%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO457^5 : 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 : n022.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 09:12:46 AM UTC 2026 % Result : Theorem 0.38s 0.60s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO457^5 : 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 % 0.16/0.34 % Computer : n022.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 00:09:53 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.38/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.60 % SZS status Theorem % 0.38/0.60 % SZS output start Proof % 0.38/0.60 ( % 0.38/0.60 (declare-sort $$unsorted 0) % 0.38/0.60 (declare-sort tptp.mu 0) % 0.38/0.60 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.q (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.p (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.38/0.60 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.38/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.38/0.60 (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)))))) % 0.38/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.38/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.38/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.38/0.60 (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))))))) % 0.38/0.60 (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))))))) % 0.38/0.60 (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)))))) % 0.38/0.60 (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)))))) % 0.38/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.38/0.60 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.38/0.60 (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)))))) % 0.38/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.60 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.60 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.60 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.38/0.60 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.38/0.60 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.38/0.60 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.38/0.60 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.38/0.60 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.38/0.60 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.38/0.60 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.38/0.60 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$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_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.38/0.60 (define tptp.mdia_s4 () (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_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.38/0.60 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mdia_s4 (_ tptp.mbox_s4 tptp.p))) (_ tptp.mdia_s4 (_ (_ tptp.mimplies tptp.q) tptp.p)))))) % 0.38/0.60 (define @t2 () (@var "Y" tptp.mu)) % 0.38/0.60 (define @t3 () (@var "X" tptp.mu)) % 0.38/0.60 (define @t4 () (@var "W" $$unsorted)) % 0.38/0.60 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.38/0.60 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.60 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.60 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.38/0.60 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.38/0.60 (define @t10 () (_ @t9 @t4)) % 0.38/0.60 (define @t11 () (not @t10)) % 0.38/0.60 (define @t12 () (@list @t9 @t4)) % 0.38/0.60 (define @t13 () (lambda @t12 @t11)) % 0.38/0.60 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.38/0.60 (define @t15 () (_ @t14 @t4)) % 0.38/0.60 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.38/0.60 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.60 (define @t18 () (_ tptp.mnot @t14)) % 0.38/0.60 (define @t19 () (_ tptp.mnot @t9)) % 0.38/0.60 (define @t20 () (_ tptp.mor @t19)) % 0.38/0.60 (define @t21 () (@list @t9 @t14 @t17)) % 0.38/0.60 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.38/0.60 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.38/0.60 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.38/0.60 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.38/0.60 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.38/0.60 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.38/0.60 (define @t28 () (_ @t27 @t3)) % 