%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO422^1 : 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 : n015.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 09:12:37 AM UTC 2026 % Result : Theorem 0.52s 0.77s % Output : Proof 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO422^1 : 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 % 0.18/0.35 % Computer : n015.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Wed Jun 3 00:07:34 EDT 2026 % 0.18/0.35 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.52/0.77 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.52/0.77 % SZS status Theorem % 0.52/0.77 % SZS output start Proof % 0.52/0.77 ( % 0.52/0.77 (declare-sort $$unsorted 0) % 0.52/0.77 (declare-sort tptp.mu 0) % 0.52/0.77 (declare-const tptp.rel_d (-> $$unsorted $$unsorted Bool)) % 0.52/0.77 (declare-const tptp.p (-> $$unsorted Bool)) % 0.52/0.77 (declare-const tptp.q (-> $$unsorted Bool)) % 0.52/0.77 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.52/0.77 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.52/0.77 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.52/0.77 (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)))))) % 0.52/0.77 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.52/0.77 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.52/0.77 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.52/0.77 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.52/0.77 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.52/0.77 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.52/0.77 (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))))))) % 0.52/0.77 (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))))))) % 0.52/0.77 (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)))))) % 0.52/0.77 (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)))))) % 0.52/0.77 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.52/0.77 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.52/0.77 (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)))))) % 0.52/0.77 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.52/0.77 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.52/0.77 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.52/0.77 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.52/0.77 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.52/0.77 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.52/0.77 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.52/0.77 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.52/0.77 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.52/0.77 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.52/0.77 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.52/0.77 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.52/0.77 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.52/0.77 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.52/0.77 (define tptp.mbox_d () (let ((_let_1 (@var "V" $$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_d _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.52/0.77 (define tptp.mdia_d () (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_d (_ tptp.mnot _let_2))) _let_1))))) % 0.52/0.77 (define @t1 () (not (_ tptp.mvalid (_ tptp.mdia_d (_ (_ tptp.mimplies (_ (_ tptp.mimplies (_ (_ tptp.mimplies tptp.p) tptp.q)) tptp.p)) tptp.p))))) % 0.52/0.77 (define @t2 () (@var "Y" tptp.mu)) % 0.52/0.77 (define @t3 () (@var "X" tptp.mu)) % 0.52/0.77 (define @t4 () (@var "W" $$unsorted)) % 0.52/0.77 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.52/0.77 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.52/0.77 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.52/0.77 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.52/0.77 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.52/0.77 (define @t10 () (_ @t9 @t4)) % 0.52/0.77 (define @t11 () (not @t10)) % 0.52/0.77 (define @t12 () (@list @t9 @t4)) % 0.52/0.77 (define @t13 () (lambda @t12 @t11)) % 0.52/0.77 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.52/0.77 (define @t15 () (_ @t14 @t4)) % 0.52/0.77 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.52/0.77 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.52/0.77 (define @t18 () (_ tptp.mnot @t14)) % 0.52/0.77 (define @t19 () (_ tptp.mnot @t9)) % 0.52/0.77 (define @t20 () (_ tptp.mor @t19)) % 0.52/0.77 (define @t21 () (@list @t9 @t14 @t17)) % 0.52/0.77 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.52/0.77 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.52/0.77 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.52/0.77 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.52/0.77 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.52/0.77 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.52/0.77 (define @t28 () (_ @t27 @t3)) % 0.52/0.77 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.52/0.77 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.52/0.77 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.52/0.77 (define @t32 () (_ @t31 @t30)) % 0.52/0.77 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.52/0.77 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.52/0.77 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.52/0.77 (define @t36 () (@list @t4)) % 0.52/0.77 (define @t37 () (lambda @t36 true)) % 0.52/0.77 (define @t38 () (@var "V" $$unsorted)) % 0.52/0.77 (define @t39 () (_ @t9 @t38)) % 0.52/0.77 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.52/0.77 (define @t41 () (@list @t38)) % 0.52/0.77 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.52/0.77 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.52/0.77 (define @t44 () (@var "S" $$unsorted)) % 0.52/0.77 (define @t45 () (_ @t40 @t44)) % 0.52/0.77 (define @t46 () (@list @t44)) % 0.52/0.77 (define @t47 () (@list @t40)) % 0.52/0.77 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.52/0.77 (define @t49 () (@var "T" $$unsorted)) % 0.52/0.77 (define @t50 () (_ @t40 @t49)) % 0.52/0.77 (define @t51 () (_ @t45 @t49)) % 0.52/0.77 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.52/0.77 (define @t53 () (@list @t49)) % 0.52/0.77 (define @t54 () (exists @t53 @t51)) % 0.52/0.77 (define @t55 () (forall @t46 @t54)) % 0.52/0.77 (define @t56 () (lambda @t47 @t55)) % 0.52/0.77 (define @t57 () (@var "U" $$unsorted)) % 0.52/0.77 (define @t58 () (_ @t45 @t57)) % 0.52/0.77 (define @t59 () (_ @t50 @t57)) % 0.52/0.77 (define @t60 () (@list @t44 @t49 @t57)) % 0.52/0.77 (define @t61 () (lambda @t47 (forall @t60 (=> (and @t51 @t59) @t58)))) % 0.52/0.77 (define @t62 () (and @t51 @t58)) % 0.52/0.77 (define @t63 () (lambda @t47 (forall @t60 (=> @t62 @t59)))) % 0.52/0.77 (define @t64 () (= @t49 @t57)) % 0.52/0.77 (define @t65 () (lambda @t47 (forall @t60 (=> @t62 @t64)))) % 0.52/0.77 (define @t66 () (@list @t57)) % 0.52/0.77 (define @t67 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t66 (=> @t58 @t64))))))) % 0.52/0.77 (define @t68 () (_ @t40 @t57)) % 0.52/0.77 (define @t69 () (_ @t68 @t49)) % 0.52/0.77 (define @t70 () (lambda @t47 (forall @t60 (=> @t51 (exists @t66 (and @t58 @t69)))))) % 0.52/0.77 (define @t71 () (lambda @t47 (forall @t60 (=> @t62 (or @t59 @t64 @t69))))) % 0.52/0.77 (define @t72 () (lambda @t47 (forall @t60 (=> @t62 (exists @t41 (and (_ @t50 @t38) (_ @t68 @t38))))))) % 0.52/0.77 (define @t73 () (forall @t36 @t10)) % 0.52/0.77 (define @t74 () (@list @t9)) % 0.52/0.77 (define @t75 () (lambda @t74 @t73)) % 0.52/0.77 (define @t76 () (lambda @t74 (forall @t36 @t11))) % 0.52/0.77 (define @t77 () (lambda @t74 (exists @t36 @t10))) % 0.52/0.77 (define @t78 () (lambda @t74 (exists @t36 @t11))) % 0.52/0.77 (define @t79 () (_ (_ tptp.rel_d @t4) @t38)) % 0.52/0.77 (define @t80 () (not @t79)) % 0.52/0.77 (define @t81 () (or @t80 @t39)) % 0.52/0.77 (define @t82 () (forall @t41 @t81)) % 0.52/0.77 (define @t83 () (lambda @t12 @t82)) % 0.52/0.77 (define @t84 () (@list @t9 @t17)) % 0.52/0.77 (define @t85 () (lambda @t84 (_ (_ tptp.mnot (_ tptp.mbox_d @t19)) @t17))) % 0.52/0.77 (define @t86 () (tptp.p @t38)) % 0.52/0.77 (define @t87 () (tptp.q @t38)) % 0.52/0.77 (define @t88 () (and (or (and @t86 (not @t87)) @t86) (not @t86))) % 0.52/0.77 (define @t89 () (tptp.rel_d @t4 @t38)) % 0.52/0.77 (define @t90 () (not @t89)) % 0.52/0.77 (define @t91 () (not (forall @t41 (or @t90 @t88)))) % 0.52/0.77 (define @t92 () (not (tptp.rel_d @t17 @t38))) % 0.52/0.77 (define @t93 () (@list @t17)) % 0.52/0.77 (define @t94 () (lambda @t93 (not (forall @t41 (or @t92 @t88))))) % 0.52/0.77 (define @t95 () (_ @t94 @t4)) % 0.52/0.77 (define @t96 () (forall @t36 @t95)) % 0.52/0.77 (define @t97 () (_ @t9 @t4)) % 0.52/0.77 (define @t98 () (lambda @t74 (forall @t36 @t97))) % 0.52/0.77 (define @t99 () (_ tptp.p @t38)) % 0.52/0.77 (define @t100 () (not @t99)) % 0.52/0.77 (define @t101 () (_ tptp.q @t38)) % 0.52/0.77 (define @t102 () (not @t101)) % 0.52/0.77 (define @t103 () (and @t99 @t102)) % 0.52/0.77 (define @t104 () (or @t103 @t99)) % 0.52/0.77 (define @t105 () (and @t104 @t100)) % 0.52/0.77 (define @t106 () (or @t92 @t105)) % 0.52/0.77 (define @t107 () (or (not (or @t100 @t101)) @t99)) % 0.52/0.77 (define @t108 () (not @t107)) % 0.52/0.77 (define @t109 () (or @t108 @t99)) % 0.52/0.77 (define @t110 () (or @t92 (not @t109))) % 0.52/0.77 (define @t111 () (_ tptp.p @t17)) % 0.52/0.77 (define @t112 () (not @t111)) % 0.52/0.77 (define @t113 () (or @t112 (_ tptp.q @t17))) % 0.52/0.77 (define @t114 () (not @t113)) % 0.52/0.77 (define @t115 () (or @t114 @t111)) % 0.52/0.77 (define @t116 () (not @t115)) % 0.52/0.77 (define @t117 () (lambda @t93 (or @t116 @t111))) % 0.52/0.77 (define @t118 () (_ @t117 @t38)) % 0.52/0.77 (define @t119 () (not @t118)) % 0.52/0.77 (define @t120 () (or @t92 @t119)) % 0.52/0.77 (define @t121 () (forall @t41 @t120)) % 0.52/0.77 (define @t122 () (not @t121)) % 0.52/0.77 (define @t123 () (lambda @t93 @t122)) % 0.52/0.77 (define @t124 () (_ @t9 @t38)) % 0.52/0.77 (define @t125 () (not @t124)) % 0.52/0.77 (define @t126 () (not (forall @t41 (or @t92 @t125)))) % 0.52/0.77 (define @t127 () (lambda @t84 @t126)) % 0.52/0.77 (define @t128 () (_ @t14 @t17)) % 0.52/0.77 (define @t129 () (@list @t14 @t17)) % 0.52/0.77 (define @t130 () (lambda @t93 @t115)) % 0.52/0.77 (define @t131 () (_ @t130 @t17)) % 0.52/0.77 (define @t132 () (not @t131)) % 0.52/0.77 (define @t133 () (or @t132 @t128)) % 0.52/0.77 (define @t134 () (lambda @t129 @t133)) % 0.52/0.77 (define @t135 () (or (not (_ @t9 @t17)) @t128)) % 0.52/0.77 (define @t136 () (lambda @t21 @t135)) % 0.52/0.77 (define @t137 () (lambda @t93 @t113)) % 0.52/0.77 (define @t138 () (_ @t137 @t17)) % 0.52/0.77 (define @t139 () (not @t138)) % 0.52/0.77 (define @t140 () (or @t139 @t128)) % 0.52/0.77 (define @t141 () (lambda @t129 @t140)) % 0.52/0.77 (define @t142 () (lambda @t129 (or @t112 @t128))) % 0.52/0.77 (define @t143 () (_ @t136 tptp.p)) % 0.52/0.77 (define @t144 () (or @t11 @t15)) % 0.52/0.77 (define @t145 () (lambda @t36 @t144)) % 0.52/0.77 (define @t146 () (@list @t14 @t4)) % 0.52/0.77 (define @t147 () (lambda @t36 @t11)) % 0.52/0.77 (define @t148 () (_ @t147 @t4)) % 0.52/0.77 (define @t149 () (or @t148 @t15)) % 0.52/0.77 (define @t150 () (lambda @t146 @t149)) % 0.52/0.77 (define @t151 () (forall @t41 (or @t90 @t125))) % 0.52/0.77 (define @t152 () (lambda @t36 @t151)) % 0.52/0.77 (define @t153 () (_ @t152 @t4)) % 0.52/0.77 (define @t154 () (not @t153)) % 0.52/0.77 (define @t155 () (lambda @t36 @t154)) % 0.52/0.77 (define @t156 () (not @t39)) % 0.52/0.77 (define @t157 () (or @t90 @t156)) % 0.52/0.77 (define @t158 () (_ @t147 @t38)) % 0.52/0.77 (define @t159 () (or @t90 @t158)) % 0.52/0.77 (define @t160 () (forall @t41 @t159)) % 0.52/0.77 (define @t161 () (lambda @t36 @t160)) % 0.52/0.77 (define @t162 () (lambda @t12 (forall @t41 (or @t90 @t124)))) % 0.52/0.77 (define @t163 () (forall @t36 @t91)) % 0.52/0.77 (define @t164 () (@quantifiers_skolemize @t163 0)) % 0.52/0.77 (define @t165 () (forall @t41 (or (not (tptp.rel_d @t164 @t38)) @t88))) % 0.52/0.77 (define @t166 () (not @t163)) % 0.52/0.77 (define @t167 () (not (not @t165))) % 0.52/0.77 (define @t168 () (@list true)) % 0.52/0.77 (define @t169 () (forall @t53 (not (tptp.rel_d @t164 @t49)))) % 0.52/0.77 (define @t170 () (@quantifiers_skolemize @t169 0)) % 0.52/0.77 (define @t171 () (_ @t40 @t44 @t49)) % 0.52/0.77 (define @t172 () (not @t51)) % 0.52/0.77 (define @t173 () (forall @t53 @t172)) % 0.52/0.77 (define @t174 () (not @t173)) % 0.52/0.77 (define @t175 () (tptp.rel_d @t164 @t170)) % 0.52/0.77 (define @t176 () (not @t169)) % 0.52/0.77 (define @t177 () (not @t175)) % 0.52/0.77 (define @t178 () (not @t177)) % 0.52/0.77 (define @t179 () (tptp.p @t170)) % 0.52/0.77 (define @t180 () (not @t179)) % 0.52/0.77 (define @t181 () (and @t179 (not (tptp.q @t170)))) % 0.52/0.77 (define @t182 () (or @t181 @t179)) % 0.52/0.77 (define @t183 () (and @t182 @t180)) % 0.52/0.77 (define @t184 () (or @t177 @t183)) % 0.52/0.77 (define @t185 () (not @t183)) % 0.52/0.77 (define @t186 () (@list false)) % 0.52/0.77 (define @t187 () (@list @t183)) % 0.52/0.77 (define @t188 () (not @t181)) % 0.52/0.77 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.52/0.77 (assume @p2 (_ tptp.mserial tptp.rel_d)) % 0.52/0.77 (assume @p3 @t1) % 0.52/0.77 (assume @p4 true) % 0.52/0.77 (step @p5 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.52/0.77 (step @p6 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.52/0.77 (step @p7 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.52/0.77 (step @p8 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.52/0.77 (step @p9 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.52/0.77 (step @p10 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.52/0.77 (step @p11 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.52/0.77 (step @p12 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.52/0.77 (step @p13 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.52/0.77 (step @p14 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.52/0.77 (step @p15 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.52/0.77 (step @p16 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.52/0.77 (step @p17 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.52/0.77 (step @p18 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.52/0.77 (step @p19 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.52/0.77 (step @p20 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.52/0.77 (step @p21 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.52/0.77 (step @p22 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.52/0.77 (step @p23 (= tptp.mserial @t56) :rule refl :args (@t56)) % 0.52/0.77 (step @p24 (= tptp.mtransitive @t61) :rule refl :args (@t61)) % 0.52/0.77 (step @p25 (= tptp.meuclidean @t63) :rule refl :args (@t63)) % 0.52/0.77 (step @p26 (= tptp.mpartially_functional @t65) :rule refl :args (@t65)) % 0.52/0.77 (step @p27 (= tptp.mfunctional @t67) :rule refl :args (@t67)) % 0.52/0.77 (step @p28 (= tptp.mweakly_dense @t70) :rule refl :args (@t70)) % 0.52/0.77 (step @p29 (= tptp.mweakly_connected @t71) :rule refl :args (@t71)) % 0.52/0.77 (step @p30 (= tptp.mweakly_directed @t72) :rule refl :args (@t72)) % 0.52/0.77 (step @p31 (= tptp.mvalid @t75) :rule refl :args (@t75)) % 0.52/0.77 (step @p32 (= tptp.minvalid @t76) :rule refl :args (@t76)) % 0.52/0.77 (step @p33 (= tptp.msatisfiable @t77) :rule refl :args (@t77)) % 0.52/0.77 (step @p34 (= tptp.mcountersatisfiable @t78) :rule refl :args (@t78)) % 0.52/0.77 (step @p35 (= tptp.mbox_d @t83) :rule refl :args (@t83)) % 0.52/0.77 (step @p36 (= tptp.mdia_d @t85) :rule refl :args (@t85)) % 0.52/0.77 (step @p37 :rule beta-reduce :args ((= @t95 @t91))) % 0.52/0.77 (step @p38 :rule cong :premises (@p37) :args (@t96)) % 0.52/0.77 (step @p39 :rule beta-reduce :args ((= (_ @t98 @t94) @t96))) % 0.52/0.77 (step @p40 :rule trans :premises (@p39 @p38)) % 0.52/0.77 (step @p41 :rule refl :args (@t86)) % 0.52/0.77 (step @p42 :rule