%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO455^3 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.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 09:12:44 AM UTC 2026 % Result : Theorem 0.50s 0.76s % Output : Proof 0.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO455^3 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n016.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 00:09:39 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.50/0.76 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.50/0.76 % SZS status Theorem % 0.50/0.76 % SZS output start Proof % 0.50/0.76 ( % 0.50/0.76 (declare-sort $$unsorted 0) % 0.50/0.76 (declare-sort tptp.mu 0) % 0.50/0.76 (declare-const tptp.rel_m (-> $$unsorted $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.p (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.q (-> $$unsorted Bool)) % 0.50/0.76 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.50/0.76 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.50/0.76 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.50/0.76 (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)))))) % 0.50/0.76 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.50/0.76 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.50/0.76 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.50/0.76 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.50/0.76 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.50/0.76 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.50/0.76 (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))))))) % 0.50/0.76 (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))))))) % 0.50/0.76 (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)))))) % 0.50/0.76 (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)))))) % 0.50/0.76 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.50/0.76 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.50/0.76 (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)))))) % 0.50/0.76 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.50/0.76 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.50/0.76 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.50/0.76 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.50/0.76 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.50/0.76 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.50/0.76 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.50/0.76 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.50/0.76 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.50/0.76 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.50/0.76 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.50/0.76 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.50/0.76 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.50/0.76 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.50/0.76 (define tptp.mbox_m () (let ((_let_1 (@var "V" $$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_m _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.50/0.76 (define tptp.mdia_m () (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_m (_ tptp.mnot _let_2))) _let_1))))) % 0.50/0.76 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ (_ tptp.mand (_ tptp.mbox_m tptp.p)) (_ tptp.mbox_m (_ (_ tptp.mor (_ tptp.mnot tptp.p)) tptp.q)))) (_ tptp.mdia_m tptp.q))))) % 0.50/0.76 (define @t2 () (@var "Y" tptp.mu)) % 0.50/0.76 (define @t3 () (@var "X" tptp.mu)) % 0.50/0.76 (define @t4 () (@var "W" $$unsorted)) % 0.50/0.76 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.50/0.76 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.50/0.76 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.50/0.76 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.50/0.76 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.50/0.76 (define @t10 () (_ @t9 @t4)) % 0.50/0.76 (define @t11 () (not @t10)) % 0.50/0.76 (define @t12 () (@list @t9 @t4)) % 0.50/0.76 (define @t13 () (lambda @t12 @t11)) % 0.50/0.76 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.50/0.76 (define @t15 () (_ @t14 @t4)) % 0.50/0.76 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.50/0.76 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.50/0.76 (define @t18 () (_ tptp.mnot @t14)) % 0.50/0.76 (define @t19 () (_ tptp.mnot @t9)) % 0.50/0.76 (define @t20 () (_ tptp.mor @t19)) % 0.50/0.76 (define @t21 () (@list @t9 @t14 @t17)) % 0.50/0.76 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.50/0.76 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.50/0.76 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.50/0.76 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.50/0.76 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.50/0.76 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.50/0.76 (define @t28 () (_ @t27 @t3)) % 0.50/0.76 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.50/0.76 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.50/0.76 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.50/0.76 (define @t32 () (_ @t31 @t30)) % 0.50/0.76 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.50/0.76 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.50/0.76 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.50/0.76 (define @t36 () (@list @t4)) % 0.50/0.76 (define @t37 () (lambda @t36 true)) % 0.50/0.76 (define @t38 () (@var "V" $$unsorted)) % 0.50/0.76 (define @t39 () (_ @t9 @t38)) % 0.50/0.76 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.50/0.76 (define @t41 () (@list @t38)) % 0.50/0.76 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.50/0.76 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.50/0.76 (define @t44 () (@var "S" $$unsorted)) % 0.50/0.76 (define @t45 () (_ @t40 @t44)) % 0.50/0.76 (define @t46 () (_ @t45 @t44)) % 0.50/0.76 (define @t47 () (@list @t44)) % 0.50/0.76 (define @t48 () (forall @t47 @t46)) % 0.50/0.76 (define @t49 () (@list @t40)) % 0.50/0.76 (define @t50 () (lambda @t49 @t48)) % 0.50/0.76 (define @t51 () (@var "T" $$unsorted)) % 0.50/0.76 (define @t52 () (_ @t40 @t51)) % 0.50/0.76 (define @t53 () (_ @t45 @t51)) % 0.50/0.76 (define @t54 () (lambda @t49 (forall (@list @t44 @t51) (=> @t53 (_ @t52 @t44))))) % 0.50/0.76 (define @t55 () (@list @t51)) % 0.50/0.76 (define @t56 () (lambda @t49 (forall @t47 (exists @t55 @t53)))) % 0.50/0.76 (define @t57 () (@var "U" $$unsorted)) % 0.50/0.76 (define @t58 () (_ @t45 @t57)) % 0.50/0.76 (define @t59 () (_ @t52 @t57)) % 0.50/0.76 (define @t60 () (@list @t44 @t51 @t57)) % 0.50/0.76 (define @t61 () (lambda @t49 (forall @t60 (=> (and @t53 @t59) @t58)))) % 0.50/0.76 (define @t62 () (and @t53 @t58)) % 0.50/0.76 (define @t63 () (lambda @t49 (forall @t60 (=> @t62 @t59)))) % 0.50/0.76 (define @t64 () (= @t51 @t57)) % 0.50/0.76 (define @t65 () (lambda @t49 (forall @t60 (=> @t62 @t64)))) % 0.50/0.76 (define @t66 () (@list @t57)) % 0.50/0.76 (define @t67 () (lambda @t49 (forall @t47 (exists @t55 (and @t53 (forall @t66 (=> @t58 @t64))))))) % 0.50/0.76 (define @t68 () (_ @t40 @t57)) % 0.50/0.76 (define @t69 () (_ @t68 @t51)) % 0.50/0.76 (define @t70 () (lambda @t49 (forall @t60 (=> @t53 (exists @t66 (and @t58 @t69)))))) % 0.50/0.76 (define @t71 () (lambda @t49 (forall @t60 (=> @t62 (or @t59 @t64 @t69))))) % 0.50/0.76 (define @t72 () (lambda @t49 (forall @t60 (=> @t62 (exists @t41 (and (_ @t52 @t38) (_ @t68 @t38))))))) % 0.50/0.76 (define @t73 () (forall @t36 @t10)) % 0.50/0.76 (define @t74 () (@list @t9)) % 0.50/0.76 (define @t75 () (lambda @t74 @t73)) % 0.50/0.76 (define @t76 () (lambda @t74 (forall @t36 @t11))) % 0.50/0.76 (define @t77 () (lambda @t74 (exists @t36 @t10))) % 0.50/0.76 (define @t78 () (lambda @t74 (exists @t36 @t11))) % 0.50/0.76 (define @t79 () (_ (_ tptp.rel_m @t4) @t38)) % 0.50/0.76 (define @t80 () (not @t79)) % 0.50/0.76 (define @t81 () (or @t80 @t39)) % 0.50/0.76 (define @t82 () (forall @t41 @t81)) % 0.50/0.76 (define @t83 () (lambda @t12 @t82)) % 0.50/0.76 (define @t84 () (@list @t9 @t17)) % 0.50/0.76 (define @t85 () (lambda @t84 (_ (_ tptp.mnot (_ tptp.mbox_m @t19)) @t17))) % 0.50/0.76 (define @t86 () (_ @t40 @t44 @t44)) % 0.50/0.76 (define @t87 () (tptp.q @t38)) % 0.50/0.76 (define @t88 () (tptp.p @t38)) % 0.50/0.76 (define @t89 () (not @t88)) % 0.50/0.76 (define @t90 () (tptp.rel_m @t4 @t38)) % 0.50/0.76 (define @t91 () (not @t90)) % 0.50/0.76 (define @t92 () (forall @t41 (or @t91 @t89 @t87))) % 0.50/0.76 (define @t93 () (forall @t41 (or @t91 @t88))) % 0.50/0.76 (define @t94 () (not @t87)) % 0.50/0.76 (define @t95 () (or (not (forall @t41 (or @t91 @t94))) (not @t93) (not @t92))) % 0.50/0.76 (define @t96 () (@quantifiers_skolemize (forall @t36 @t95) 0)) % 0.50/0.76 (define @t97 () (@list @t96)) % 0.50/0.76 (define @t98 () (not (tptp.rel_m @t17 @t38))) % 0.50/0.76 (define @t99 () (forall @t41 (or @t98 @t89 @t87))) % 0.50/0.76 (define @t100 () (not @t99)) % 0.50/0.76 (define @t101 () (forall @t41 (or @t98 @t88))) % 0.50/0.76 (define @t102 () (not @t101)) % 0.50/0.76 (define @t103 () (not (forall @t41 (or @t98 @t94)))) % 0.50/0.76 (define @t104 () (@list @t17)) % 0.50/0.76 (define @t105 () (lambda @t104 (or @t103 @t102 @t100))) % 0.50/0.76 (define @t106 () (_ @t105 @t4)) % 0.50/0.76 (define @t107 () (forall @t36 @t106)) % 0.50/0.76 (define @t108 () (_ @t9 @t4)) % 0.50/0.76 (define @t109 () (lambda @t74 (forall @t36 @t108))) % 0.50/0.76 (define @t110 () (lambda @t104 @t103)) % 0.50/0.76 (define @t111 () (_ @t110 @t17)) % 0.50/0.76 (define @t112 () (or @t111 @t102 @t100)) % 0.50/0.76 (define @t113 () (lambda @t104 @t112)) % 0.50/0.76 (define @t114 () (_ @t14 @t17)) % 0.50/0.76 (define @t115 () (or @t114 @t102 @t100)) % 0.50/0.76 (define @t116 () (@list @t14 @t17)) % 0.50/0.76 (define @t117 () (_ @t9 @t38)) % 0.50/0.76 (define @t118 () (not @t117)) % 0.50/0.76 (define @t119 () (not (forall @t41 (or @t98 @t118)))) % 0.50/0.76 (define @t120 () (_ (lambda @t84 @t119) tptp.q)) % 0.50/0.76 (define @t121 () (or @t102 @t100)) % 0.50/0.76 (define @t122 () (not @t121)) % 0.50/0.76 (define @t123 () (lambda @t104 @t122)) % 0.50/0.76 (define @t124 () (_ @t123 @t17)) % 0.50/0.76 (define @t125 () (not @t124)) % 0.50/0.76 (define @t126 () (or @t125 @t114)) % 0.50/0.76 (define @t127 () (lambda @t116 @t126)) % 0.50/0.76 (define @t128 () (not (_ @t9 @t17))) % 0.50/0.76 (define @t129 () (or @t128 @t114)) % 0.50/0.76 (define @t130 () (lambda @t21 @t129)) % 0.50/0.76 (define @t131 () (lambda @t36 @t92)) % 0.50/0.76 (define @t132 () (_ @t131 @t17)) % 0.50/0.76 (define @t133 () (not @t132)) % 0.50/0.76 (define @t134 () (or @t102 @t133)) % 0.50/0.76 (define @t135 () (not @t134)) % 0.50/0.76 (define @t136 () (lambda @t104 @t135)) % 0.50/0.76 (define @t137 () (not @t114)) % 0.50/0.76 (define @t138 () (_ tptp.q @t38)) % 0.50/0.76 (define @t139 () (_ tptp.p @t38)) % 0.50/0.76 (define @t140 () (not @t139)) % 0.50/0.76 (define @t141 () (or @t91 @t140 @t138)) % 0.50/0.76 (define @t142 () (or @t140 @t138)) % 0.50/0.76 (define @t143 () (not (_ tptp.p @t4))) % 0.50/0.76 (define @t144 () (lambda @t36 (or @t143 (_ tptp.q @t4)))) % 0.50/0.76 (define @t145 () (_ @t144 @t38)) % 0.50/0.76 (define @t146 () (or @t91 @t145)) % 0.50/0.76 (define @t147 () (forall @t41 @t146)) % 0.50/0.76 (define @t148 () (lambda @t36 @t147)) % 0.50/0.76 (define @t149 () (lambda @t12 (forall @t41 (or @t91 @t117)))) % 0.50/0.76 (define @t150 () (@list @t14 @t4)) % 0.50/0.76 (define @t151 () (lambda @t36 @t143)) % 0.50/0.76 (define @t152 () (_ @t151 @t4)) % 0.50/0.76 (define @t153 () (or @t152 @t15)) % 0.50/0.76 (define @t154 () (lambda @t150 @t153)) % 0.50/0.76 (define @t155 () (_ @t13 tptp.p)) % 0.50/0.76 (define @t156 () (lambda @t36 @t93)) % 0.50/0.76 (define @t157 () (_ @t156 @t17)) % 0.50/0.76 (define @t158 () (not @t157)) % 0.50/0.76 (define @t159 () (or @t158 @t137)) % 0.50/0.76 (define @t160 () (not @t159)) % 0.50/0.76 (define @t161 () (lambda @t116 @t160)) % 0.50/0.76 (define @t162 () (not (or @t128 @t137))) % 0.50/0.76 (define @t163 () (lambda @t21 @t162)) % 0.50/0.76 (define @t164 () (_ @t149 tptp.p)) % 0.50/0.76 (define @t165 () (forall @t41 (or @t91 @t118))) % 0.50/0.76 (define @t166 () (lambda @t36 @t165)) % 0.50/0.76 (define @t167 () (_ @t166 @t4)) % 0.50/0.76 (define @t168 () (not @t167)) % 0.50/0.76 (define @t169 () (lambda @t36 @t168)) % 0.50/0.76 (define @t170 () (not @t39)) % 0.50/0.76 (define @t171 () (or @t91 @t170)) % 0.50/0.76 (define @t172 () (lambda @t36 @t11)) % 0.50/0.76 (define @t173 () (_ @t172 @t38)) % 0.50/0.76 (define @t174 () (or @t91 @t173)) % 0.50/0.76 (define @t175 () (forall @t41 @t174)) % 0.50/0.76 (define @t176 () (lambda @t36 @t175)) % 0.50/0.76 (define @t177 () (not @t15)) % 0.50/0.76 (define @t178 () (or @t11 @t177)) % 0.50/0.76 (define @t179 () (lambda @t36 @t178)) % 0.50/0.76 (define @t180 () (_ @t179 @t4)) % 0.50/0.76 (define @t181 () (not @t180)) % 0.50/0.76 (define @t182 () (lambda @t36 @t181)) % 0.50/0.76 (define @t183 () (lambda @t36 @t177)) % 0.50/0.76 (define @t184 () (_ @t183 @t4)) % 0.50/0.76 (define @t185 () (or @t11 @t184)) % 0.50/0.76 (define @t186 () (lambda @t36 @t185)) % 0.50/0.76 (define @t187 () (or @t11 @t15)) % 0.50/0.76 (define @t188 () (lambda @t150 @t187)) % 0.50/0.76 (define @t189 () (_ @t172 @t4)) % 0.50/0.76 (define @t190 () (or @t189 @t15)) % 0.50/0.76 (define @t191 () (lambda @t150 @t190)) % 0.50/0.76 (define @t192 () (lambda @t36 @t187)) % 0.50/0.76 (define @t193 () (not (tptp.rel_m @t96 @t38))) % 0.50/0.76 (define @t194 () (forall @t41 (or @t193 @t89 @t87))) % 0.50/0.76 (define @t195 () (not @t194)) % 0.50/0.76 (define @t196 () (forall @t41 (or @t193 @t88))) % 0.50/0.76 (define @t197 () (not @t196)) % 0.50/0.76 (define @t198 () (forall @t41 (or @t193 @t94))) % 0.50/0.76 (define @t199 () (not @t198)) % 0.50/0.76 (define @t200 () (or @t199 @t197 @t195)) % 0.50/0.76 (define @t201 () (@list true)) % 0.50/0.76 (define @t202 () (@list @t200)) % 0.50/0.76 (define @t203 () (tptp.q @t96)) % 0.50/0.76 (define @t204 () (not @t203)) % 0.50/0.76 (define @t205 () (tptp.rel_m @t96 @t96)) % 0.50/0.76 (define @t206 () (not @t205)) % 0.50/0.76 (define @t207 () (or @t206 @t204)) % 0.50/0.76 (define @t208 () (@list false false)) % 0.50/0.76 (define @t209 () (tptp.p @t96)) % 0.50/0.76 (define @t210 () (or @t206 @t209)) % 0.50/0.76 (define @t211 () (not @t209)) % 0.50/0.76 (define @t212 () (or @t206 @t211 @t203)) % 0.50/0.76 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.50/0.76 (assume @p2 (_ tptp.mreflexive tptp.rel_m)) % 0.50/0.76 (assume @p3 @t1) % 0.50/0.76 (assume @p4 true) % 0.50/0.76 (step @p5 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.50/0.76 (step @p6 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.50/0.76 (step @p7 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.50/0.76 (step @p8 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.50/0.76 (step @p9 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.50/0.76 (step @p10 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.50/0.76 (step @p11 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.50/0.76 (step @p12 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.50/0.76 (step @p13 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.50/0.76 (step @p14 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.50/0.76 (step @p15 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.50/0.76 (step @p16 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.50/0.76 (step @p17 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.50/0.76 (step @p18 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.50/0.76 (step @p19 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.50/0.76 (step @p20 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.50/0.76 (step @p21 (= tptp.mreflexive @t50) :rule refl :args (@t50)) % 0.50/0.76 (step @p22 (= tptp.msymmetric @t54) :rule refl :args (@t54)) % 0.50/0.76 (step @p23 (= tptp.mserial @t56) :rule refl :args (@t56)) % 0.50/0.76 (step @p24 (= tptp.mtransitive @t61) :rule refl :args (@t61)) % 0.50/0.76 (step @p25 (= tptp.meuclidean @t63) :rule refl :args (@t63)) % 0.50/0.76 (step @p26 (= tptp.mpartially_functional @t65) :rule refl :args (@t65)) % 0.50/0.76 (step @p27 (= tptp.mfunctional @t67) :rule refl :args (@t67)) % 0.50/0.76 (step @p28 (= tptp.mweakly_dense @t70) :rule refl :args (@t70)) % 0.50/0.76 (step @p29 (= tptp.mweakly_connected @t71) :rule refl :args (@t71)) % 0.50/0.76 (step @p30 (= tptp.mweakly_directed @t72) :rule refl :args (@t72)) % 0.50/0.76 (step @p31 (= tptp.mvalid @t75) :rule refl :args (@t75)) % 0.50/0.76 (step @p32 (= tptp.minvalid @t76) :rule refl :args (@t76)) % 0.50/0.76 (step @p33 (= tptp.msatisfiable @t77) :rule refl :args (@t77)) % 0.50/0.76 (step @p34 (= tptp.mcountersatisfiable @t78) :rule refl :args (@t78)) % 0.50/0.76 (step @p35 (= tptp.mbox_m @t83) :rule refl :args (@t83)) % 0.50/0.76 (step @p36 (= tptp.mdia_m @t85) :rule refl :args (@t85)) % 0.50/0.76 (step @p37 :rule beta-reduce :args ((= (_ (lambda @t49 (forall @t47 @t86)) tptp.rel_m) (forall @t47 (tptp.rel_m @t44 @t44))))) % 0.50/0.76 (step @p38 :rule refl :args (tptp.rel_m)) % 0.50/0.76 (step @p39 :rule refl :args (@t86)) % 0.50/0.76 (step @p40 :rule refl :args (@t46)) % 0.50/0.76 (step @p41 :rule cong :premises (@p40 @p39) :args ((= @t46 @t86))) % 0.50/0.76 (step @p42 :rule symm :premises (@p41)) % 0.50/0.76 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 0.50/0.76 (step @p44 :rule cong :premises (@p43) :args (@t48)) % 0.50/0.76 (step @p45 :rule cong :premises (@p44) :args (@t50)) % 0.50/0.76 (step @p46 :rule trans :premises (@p21 @p45)) % 0.50/0.76 (step @p47 :rule ho_cong :premises (@p46 @p38)) % 0.50/0.76 (step @p48 :rule trans :premises (@p47 @p37)) % 0.50/0.76 (step @p49 :rule eq_resolve :premises (@p2 @p48)) % 0.50/0.76 (step @p50 :rule instantiate :premises (@p49) :args (@t97)) % 0.50/0.76 (step @p51 :rule beta-reduce :args ((= @t106 @t95))) % 0.50/0.76 (step @p52 :rule cong :premises (@p51) :args (@t107)) % 0.50/0.76 (step @p53 :rule beta-reduce :args ((= (_ @t109 @t105) @t107))) % 0.50/0.76 (step @p54 :rule trans :premises (@p53 @p52)) % 0.50/0.76 (step @p55 :rule refl :args (@t100)) % 0.50/0.76 (step @p56 :rule refl :args (@t102)) % 0.50/0.76 (step @p57 :rule beta-reduce :args ((= @t111 @t103))) % 0.50/0.76 (step @p58 :rule nary_cong :premises (@p57 @p56 @p55) :args (@t112)) % 0.50/0.76 (step @p59 :rule cong :premises (@p58) :args (@t113)) % 0.50/0.76 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t116 @t115) @t110) @t113))) % 0.50/0.76 (step @p61 :rule trans :premises (@p60 @p59)) % 0.50/0.76 (step @p62 :rule beta-reduce :args ((= @t120 @t110))) % 0.50/0.76 (step @p63 :rule aci_norm :args ((= (or @t121 @t114) @t115))) % 0.50/0.76 (step @p64 :rule refl :args (@t114)) % 0.50/0.76 (step @p65 :rule bool-double-not-elim :args (@t121)) % 0.50/0.76 (step @p66 :rule beta-reduce :args ((= @t124 @t122))) % 0.50/0.76 (step @p67 :rule cong :premises (@p66) :args (@t125)) % 0.50/0.76 (step @p68 :rule trans :premises (@p67 @p65)) % 0.50/0.76 (step @p69 :rule nary_cong :premises (@p68 @p64) :args (@t126)) % 0.50/0.76 (step @p70 :rule trans :premises (@p69 @p63)) % 0.50/0.76 (step @p71 :rule cong :premises (@p70) :args (@t127)) % 0.50/0.76 (step @p72 :rule beta-reduce :args ((= (_ @t130 @t123) @t127))) % 0.50/0.76 (step @p73 :rule trans :premises (@p72 @p71)) % 0.50/0.76 (step @p74 :rule beta-reduce :args ((= @t132 @t99))) % 0.50/0.76 (step @p75 :rule cong :premises (@p74) :args (@t133)) % 0.50/0.76 (step @p76 :rule nary_cong :premises (@p56 @p75) :args (@t134)) % 0.50/0.76 (step @p77 :rule cong :premises (@p76) :args (@t135)) % 0.50/0.76 (step @p78 :rule cong :premises (@p77) :args (@t136)) % 0.50/0.76 (step @p79 :rule beta-reduce :args ((= (_ (lambda @t116 (not (or @t102 @t137))) @t131) @t136))) % 0.50/0.76 (step @p80 :rule trans :premises (@p79 @p78)) % 0.50/0.76 (step @p81 :rule refl :args (@t87)) % 0.50/0.76 (step @p82 :rule refl :args (@t138)) % 0.50/0.76 (step @p83 :rule cong :premises (@p82 @p81) :args ((= @t138 @t87))) % 0.50/0.76 (step @p84 :rule symm :premises (@p83)) % 0.50/0.76 (step @p85 :rule eq_resolve :premises (@p82 @p84)) % 0.50/0.76 (step @p86 :rule refl :args (@t88)) % 0.50/0.76 (step @p87 :rule refl :args (@t139)) % 0.50/0.76 (step @p88 :rule cong :premises (@p87 @p86) :args ((= @t139 @t88))) % 0.50/0.76 (step @p89 :rule symm :premises (@p88)) % 0.50/0.76 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 0.50/0.76 (step @p91 :rule cong :premises (@p90) :args (@t140)) % 0.50/0.76 (step @p92 :rule refl :args (@t91)) % 0.50/0.76 (step @p93 :rule nary_cong :premises (@p92 @p91 @p85) :args (@t141)) % 0.50/0.76 (step @p94 :rule cong :premises (@p93) :args ((forall @t41 @t141))) % 0.50/0.76 (step @p95 :rule aci_norm :args ((= (or @t91 @t142) @t141))) % 0.50/0.76 (step @p96 :rule beta-reduce :args ((= @t145 @t142))) % 0.50/0.76 (step @p97 :rule refl :args (@t91)) % 0.50/0.76 (step @p98 :rule nary_cong :premises (@p97 @p96) :args (@t146)) % 0.50/0.76 (step @p99 :rule trans :premises (@p98 @p95)) % 0.50/0.76 (step @p100 :rule cong :premises (@p99) :args (@t147)) % 0.50/0.76 (step @p101 :rule trans :premises (@p100 @p94)) % 0.50/0.76 (step @p102 :rule cong :premises (@p101) :args (@t148)) % 0.50/0.76 (step @p103 :rule beta-reduce :args ((= (_ @t149 @t144) @t148))) % 0.50/0.76 (step @p104 :rule trans :premises (@p103 @p102)) % 0.50/0.76 (step @p105 :rule beta-reduce :args ((= (_ (lambda @t150 (or @t143 @t15)) tptp.q) @t144))) % 0.50/0.76 (step @p106 :rule refl :args (tptp.q)) % 0.50/0.76 (step @p107 :rule refl :args (@t15)) % 0.50/0.76 (step @p108 :rule beta-reduce :args ((= @t152 @t143))) % 0.50/0.76 (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t153)) % 0.50/0.76 (step @p110 :rule cong :premises (@p109) :args (@t154)) % 0.50/0.76 (step @p111 :rule beta-reduce :args ((= (_ @t16 @t151) @t154))) % 0.50/0.76 (step @p112 :rule trans :premises (@p111 @p110)) % 0.50/0.76 (step @p113 :rule beta-reduce :args ((= @t155 @t151))) % 0.50/0.76 (step @p114 :rule refl :args (@t16)) % 0.50/0.76 (step @p115 :rule ho_cong :premises (@p114 @p113)) % 0.50/0.76 (step @p116 :rule trans :premises (@p115 @p112)) % 0.50/0.76 (step @p117 :rule ho_cong :premises (@p116 @p106)) % 0.50/0.76 (step @p118 :rule trans :premises (@p117 @p105)) % 0.50/0.76 (step @p119 :rule refl :args (@t149)) % 0.50/0.76 (step @p120 :rule ho_cong :premises (@p119 @p118)) % 0.50/0.76 (step @p121 :rule trans :premises (@p120 @p104)) % 0.50/0.76 (step @p122 :rule refl :args (@t137)) % 0.50/0.76 (step @p123 :rule beta-reduce :args ((= @t157 @t101))) % 0.50/0.76 (step @p124 :rule cong :premises (@p123) :args (@t158)) % 0.50/0.76 (step @p125 :rule nary_cong :premises (@p124 @p122) :args (@t159)) % 0.50/0.76 (step @p126 :rule cong :premises (@p125) :args (@t160)) % 0.50/0.76 (step @p127 :rule cong :premises (@p126) :args (@t161)) % 0.50/0.76 (step @p128 :rule beta-reduce :args ((= (_ @t163 @t156) @t161))) % 0.50/0.76 (step @p129 :rule trans :premises (@p128 @p127)) % 0.50/0.76 (step @p130 :rule beta-reduce :args ((= @t164 @t156))) % 0.50/0.76 (step @p131 :rule refl :args (@t163)) % 0.50/0.76 (step @p132 :rule ho_cong :premises (@p131 @p130)) % 0.50/0.76 (step @p133 :rule trans :premises (@p132 @p129)) % 0.50/0.76 (step @p134 :rule ho_cong :premises (@p133 @p121)) % 0.50/0.76 (step @p135 :rule trans :premises (@p134 @p80)) % 0.50/0.76 (step @p136 :rule refl :args (@t130)) % 0.50/0.76 (step @p137 :rule ho_cong :premises (@p136 @p135)) % 0.50/0.76 (step @p138 :rule trans :premises (@p137 @p73)) % 0.50/0.76 (step @p139 :rule ho_cong :premises (@p138 @p62)) % 0.50/0.76 (step @p140 :rule trans :premises (@p139 @p61)) % 0.50/0.76 (step @p141 :rule refl :args (@t109)) % 0.50/0.76 (step @p142 :rule ho_cong :premises (@p141 @p140)) % 0.50/0.76 (step @p143 :rule trans :premises (@p142 @p54)) % 0.50/0.76 (step @p144 :rule cong :premises (@p143) :args ((not (_ @t109 (_ (_ @t130 (_ (_ @t163 @t164) (_ @t149 (_ (_ @t16 @t155) tptp.q)))) @t120))))) % 0.50/0.76 (step @p145 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t165)) @t17) @t119))) % 0.50/0.76 (step @p146 :rule refl :args (@t17)) % 0.50/0.76 (step @p147 :rule beta-reduce :args ((= @t167 @t165))) % 0.50/0.76 (step @p148 :rule cong :premises (@p147) :args (@t168)) % 0.50/0.76 (step @p149 :rule cong :premises (@p148) :args (@t169)) % 0.50/0.76 (step @p150 :rule beta-reduce :args ((= (_ @t13 @t166) @t169))) % 0.50/0.76 (step @p151 :rule trans :premises (@p150 @p149)) % 0.50/0.76 (step @p152 :rule refl :args (@t117)) % 0.50/0.76 (step @p153 :rule refl :args (@t39)) % 0.50/0.76 (step @p154 :rule cong :premises (@p153 @p152) :args ((= @t39 @t117))) % 0.50/0.76 (step @p155 :rule symm :premises (@p154)) % 0.50/0.76 (step @p156 :rule eq_resolve :premises (@p153 @p155)) % 0.50/0.76 (step @p157 :rule cong :premises (@p156) :args (@t170)) % 0.50/0.76 (step @p158 :rule nary_cong :premises (@p92 @p157) :args (@t171)) % 0.50/0.76 (step @p159 :rule cong :premises (@p158) :args ((forall @t41 @t171))) % 0.50/0.76 (step @p160 :rule beta-reduce :args ((= @t173 @t170))) % 0.50/0.76 (step @p161 :rule nary_cong :premises (@p97 @p160) :args (@t174)) % 0.50/0.76 (step @p162 :rule cong :premises (@p161) :args (@t175)) % 0.50/0.76 (step @p163 :rule trans :premises (@p162 @p159)) % 0.50/0.76 (step @p164 :rule cong :premises (@p163) :args (@t176)) % 0.50/0.76 (step @p165 :rule beta-reduce :args ((= (_ @t149 @t172) @t176))) % 0.50/0.76 (step @p166 :rule trans :premises (@p165 @p164)) % 0.50/0.76 (step @p167 :rule beta-reduce :args ((= (_ @t13 @t9) @t172))) % 0.50/0.76 (step @p168 :rule ho_cong :premises (@p119 @p167)) % 0.50/0.76 (step @p169 :rule trans :premises (@p168 @p166)) % 0.50/0.76 (step @p170 :rule refl :args (@t13)) % 0.50/0.76 (step @p171 :rule ho_cong :premises (@p170 @p169)) % 0.50/0.76 (step @p172 :rule trans :premises (@p171 @p151)) % 0.50/0.76 (step @p173 :rule ho_cong :premises (@p172 @p146)) % 0.50/0.76 (step @p174 :rule trans :premises (@p173 @p145)) % 0.50/0.76 (step @p175 :rule refl :args (@t9)) % 0.50/0.76 (step @p176 :rule ho_cong :premises (@p7 @p175)) % 0.50/0.76 (step @p177 :rule refl :args (@t90)) % 0.50/0.76 (step @p178 :rule refl :args (@t79)) % 0.50/0.76 (step @p179 :rule cong :premises (@p178 @p177) :args ((= @t79 @t90))) % 0.50/0.76 (step @p180 :rule symm :premises (@p179)) % 0.50/0.76 (step @p181 :rule eq_resolve :premises (@p178 @p180)) % 0.50/0.76 (step @p182 :rule cong :premises (@p181) :args (@t80)) % 0.50/0.76 (step @p183 :rule nary_cong :premises (@p182 @p156) :args (@t81)) % 0.50/0.76 (step @p184 :rule cong :premises (@p183) :args (@t82)) % 0.50/0.76 (step @p185 :rule cong :premises (@p184) :args (@t83)) % 0.50/0.76 (step @p186 :rule trans :premises (@p35 @p185)) % 0.50/0.76 (step @p187 :rule ho_cong :premises (@p186 @p176)) % 0.50/0.76 (step @p188 :rule ho_cong :premises (@p7 @p187)) % 0.50/0.76 (step @p189 :rule ho_cong :premises (@p188 @p146)) % 0.50/0.76 (step @p190 :rule trans :premises (@p189 @p174)) % 0.50/0.76 (step @p191 :rule cong :premises (@p190) :args (@t85)) % 0.50/0.76 (step @p192 :rule trans :premises (@p36 @p191)) % 0.50/0.76 (step @p193 :rule ho_cong :premises (@p192 @p106)) % 0.50/0.76 (step @p194 :rule refl :args (tptp.p)) % 0.50/0.76 (step @p195 :rule ho_cong :premises (@p7 @p194)) % 0.50/0.76 (step @p196 :rule ho_cong :premises (@p8 @p195)) % 0.50/0.76 (step @p197 :rule ho_cong :premises (@p196 @p106)) % 0.50/0.76 (step @p198 :rule ho_cong :premises (@p186 @p197)) % 0.50/0.76 (step @p199 :rule ho_cong :premises (@p186 @p194)) % 0.50/0.76 (step @p200 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t178)) @t17) @t162))) % 0.50/0.76 (step @p201 :rule beta-reduce :args ((= @t180 @t178))) % 0.50/0.76 (step @p202 :rule cong :premises (@p201) :args (@t181)) % 0.50/0.76 (step @p203 :rule cong :premises (@p202) :args (@t182)) % 0.50/0.76 (step @p204 :rule beta-reduce :args ((= (_ @t13 @t179) @t182))) % 0.50/0.76 (step @p205 :rule trans :premises (@p204 @p203)) % 0.50/0.76 (step @p206 :rule beta-reduce :args ((= @t184 @t177))) % 0.50/0.76 (step @p207 :rule refl :args (@t11)) % 0.50/0.76 (step @p208 :rule nary_cong :premises (@p207 @p206) :args (@t185)) % 0.50/0.76 (step @p209 :rule cong :premises (@p208) :args (@t186)) % 0.50/0.76 (step @p210 :rule beta-reduce :args ((= (_ @t188 @t183) @t186))) % 0.50/0.76 (step @p211 :rule trans :premises (@p210 @p209)) % 0.50/0.76 (step @p212 :rule beta-reduce :args ((= (_ @t13 @t14) @t183))) % 0.50/0.76 (step @p213 :rule beta-reduce :args ((= @t189 @t11))) % 0.50/0.76 (step @p214 :rule nary_cong :premises (@p213 @p107) :args (@t190)) % 0.50/0.76 (step @p215 :rule cong :premises (@p214) :args (@t191)) % 0.50/0.76 (step @p216 :rule beta-reduce :args ((= (_ @t16 @t172) @t191))) % 0.50/0.76 (step @p217 :rule trans :premises (@p216 @p215)) % 0.50/0.76 (step @p218 :rule ho_cong :premises (@p114 @p167)) % 0.50/0.76 (step @p219 :rule trans :premises (@p218 @p217)) % 0.50/0.76 (step @p220 :rule ho_cong :premises (@p219 @p212)) % 0.50/0.76 (step @p221 :rule trans :premises (@p220 @p211)) % 0.50/0.76 (step @p222 :rule ho_cong :premises (@p170 @p221)) % 0.50/0.76 (step @p223 :rule trans :premises (@p222 @p205)) % 0.50/0.76 (step @p224 :rule ho_cong :premises (@p223 @p146)) % 0.50/0.76 (step @p225 :rule trans :premises (@p224 @p200)) % 0.50/0.76 (step @p226 :rule refl :args (@t14)) % 0.50/0.76 (step @p227 :rule ho_cong :premises (@p7 @p226)) % 0.50/0.76 (step @p228 :rule ho_cong :premises (@p8 @p176)) % 0.50/0.76 (step @p229 :rule ho_cong :premises (@p228 @p227)) % 0.50/0.76 (step @p230 :rule ho_cong :premises (@p7 @p229)) % 0.50/0.76 (step @p231 :rule ho_cong :premises (@p230 @p146)) % 0.50/0.76 (step @p232 :rule trans :premises (@p231 @p225)) % 0.50/0.76 (step @p233 :rule cong :premises (@p232) :args (@t22)) % 0.50/0.76 (step @p234 :rule trans :premises (@p9 @p233)) % 0.50/0.76 (step @p235 :rule ho_cong :premises (@p234 @p199)) % 0.50/0.76 (step @p236 :rule ho_cong :premises (@p235 @p198)) % 0.50/0.76 (step @p237 :rule beta-reduce :args ((= (_ @t192 @t17) @t129))) % 0.50/0.76 (step @p238 :rule beta-reduce :args ((= (_ @t188 @t14) @t192))) % 0.50/0.76 (step @p239 :rule ho_cong :premises (@p219 @p226)) % 0.50/0.76 (step @p240 :rule trans :premises (@p239 @p238)) % 0.50/0.76 (step @p241 :rule ho_cong :premises (@p240 @p146)) % 0.50/0.76 (step @p242 :rule trans :premises (@p241 @p237)) % 0.50/0.76 (step @p243 :rule ho_cong :premises (@p228 @p226)) % 0.50/0.76 (step @p244 :rule ho_cong :premises (@p243 @p146)) % 0.50/0.76 (step @p245 :rule trans :premises (@p244 @p242)) % 0.50/0.76 (step @p246 :rule cong :premises (@p245) :args (@t23)) % 0.50/0.76 (step @p247 :rule trans :premises (@p10 @p246)) % 0.50/0.76 (step @p248 :rule ho_cong :premises (@p247 @p236)) % 0.50/0.76 (step @p249 :rule ho_cong :premises (@p248 @p193)) % 0.50/0.76 (step @p250 :rule refl :args (@t108)) % 0.50/0.76 (step @p251 :rule refl :args (@t10)) % 0.50/0.76 (step @p252 :rule cong :premises (@p251 @p250) :args ((= @t10 @t108))) % 0.50/0.76 (step @p253 :rule symm :premises (@p252)) % 0.50/0.76 (step @p254 :rule eq_resolve :premises (@p251 @p253)) % 0.50/0.76 (step @p255 :rule cong :premises (@p254) :args (@t73)) % 0.50/0.76 (step @p256 :rule cong :premises (@p255) :args (@t75)) % 0.50/0.76 (step @p257 :rule trans :premises (@p31 @p256)) % 0.50/0.76 (step @p258 :rule ho_cong :premises (@p257 @p249)) % 0.50/0.76 (step @p259 :rule cong :premises (@p258) :args (@t1)) % 0.50/0.76 (step @p260 :rule trans :premises (@p259 @p144)) % 0.50/0.76 (step @p261 :rule eq_resolve :premises (@p3 @p260)) % 0.50/0.76 (step @p262 :rule skolemize :premises (@p261)) % 0.50/0.76 (step @p263 :rule bool-double-not-elim :args (@t194)) % 0.50/0.76 (step @p264 :rule refl :args (@t200)) % 0.50/0.76 (step @p265 :rule nary_cong :premises (@p264 @p263) :args ((or @t200 (not @t195)))) % 0.50/0.77 (step @p266 :rule cnf_or_neg :args (@t200 2)) % 0.50/0.77 (step @p267 :rule eq_resolve :premises (@p266 @p265)) % 0.50/0.77 (step @p268 :rule reordering :premises (@p267) :args ((or @t194 @t200))) % 0.50/0.77 (step @p269 :rule chain_m_resolution :premises (@p268 @p262) :args (@t194 @t201 @t202)) % 0.50/0.77 (step @p270 :rule instantiate :premises (@p269) :args (@t97)) % 0.50/0.77 (step @p271 :rule bool-double-not-elim :args (@t198)) % 0.50/0.77 (step @p272 :rule nary_cong :premises (@p264 @p271) :args ((or @t200 (not @t199)))) % 0.50/0.77 (step @p273 :rule cnf_or_neg :args (@t200 0)) % 0.50/0.77 (step @p274 :rule eq_resolve :premises (@p273 @p272)) % 0.50/0.77 (step @p275 :rule reordering :premises (@p274) :args ((or @t198 @t200))) % 0.50/0.77 (step @p276 :rule chain_m_resolution :premises (@p275 @p262) :args (@t198 @t201 @t202)) % 0.50/0.77 (step @p277 :rule instantiate :premises (@p276) :args (@t97)) % 0.50/0.77 (step @p278 :rule cnf_or_pos :args (@t207)) % 0.50/0.77 (step @p279 :rule reordering :premises (@p278) :args ((or @t206 @t204 (not @t207)))) % 0.50/0.77 (step @p280 :rule chain_m_resolution :premises (@p279 @p50 @p277) :args (@t204 @t208 (@list @t205 @t207))) % 0.50/0.77 (step @p281 :rule bool-double-not-elim :args (@t196)) % 0.50/0.77 (step @p282 :rule nary_cong :premises (@p264 @p281) :args ((or @t200 (not @t197)))) % 0.50/0.77 (step @p283 :rule cnf_or_neg :args (@t200 1)) % 0.50/0.77 (step @p284 :rule eq_resolve :premises (@p283 @p282)) % 0.50/0.77 (step @p285 :rule reordering :premises (@p284) :args ((or @t196 @t200))) % 0.50/0.77 (step @p286 :rule chain_m_resolution :premises (@p285 @p262) :args (@t196 @t201 @t202)) % 0.50/0.77 (step @p287 :rule instantiate :premises (@p286) :args (@t97)) % 0.50/0.77 (step @p288 :rule cnf_or_pos :args (@t210)) % 0.50/0.77 (step @p289 :rule reordering :premises (@p288) :args ((or @t206 @t209 (not @t210)))) % 0.50/0.77 (step @p290 :rule chain_m_resolution :premises (@p289 @p50 @p287) :args (@t209 @t208 (@list @t205 @t210))) % 0.50/0.77 (step @p291 :rule cnf_or_pos :args (@t212)) % 0.50/0.77 (step @p292 :rule reordering :premises (@p291) :args ((or @t206 @t203 @t211 (not @t212)))) % 0.50/0.77 (step @p293 false :rule chain_m_resolution :premises (@p292 @p290 @p280 @p270 @p50) :args (false (@list false true false false) (@list @t209 @t203 @t212 @t205))) % 0.50/0.77 ) % 0.50/0.77 % SZS output end Proof % 0.50/0.77 % cvc5 exiting %------------------------------------------------------------------------------