 :rule beta-reduce :args ((= @t166 @t163))) % 0.63/0.88 (step @p190 :rule refl :args (@t97)) % 0.63/0.88 (step @p191 :rule nary_cong :premises (@p190 @p189) :args (@t167)) % 0.63/0.88 (step @p192 :rule cong :premises (@p191) :args (@t168)) % 0.63/0.88 (step @p193 :rule trans :premises (@p192 @p188)) % 0.63/0.88 (step @p194 :rule cong :premises (@p193) :args (@t169)) % 0.63/0.88 (step @p195 :rule beta-reduce :args ((= (_ @t170 @t165) @t169))) % 0.63/0.88 (step @p196 :rule trans :premises (@p195 @p194)) % 0.63/0.88 (step @p197 :rule beta-reduce :args ((= (_ @t19 @t15) @t165))) % 0.63/0.88 (step @p198 :rule refl :args (@t170)) % 0.63/0.88 (step @p199 :rule ho_cong :premises (@p198 @p197)) % 0.63/0.88 (step @p200 :rule trans :premises (@p199 @p196)) % 0.63/0.88 (step @p201 :rule ho_cong :premises (@p155 @p200)) % 0.63/0.88 (step @p202 :rule trans :premises (@p201 @p179)) % 0.63/0.88 (step @p203 :rule ho_cong :premises (@p202 @p51)) % 0.63/0.88 (step @p204 :rule trans :premises (@p203 @p174)) % 0.63/0.88 (step @p205 :rule refl :args (@t15)) % 0.63/0.88 (step @p206 :rule ho_cong :premises (@p9 @p205)) % 0.63/0.88 (step @p207 :rule refl :args (@t96)) % 0.63/0.88 (step @p208 :rule refl :args (@t89)) % 0.63/0.88 (step @p209 :rule cong :premises (@p208 @p207) :args ((= @t89 @t96))) % 0.63/0.88 (step @p210 :rule symm :premises (@p209)) % 0.63/0.88 (step @p211 :rule eq_resolve :premises (@p208 @p210)) % 0.63/0.88 (step @p212 :rule cong :premises (@p211) :args (@t90)) % 0.63/0.88 (step @p213 :rule nary_cong :premises (@p212 @p184) :args (@t91)) % 0.63/0.88 (step @p214 :rule cong :premises (@p213) :args (@t92)) % 0.63/0.88 (step @p215 :rule cong :premises (@p214) :args (@t93)) % 0.63/0.89 (step @p216 :rule trans :premises (@p37 @p215)) % 0.63/0.89 (step @p217 :rule ho_cong :premises (@p216 @p206)) % 0.63/0.89 (step @p218 :rule ho_cong :premises (@p9 @p217)) % 0.63/0.89 (step @p219 :rule ho_cong :premises (@p218 @p51)) % 0.63/0.89 (step @p220 :rule trans :premises (@p219 @p204)) % 0.63/0.89 (step @p221 :rule cong :premises (@p220) :args (@t95)) % 0.63/0.89 (step @p222 :rule trans :premises (@p38 @p221)) % 0.63/0.89 (step @p223 :rule ho_cong :premises (@p222 @p173)) % 0.63/0.89 (step @p224 :rule ho_cong :premises (@p223 @p51)) % 0.63/0.89 (step @p225 :rule cong :premises (@p224) :args (@t7)) % 0.63/0.89 (step @p226 :rule ho_cong :premises (@p166 @p225)) % 0.63/0.89 (step @p227 :rule refl :args (@t102)) % 0.63/0.89 (step @p228 :rule refl :args (@t16)) % 0.63/0.89 (step @p229 :rule cong :premises (@p228 @p227) :args ((= @t16 @t102))) % 0.63/0.89 (step @p230 :rule symm :premises (@p229)) % 0.63/0.89 (step @p231 :rule eq_resolve :premises (@p228 @p230)) % 0.63/0.89 (step @p232 :rule cong :premises (@p231) :args (@t83)) % 0.63/0.89 (step @p233 :rule cong :premises (@p232) :args (@t85)) % 0.63/0.89 (step @p234 :rule trans :premises (@p33 @p233)) % 0.63/0.89 (step @p235 :rule ho_cong :premises (@p234 @p226)) % 0.63/0.89 (step @p236 :rule cong :premises (@p235) :args (@t8)) % 0.63/0.89 (step @p237 :rule trans :premises (@p236 @p123)) % 0.63/0.89 (step @p238 :rule eq_resolve :premises (@p5 @p237)) % 0.63/0.89 (step @p239 :rule refl :args (@t173)) % 0.63/0.89 (step @p240 :rule bool-double-not-elim :args (@t171)) % 0.63/0.89 (step @p241 :rule nary_cong :premises (@p240 @p239) :args ((or (not @t174) @t173))) % 0.63/0.89 (step @p242 :rule bool-double-not-elim :args (@t173)) % 0.63/0.89 (step @p243 :rule refl :args (@t174)) % 0.63/0.89 (step @p244 :rule cong :premises (@p243 @p242) :args ((=> @t174 @t175))) % 0.63/0.89 (assume-push @p273 @t174) % 0.63/0.89 (step @p246 :rule skolemize :premises (@p238)) % 0.63/0.89 (step-pop @p274 :rule scope :premises (@p246)) % 0.63/0.89 (step @p247 :rule process_scope :premises (@p274) :args (@t175)) % 0.63/0.89 (step @p249 :rule eq_resolve :premises (@p247 @p244)) % 0.63/0.89 (step @p250 :rule implies_elim :premises (@p249)) % 0.63/0.89 (step @p251 :rule eq_resolve :premises (@p250 @p241)) % 0.63/0.89 (step @p252 :rule chain_m_resolution :premises (@p251 @p238) :args (@t173 (@list true) (@list @t171))) % 0.63/0.89 (step @p253 :rule beta-reduce :args ((= (_ (lambda @t59 (forall @t57 @t176)) tptp.rel_s5) (forall @t57 (tptp.rel_s5 @t54 @t54))))) % 0.63/0.89 (step @p254 :rule refl :args (tptp.rel_s5)) % 0.63/0.89 (step @p255 :rule refl :args (@t176)) % 0.63/0.89 (step @p256 :rule refl :args (@t56)) % 0.63/0.89 (step @p257 :rule cong :premises (@p256 @p255) :args ((= @t56 @t176))) % 0.63/0.89 (step @p258 :rule symm :premises (@p257)) % 0.63/0.89 (step @p259 :rule eq_resolve :premises (@p256 @p258)) % 0.63/0.89 (step @p260 :rule cong :premises (@p259) :args (@t58)) % 0.63/0.89 (step @p261 :rule cong :premises (@p260) :args (@t60)) % 0.63/0.89 (step @p262 :rule trans :premises (@p23 @p261)) % 0.63/0.89 (step @p263 :rule ho_cong :premises (@p262 @p254)) % 0.63/0.89 (step @p264 :rule trans :premises (@p263 @p253)) % 0.63/0.89 (step @p265 :rule eq_resolve :premises (@p2 @p264)) % 0.63/0.89 (step @p266 :rule instantiate :premises (@p265) :args (@t177)) % 0.63/0.89 (assume-push @p275 @t173) % 0.63/0.89 (step @p268 :rule instantiate :premises (@p252) :args (@t177)) % 0.63/0.89 (step-pop @p276 :rule scope :premises (@p268)) % 0.63/0.89 (step @p269 :rule process_scope :premises (@p276) :args ((not @t178))) % 0.63/0.89 (step @p271 :rule implies_elim :premises (@p269)) % 0.63/0.89 (step @p272 false :rule chain_m_resolution :premises (@p271 @p266 @p252) :args (false (@list false false) (@list @t178 @t173))) % 0.63/0.89 ) % 0.63/0.89 % SZS output end Proof % 0.63/0.89 % cvc5 exiting %------------------------------------------------------------------------------