refl :args (@t99)) % 0.52/0.77 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t99 @t86))) % 0.52/0.77 (step @p44 :rule symm :premises (@p43)) % 0.52/0.77 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.52/0.77 (step @p46 :rule cong :premises (@p45) :args (@t100)) % 0.52/0.77 (step @p47 :rule refl :args (@t87)) % 0.52/0.77 (step @p48 :rule refl :args (@t101)) % 0.52/0.77 (step @p49 :rule cong :premises (@p48 @p47) :args ((= @t101 @t87))) % 0.52/0.77 (step @p50 :rule symm :premises (@p49)) % 0.52/0.77 (step @p51 :rule eq_resolve :premises (@p48 @p50)) % 0.52/0.77 (step @p52 :rule cong :premises (@p51) :args (@t102)) % 0.52/0.77 (step @p53 :rule nary_cong :premises (@p45 @p52) :args (@t103)) % 0.52/0.77 (step @p54 :rule nary_cong :premises (@p53 @p45) :args (@t104)) % 0.52/0.77 (step @p55 :rule nary_cong :premises (@p54 @p46) :args (@t105)) % 0.52/0.77 (step @p56 :rule refl :args (@t92)) % 0.52/0.77 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t106)) % 0.52/0.77 (step @p58 :rule cong :premises (@p57) :args ((forall @t41 @t106))) % 0.52/0.77 (step @p59 :rule refl :args (@t100)) % 0.52/0.77 (step @p60 :rule refl :args (@t102)) % 0.52/0.77 (step @p61 :rule bool-double-not-elim :args (@t99)) % 0.52/0.77 (step @p62 :rule nary_cong :premises (@p61 @p60) :args ((and (not @t100) @t102))) % 0.52/0.77 (step @p63 :rule bool-or-de-morgan :args (@t100 @t101 false)) % 0.52/0.77 (step @p64 :rule trans :premises (@p63 @p62)) % 0.52/0.77 (step @p65 :rule nary_cong :premises (@p64 @p42) :args (@t107)) % 0.52/0.77 (step @p66 :rule nary_cong :premises (@p65 @p59) :args ((and @t107 @t100))) % 0.52/0.77 (step @p67 :rule bool-double-not-elim :args (@t107)) % 0.52/0.77 (step @p68 :rule nary_cong :premises (@p67 @p59) :args ((and (not @t108) @t100))) % 0.52/0.77 (step @p69 :rule bool-or-de-morgan :args (@t108 @t99 false)) % 0.52/0.77 (step @p70 :rule trans :premises (@p69 @p68)) % 0.52/0.77 (step @p71 :rule trans :premises (@p70 @p66)) % 0.52/0.77 (step @p72 :rule nary_cong :premises (@p56 @p71) :args (@t110)) % 0.52/0.77 (step @p73 :rule cong :premises (@p72) :args ((forall @t41 @t110))) % 0.52/0.77 (step @p74 :rule trans :premises (@p73 @p58)) % 0.52/0.77 (step @p75 :rule beta-reduce :args ((= @t118 @t109))) % 0.52/0.77 (step @p76 :rule cong :premises (@p75) :args (@t119)) % 0.52/0.77 (step @p77 :rule refl :args (@t92)) % 0.52/0.77 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t120)) % 0.52/0.77 (step @p79 :rule cong :premises (@p78) :args (@t121)) % 0.52/0.77 (step @p80 :rule trans :premises (@p79 @p74)) % 0.52/0.77 (step @p81 :rule cong :premises (@p80) :args (@t122)) % 0.52/0.77 (step @p82 :rule cong :premises (@p81) :args (@t123)) % 0.52/0.77 (step @p83 :rule beta-reduce :args ((= (_ @t127 @t117) @t123))) % 0.52/0.77 (step @p84 :rule trans :premises (@p83 @p82)) % 0.52/0.77 (step @p85 :rule beta-reduce :args ((= (_ (lambda @t129 (or @t116 @t128)) tptp.p) @t117))) % 0.52/0.77 (step @p86 :rule refl :args (tptp.p)) % 0.52/0.77 (step @p87 :rule refl :args (@t128)) % 0.52/0.77 (step @p88 :rule beta-reduce :args ((= @t131 @t115))) % 0.52/0.77 (step @p89 :rule cong :premises (@p88) :args (@t132)) % 0.52/0.77 (step @p90 :rule nary_cong :premises (@p89 @p87) :args (@t133)) % 0.52/0.77 (step @p91 :rule cong :premises (@p90) :args (@t134)) % 0.52/0.77 (step @p92 :rule beta-reduce :args ((= (_ @t136 @t130) @t134))) % 0.52/0.77 (step @p93 :rule trans :premises (@p92 @p91)) % 0.52/0.77 (step @p94 :rule beta-reduce :args ((= (_ (lambda @t129 (or @t114 @t128)) tptp.p) @t130))) % 0.52/0.77 (step @p95 :rule beta-reduce :args ((= @t138 @t113))) % 0.52/0.77 (step @p96 :rule cong :premises (@p95) :args (@t139)) % 0.52/0.77 (step @p97 :rule nary_cong :premises (@p96 @p87) :args (@t140)) % 0.52/0.77 (step @p98 :rule cong :premises (@p97) :args (@t141)) % 0.52/0.77 (step @p99 :rule beta-reduce :args ((= (_ @t136 @t137) @t141))) % 0.52/0.77 (step @p100 :rule trans :premises (@p99 @p98)) % 0.52/0.77 (step @p101 :rule beta-reduce :args ((= (_ @t142 tptp.q) @t137))) % 0.52/0.77 (step @p102 :rule refl :args (tptp.q)) % 0.52/0.77 (step @p103 :rule beta-reduce :args ((= @t143 @t142))) % 0.52/0.77 (step @p104 :rule ho_cong :premises (@p103 @p102)) % 0.52/0.77 (step @p105 :rule trans :premises (@p104 @p101)) % 0.52/0.77 (step @p106 :rule refl :args (@t136)) % 0.52/0.77 (step @p107 :rule ho_cong :premises (@p106 @p105)) % 0.52/0.77 (step @p108 :rule trans :premises (@p107 @p100)) % 0.52/0.77 (step @p109 :rule ho_cong :premises (@p108 @p86)) % 0.52/0.77 (step @p110 :rule trans :premises (@p109 @p94)) % 0.52/0.77 (step @p111 :rule ho_cong :premises (@p106 @p110)) % 0.52/0.77 (step @p112 :rule trans :premises (@p111 @p93)) % 0.52/0.77 (step @p113 :rule ho_cong :premises (@p112 @p86)) % 0.52/0.77 (step @p114 :rule trans :premises (@p113 @p85)) % 0.52/0.77 (step @p115 :rule refl :args (@t127)) % 0.52/0.77 (step @p116 :rule ho_cong :premises (@p115 @p114)) % 0.52/0.77 (step @p117 :rule trans :premises (@p116 @p84)) % 0.52/0.77 (step @p118 :rule refl :args (@t98)) % 0.52/0.77 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 0.52/0.77 (step @p120 :rule trans :premises (@p119 @p40)) % 0.52/0.77 (step @p121 :rule cong :premises (@p120) :args ((not (_ @t98 (_ @t127 (_ (_ @t136 (_ (_ @t136 (_ @t143 tptp.q)) tptp.p)) tptp.p)))))) % 0.52/0.77 (step @p122 :rule beta-reduce :args ((= (_ @t145 @t17) @t135))) % 0.52/0.77 (step @p123 :rule refl :args (@t17)) % 0.52/0.77 (step @p124 :rule beta-reduce :args ((= (_ (lambda @t146 @t144) @t14) @t145))) % 0.52/0.77 (step @p125 :rule refl :args (@t14)) % 0.52/0.77 (step @p126 :rule refl :args (@t15)) % 0.52/0.77 (step @p127 :rule beta-reduce :args ((= @t148 @t11))) % 0.52/0.77 (step @p128 :rule nary_cong :premises (@p127 @p126) :args (@t149)) % 0.52/0.77 (step @p129 :rule cong :premises (@p128) :args (@t150)) % 0.52/0.77 (step @p130 :rule beta-reduce :args ((= (_ @t16 @t147) @t150))) % 0.52/0.77 (step @p131 :rule trans :premises (@p130 @p129)) % 0.52/0.77 (step @p132 :rule beta-reduce :args ((= (_ @t13 @t9) @t147))) % 0.52/0.77 (step @p133 :rule refl :args (@t16)) % 0.52/0.77 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.52/0.77 (step @p135 :rule trans :premises (@p134 @p131)) % 0.52/0.77 (step @p136 :rule ho_cong :premises (@p135 @p125)) % 0.52/0.77 (step @p137 :rule trans :premises (@p136 @p124)) % 0.52/0.77 (step @p138 :rule ho_cong :premises (@p137 @p123)) % 0.52/0.77 (step @p139 :rule trans :premises (@p138 @p122)) % 0.52/0.77 (step @p140 :rule refl :args (@t9)) % 0.52/0.77 (step @p141 :rule ho_cong :premises (@p7 @p140)) % 0.52/0.77 (step @p142 :rule ho_cong :premises (@p8 @p141)) % 0.52/0.77 (step @p143 :rule ho_cong :premises (@p142 @p125)) % 0.52/0.77 (step @p144 :rule ho_cong :premises (@p143 @p123)) % 0.52/0.77 (step @p145 :rule trans :premises (@p144 @p139)) % 0.52/0.77 (step @p146 :rule cong :premises (@p145) :args (@t23)) % 0.52/0.77 (step @p147 :rule trans :premises (@p10 @p146)) % 0.52/0.77 (step @p148 :rule ho_cong :premises (@p147 @p86)) % 0.52/0.77 (step @p149 :rule ho_cong :premises (@p148 @p102)) % 0.52/0.77 (step @p150 :rule ho_cong :premises (@p147 @p149)) % 0.52/0.77 (step @p151 :rule ho_cong :premises (@p150 @p86)) % 0.52/0.77 (step @p152 :rule ho_cong :premises (@p147 @p151)) % 0.52/0.77 (step @p153 :rule ho_cong :premises (@p152 @p86)) % 0.52/0.77 (step @p154 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t151)) @t17) @t126))) % 0.52/0.77 (step @p155 :rule beta-reduce :args ((= @t153 @t151))) % 0.52/0.77 (step @p156 :rule cong :premises (@p155) :args (@t154)) % 0.52/0.77 (step @p157 :rule cong :premises (@p156) :args (@t155)) % 0.52/0.77 (step @p158 :rule beta-reduce :args ((= (_ @t13 @t152) @t155))) % 0.52/0.77 (step @p159 :rule trans :premises (@p158 @p157)) % 0.52/0.77 (step @p160 :rule refl :args (@t124)) % 0.52/0.77 (step @p161 :rule refl :args (@t39)) % 0.52/0.77 (step @p162 :rule cong :premises (@p161 @p160) :args ((= @t39 @t124))) % 0.52/0.77 (step @p163 :rule symm :premises (@p162)) % 0.52/0.77 (step @p164 :rule eq_resolve :premises (@p161 @p163)) % 0.52/0.77 (step @p165 :rule cong :premises (@p164) :args (@t156)) % 0.52/0.77 (step @p166 :rule refl :args (@t90)) % 0.52/0.77 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t157)) % 0.52/0.77 (step @p168 :rule cong :premises (@p167) :args ((forall @t41 @t157))) % 0.52/0.77 (step @p169 :rule beta-reduce :args ((= @t158 @t156))) % 0.52/0.77 (step @p170 :rule refl :args (@t90)) % 0.52/0.77 (step @p171 :rule nary_cong :premises (@p170 @p169) :args (@t159)) % 0.52/0.77 (step @p172 :rule cong :premises (@p171) :args (@t160)) % 0.52/0.77 (step @p173 :rule trans :premises (@p172 @p168)) % 0.52/0.77 (step @p174 :rule cong :premises (@p173) :args (@t161)) % 0.52/0.77 (step @p175 :rule beta-reduce :args ((= (_ @t162 @t147) @t161))) % 0.52/0.77 (step @p176 :rule trans :premises (@p175 @p174)) % 0.52/0.77 (step @p177 :rule refl :args (@t162)) % 0.52/0.77 (step @p178 :rule ho_cong :premises (@p177 @p132)) % 0.52/0.77 (step @p179 :rule trans :premises (@p178 @p176)) % 0.52/0.77 (step @p180 :rule refl :args (@t13)) % 0.52/0.77 (step @p181 :rule ho_cong :premises (@p180 @p179)) % 0.52/0.77 (step @p182 :rule trans :premises (@p181 @p159)) % 0.52/0.77 (step @p183 :rule ho_cong :premises (@p182 @p123)) % 0.52/0.77 (step @p184 :rule trans :premises (@p183 @p154)) % 0.52/0.77 (step @p185 :rule refl :args (@t89)) % 0.52/0.77 (step @p186 :rule refl :args (@t79)) % 0.52/0.77 (step @p187 :rule cong :premises (@p186 @p185) :args ((= @t79 @t89))) % 0.52/0.77 (step @p188 :rule symm :premises (@p187)) % 0.52/0.77 (step @p189 :rule eq_resolve :premises (@p186 @p188)) % 0.52/0.77 (step @p190 :rule cong :premises (@p189) :args (@t80)) % 0.52/0.77 (step @p191 :rule nary_cong :premises (@p190 @p164) :args (@t81)) % 0.52/0.77 (step @p192 :rule cong :premises (@p191) :args (@t82)) % 0.52/0.77 (step @p193 :rule cong :premises (@p192) :args (@t83)) % 0.52/0.77 (step @p194 :rule trans :premises (@p35 @p193)) % 0.52/0.77 (step @p195 :rule ho_cong :premises (@p194 @p141)) % 0.52/0.77 (step @p196 :rule ho_cong :premises (@p7 @p195)) % 0.52/0.77 (step @p197 :rule ho_cong :premises (@p196 @p123)) % 0.52/0.77 (step @p198 :rule trans :premises (@p197 @p184)) % 0.52/0.77 (step @p199 :rule cong :premises (@p198) :args (@t85)) % 0.52/0.77 (step @p200 :rule trans :premises (@p36 @p199)) % 0.52/0.77 (step @p201 :rule ho_cong :premises (@p200 @p153)) % 0.52/0.77 (step @p202 :rule refl :args (@t97)) % 0.52/0.77 (step @p203 :rule refl :args (@t10)) % 0.52/0.77 (step @p204 :rule cong :premises (@p203 @p202) :args ((= @t10 @t97))) % 0.52/0.77 (step @p205 :rule symm :premises (@p204)) % 0.52/0.77 (step @p206 :rule eq_resolve :premises (@p203 @p205)) % 0.52/0.77 (step @p207 :rule cong :premises (@p206) :args (@t73)) % 0.52/0.77 (step @p208 :rule cong :premises (@p207) :args (@t75)) % 0.52/0.77 (step @p209 :rule trans :premises (@p31 @p208)) % 0.52/0.77 (step @p210 :rule ho_cong :premises (@p209 @p201)) % 0.52/0.77 (step @p211 :rule cong :premises (@p210) :args (@t1)) % 0.52/0.77 (step @p212 :rule trans :premises (@p211 @p121)) % 0.52/0.77 (step @p213 :rule eq_resolve :premises (@p3 @p212)) % 0.52/0.77 (step @p214 :rule refl :args (@t165)) % 0.52/0.77 (step @p215 :rule bool-double-not-elim :args (@t163)) % 0.52/0.77 (step @p216 :rule nary_cong :premises (@p215 @p214) :args ((or (not @t166) @t165))) % 0.52/0.77 (step @p217 :rule bool-double-not-elim :args (@t165)) % 0.52/0.77 (step @p218 :rule refl :args (@t166)) % 0.52/0.77 (step @p219 :rule cong :premises (@p218 @p217) :args ((=> @t166 @t167))) % 0.52/0.77 (assume-push @p277 @t166) % 0.52/0.77 (step @p221 :rule skolemize :premises (@p213)) % 0.52/0.77 (step-pop @p278 :rule scope :premises (@p221)) % 0.52/0.77 (step @p222 :rule process_scope :premises (@p278) :args (@t167)) % 0.52/0.77 (step @p224 :rule eq_resolve :premises (@p222 @p219)) % 0.52/0.77 (step @p225 :rule implies_elim :premises (@p224)) % 0.52/0.77 (step @p226 :rule eq_resolve :premises (@p225 @p216)) % 0.52/0.77 (step @p227 :rule chain_m_resolution :premises (@p226 @p213) :args (@t165 @t168 (@list @t163))) % 0.52/0.77 (step @p228 :rule instantiate :premises (@p227) :args ((@list @t170))) % 0.52/0.77 (step @p229 :rule beta-reduce :args ((= (_ (lambda @t47 (forall @t46 (not (forall @t53 (not @t171))))) tptp.rel_d) (forall @t46 (not (forall @t53 (not (tptp.rel_d @t44 @t49)))))))) % 0.52/0.77 (step @p230 :rule refl :args (tptp.rel_d)) % 0.52/0.77 (step @p231 :rule refl :args (@t171)) % 0.52/0.77 (step @p232 :rule refl :args (@t51)) % 0.52/0.77 (step @p233 :rule cong :premises (@p232 @p231) :args ((= @t51 @t171))) % 0.52/0.77 (step @p234 :rule symm :premises (@p233)) % 0.52/0.77 (step @p235 :rule eq_resolve :premises (@p232 @p234)) % 0.52/0.77 (step @p236 :rule cong :premises (@p235) :args (@t172)) % 0.52/0.77 (step @p237 :rule cong :premises (@p236) :args (@t173)) % 0.52/0.77 (step @p238 :rule cong :premises (@p237) :args (@t174)) % 0.52/0.77 (step @p239 :rule exists-elim :args ((= @t54 @t174))) % 0.52/0.77 (step @p240 :rule trans :premises (@p239 @p238)) % 0.52/0.77 (step @p241 :rule cong :premises (@p240) :args (@t55)) % 0.52/0.78 (step @p242 :rule cong :premises (@p241) :args (@t56)) % 0.52/0.78 (step @p243 :rule trans :premises (@p23 @p242)) % 0.52/0.78 (step @p244 :rule ho_cong :premises (@p243 @p230)) % 0.52/0.78 (step @p245 :rule trans :premises (@p244 @p229)) % 0.52/0.78 (step @p246 :rule eq_resolve :premises (@p2 @p245)) % 0.52/0.78 (step @p247 :rule instantiate :premises (@p246) :args ((@list @t164))) % 0.52/0.78 (step @p248 :rule refl :args (@t175)) % 0.52/0.78 (step @p249 :rule bool-double-not-elim :args (@t169)) % 0.52/0.78 (step @p250 :rule nary_cong :premises (@p249 @p248) :args ((or (not @t176) @t175))) % 0.52/0.78 (step @p251 :rule bool-double-not-elim :args (@t175)) % 0.52/0.78 (step @p252 :rule refl :args (@t176)) % 0.52/0.78 (step @p253 :rule cong :premises (@p252 @p251) :args ((=> @t176 @t178))) % 0.52/0.78 (assume-push @p279 @t176) % 0.52/0.78 (step @p255 :rule skolemize :premises (@p247)) % 0.52/0.78 (step-pop @p280 :rule scope :premises (@p255)) % 0.52/0.78 (step @p256 :rule process_scope :premises (@p280) :args (@t178)) % 0.52/0.78 (step @p258 :rule eq_resolve :premises (@p256 @p253)) % 0.52/0.78 (step @p259 :rule implies_elim :premises (@p258)) % 0.52/0.78 (step @p260 :rule eq_resolve :premises (@p259 @p250)) % 0.52/0.78 (step @p261 :rule chain_m_resolution :premises (@p260 @p247) :args (@t175 @t168 (@list @t169))) % 0.52/0.78 (step @p262 :rule cnf_or_pos :args (@t184)) % 0.52/0.78 (step @p263 :rule reordering :premises (@p262) :args ((or @t177 @t183 (not @t184)))) % 0.52/0.78 (step @p264 :rule chain_m_resolution :premises (@p263 @p261 @p228) :args (@t183 (@list false false) (@list @t175 @t184))) % 0.52/0.78 (step @p265 :rule cnf_and_pos :args (@t183 0)) % 0.52/0.78 (step @p266 :rule reordering :premises (@p265) :args ((or @t182 @t185))) % 0.52/0.78 (step @p267 :rule chain_m_resolution :premises (@p266 @p264) :args (@t182 @t186 @t187)) % 0.52/0.78 (step @p268 :rule cnf_and_pos :args (@t183 1)) % 0.52/0.78 (step @p269 :rule reordering :premises (@p268) :args ((or @t180 @t185))) % 0.52/0.78 (step @p270 :rule chain_m_resolution :premises (@p269 @p264) :args (@t180 @t186 @t187)) % 0.52/0.78 (step @p271 :rule cnf_and_pos :args (@t181 0)) % 0.52/0.78 (step @p272 :rule reordering :premises (@p271) :args ((or @t179 @t188))) % 0.52/0.78 (step @p273 :rule chain_m_resolution :premises (@p272 @p270) :args (@t188 @t168 (@list @t179))) % 0.52/0.78 (step @p274 :rule cnf_or_pos :args (@t182)) % 0.52/0.78 (step @p275 :rule reordering :premises (@p274) :args ((or @t179 @t181 (not @t182)))) % 0.52/0.78 (step @p276 false :rule chain_m_resolution :premises (@p275 @p273 @p270 @p267) :args (false (@list true true false) (@list @t181 @t179 @t182))) % 0.52/0.78 ) % 0.52/0.78 % SZS output end Proof % 0.52/0.78 % cvc5 exiting %------------------------------------------------------------------------------