0.38/0.60 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.38/0.60 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.60 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.38/0.60 (define @t32 () (_ @t31 @t30)) % 0.38/0.60 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.38/0.60 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.38/0.60 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.38/0.60 (define @t36 () (@list @t4)) % 0.38/0.60 (define @t37 () (lambda @t36 true)) % 0.38/0.60 (define @t38 () (@var "V" $$unsorted)) % 0.38/0.60 (define @t39 () (_ @t9 @t38)) % 0.38/0.60 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.60 (define @t41 () (@list @t38)) % 0.38/0.60 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.38/0.60 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.38/0.60 (define @t44 () (@var "S" $$unsorted)) % 0.38/0.60 (define @t45 () (_ @t40 @t44)) % 0.38/0.60 (define @t46 () (_ @t45 @t44)) % 0.38/0.60 (define @t47 () (@list @t44)) % 0.38/0.60 (define @t48 () (forall @t47 @t46)) % 0.38/0.60 (define @t49 () (@list @t40)) % 0.38/0.60 (define @t50 () (lambda @t49 @t48)) % 0.38/0.60 (define @t51 () (@var "T" $$unsorted)) % 0.38/0.60 (define @t52 () (_ @t40 @t51)) % 0.38/0.60 (define @t53 () (_ @t45 @t51)) % 0.38/0.60 (define @t54 () (lambda @t49 (forall (@list @t44 @t51) (=> @t53 (_ @t52 @t44))))) % 0.38/0.60 (define @t55 () (@list @t51)) % 0.38/0.60 (define @t56 () (lambda @t49 (forall @t47 (exists @t55 @t53)))) % 0.38/0.60 (define @t57 () (@var "U" $$unsorted)) % 0.38/0.60 (define @t58 () (_ @t45 @t57)) % 0.38/0.60 (define @t59 () (_ @t52 @t57)) % 0.38/0.60 (define @t60 () (@list @t44 @t51 @t57)) % 0.38/0.60 (define @t61 () (lambda @t49 (forall @t60 (=> (and @t53 @t59) @t58)))) % 0.38/0.60 (define @t62 () (and @t53 @t58)) % 0.38/0.60 (define @t63 () (lambda @t49 (forall @t60 (=> @t62 @t59)))) % 0.38/0.60 (define @t64 () (= @t51 @t57)) % 0.38/0.60 (define @t65 () (lambda @t49 (forall @t60 (=> @t62 @t64)))) % 0.38/0.60 (define @t66 () (@list @t57)) % 0.38/0.60 (define @t67 () (lambda @t49 (forall @t47 (exists @t55 (and @t53 (forall @t66 (=> @t58 @t64))))))) % 0.38/0.60 (define @t68 () (_ @t40 @t57)) % 0.38/0.60 (define @t69 () (_ @t68 @t51)) % 0.38/0.60 (define @t70 () (lambda @t49 (forall @t60 (=> @t53 (exists @t66 (and @t58 @t69)))))) % 0.38/0.60 (define @t71 () (lambda @t49 (forall @t60 (=> @t62 (or @t59 @t64 @t69))))) % 0.38/0.60 (define @t72 () (lambda @t49 (forall @t60 (=> @t62 (exists @t41 (and (_ @t52 @t38) (_ @t68 @t38))))))) % 0.38/0.60 (define @t73 () (forall @t36 @t10)) % 0.38/0.60 (define @t74 () (@list @t9)) % 0.38/0.60 (define @t75 () (lambda @t74 @t73)) % 0.38/0.60 (define @t76 () (lambda @t74 (forall @t36 @t11))) % 0.38/0.60 (define @t77 () (lambda @t74 (exists @t36 @t10))) % 0.38/0.60 (define @t78 () (lambda @t74 (exists @t36 @t11))) % 0.38/0.60 (define @t79 () (_ (_ tptp.rel_s4 @t4) @t38)) % 0.38/0.60 (define @t80 () (not @t79)) % 0.38/0.60 (define @t81 () (or @t80 @t39)) % 0.38/0.60 (define @t82 () (forall @t41 @t81)) % 0.38/0.60 (define @t83 () (lambda @t12 @t82)) % 0.38/0.60 (define @t84 () (@list @t9 @t17)) % 0.38/0.60 (define @t85 () (lambda @t84 (_ (_ tptp.mnot (_ tptp.mbox_s4 @t19)) @t17))) % 0.38/0.60 (define @t86 () (forall @t47 (tptp.rel_s4 @t44 @t44))) % 0.38/0.60 (define @t87 () (_ @t40 @t44 @t44)) % 0.38/0.60 (define @t88 () (@var "BOUND_VARIABLE_8429" $$unsorted)) % 0.38/0.60 (define @t89 () (tptp.p @t88)) % 0.38/0.60 (define @t90 () (@var "BOUND_VARIABLE_8507" $$unsorted)) % 0.38/0.60 (define @t91 () (@list @t88)) % 0.38/0.60 (define @t92 () (not (forall @t91 (or (not (tptp.rel_s4 @t90 @t88)) @t89)))) % 0.38/0.60 (define @t93 () (not (tptp.rel_s4 @t4 @t90))) % 0.38/0.60 (define @t94 () (tptp.p @t38)) % 0.38/0.60 (define @t95 () (tptp.q @t38)) % 0.38/0.60 (define @t96 () (and @t95 (not @t94))) % 0.38/0.60 (define @t97 () (tptp.rel_s4 @t4 @t38)) % 0.38/0.60 (define @t98 () (not @t97)) % 0.38/0.60 (define @t99 () (not (forall @t41 (or @t98 @t96)))) % 0.38/0.60 (define @t100 () (or @t99 @t93 @t92)) % 0.38/0.60 (define @t101 () (or @t93 @t92)) % 0.38/0.60 (define @t102 () (or @t101 @t99)) % 0.38/0.60 (define @t103 () (@list @t4 @t90)) % 0.38/0.60 (define @t104 () (forall @t103 @t102)) % 0.38/0.60 (define @t105 () (@list @t90)) % 0.38/0.60 (define @t106 () (forall @t105 @t102)) % 0.38/0.60 (define @t107 () (forall @t105 @t101)) % 0.38/0.60 (define @t108 () (@list @t38)) % 0.38/0.60 (define @t109 () (or @t107 @t99)) % 0.38/0.60 (define @t110 () (forall @t91 (or (not (tptp.rel_s4 @t38 @t88)) @t89))) % 0.38/0.60 (define @t111 () (not @t110)) % 0.38/0.60 (define @t112 () (or (forall @t41 (or @t98 @t111)) @t99)) % 0.38/0.60 (define @t113 () (not (tptp.rel_s4 @t17 @t38))) % 0.38/0.60 (define @t114 () (not (forall @t41 (or @t113 @t96)))) % 0.38/0.60 (define @t115 () (forall @t41 (or @t113 @t111))) % 0.38/0.60 (define @t116 () (@list @t17)) % 0.38/0.60 (define @t117 () (lambda @t116 (or @t115 @t114))) % 0.38/0.60 (define @t118 () (_ @t117 @t4)) % 0.38/0.60 (define @t119 () (forall @t36 @t118)) % 0.38/0.60 (define @t120 () (_ @t9 @t4)) % 0.38/0.60 (define @t121 () (lambda @t74 (forall @t36 @t120))) % 0.38/0.60 (define @t122 () (lambda @t116 @t114)) % 0.38/0.60 (define @t123 () (_ @t122 @t17)) % 0.38/0.60 (define @t124 () (or @t115 @t123)) % 0.38/0.60 (define @t125 () (lambda @t116 @t124)) % 0.38/0.60 (define @t126 () (_ @t14 @t17)) % 0.38/0.60 (define @t127 () (@list @t14 @t17)) % 0.38/0.60 (define @t128 () (_ tptp.p @t38)) % 0.38/0.60 (define @t129 () (not @t128)) % 0.38/0.60 (define @t130 () (_ tptp.q @t38)) % 0.38/0.60 (define @t131 () (and @t130 @t129)) % 0.38/0.60 (define @t132 () (or @t113 @t131)) % 0.38/0.60 (define @t133 () (not @t130)) % 0.38/0.60 (define @t134 () (or @t133 @t128)) % 0.38/0.60 (define @t135 () (or @t113 (not @t134))) % 0.38/0.60 (define @t136 () (not (_ tptp.q @t17))) % 0.38/0.60 (define @t137 () (lambda @t116 (or @t136 (_ tptp.p @t17)))) % 0.38/0.60 (define @t138 () (_ @t137 @t38)) % 0.38/0.60 (define @t139 () (not @t138)) % 0.38/0.60 (define @t140 () (or @t113 @t139)) % 0.38/0.60 (define @t141 () (forall @t41 @t140)) % 0.38/0.60 (define @t142 () (not @t141)) % 0.38/0.60 (define @t143 () (lambda @t116 @t142)) % 0.38/0.60 (define @t144 () (_ @t9 @t38)) % 0.38/0.60 (define @t145 () (not @t144)) % 0.38/0.60 (define @t146 () (not (forall @t41 (or @t113 @t145)))) % 0.38/0.60 (define @t147 () (lambda @t84 @t146)) % 0.38/0.60 (define @t148 () (lambda @t127 (or @t136 @t126))) % 0.38/0.60 (define @t149 () (or (not (_ @t9 @t17)) @t126)) % 0.38/0.60 (define @t150 () (lambda @t21 @t149)) % 0.38/0.60 (define @t151 () (_ @t150 tptp.q)) % 0.38/0.60 (define @t152 () (not @t115)) % 0.38/0.60 (define @t153 () (lambda @t116 @t152)) % 0.38/0.60 (define @t154 () (_ @t153 @t17)) % 0.38/0.60 (define @t155 () (not @t154)) % 0.38/0.60 (define @t156 () (or @t155 @t126)) % 0.38/0.60 (define @t157 () (lambda @t127 @t156)) % 0.38/0.60 (define @t158 () (forall @t41 (or @t98 @t94))) % 0.38/0.60 (define @t159 () (lambda @t36 @t158)) % 0.38/0.60 (define @t160 () (not (_ @t159 @t38))) % 0.38/0.60 (define @t161 () (or @t113 @t160)) % 0.38/0.60 (define @t162 () (forall @t41 @t161)) % 0.38/0.60 (define @t163 () (not @t162)) % 0.38/0.60 (define @t164 () (lambda @t116 @t163)) % 0.38/0.60 (define @t165 () (lambda @t12 (forall @t41 (or @t98 @t144)))) % 0.38/0.60 (define @t166 () (_ @t165 tptp.p)) % 0.38/0.60 (define @t167 () (or @t11 @t15)) % 0.38/0.60 (define @t168 () (lambda @t36 @t167)) % 0.38/0.60 (define @t169 () (@list @t14 @t4)) % 0.38/0.60 (define @t170 () (lambda @t36 @t11)) % 0.38/0.60 (define @t171 () (_ @t170 @t4)) % 0.38/0.60 (define @t172 () (or @t171 @t15)) % 0.38/0.60 (define @t173 () (lambda @t169 @t172)) % 0.38/0.60 (define @t174 () (forall @t41 (or @t98 @t145))) % 0.38/0.60 (define @t175 () (lambda @t36 @t174)) % 0.38/0.60 (define @t176 () (_ @t175 @t4)) % 0.38/0.60 (define @t177 () (not @t176)) % 0.38/0.60 (define @t178 () (lambda @t36 @t177)) % 0.38/0.60 (define @t179 () (not @t39)) % 0.38/0.60 (define @t180 () (or @t98 @t179)) % 0.38/0.60 (define @t181 () (_ @t170 @t38)) % 0.38/0.60 (define @t182 () (or @t98 @t181)) % 0.38/0.60 (define @t183 () (forall @t41 @t182)) % 0.38/0.60 (define @t184 () (lambda @t36 @t183)) % 0.38/0.60 (define @t185 () (forall @t103 @t100)) % 0.38/0.60 (define @t186 () (@quantifiers_skolemize @t185 1)) % 0.38/0.60 (define @t187 () (forall @t91 (or (not (tptp.rel_s4 @t186 @t88)) @t89))) % 0.38/0.60 (define @t188 () (not @t187)) % 0.38/0.60 (define @t189 () (@quantifiers_skolemize @t185 0)) % 0.38/0.60 (define @t190 () (tptp.rel_s4 @t189 @t186)) % 0.38/0.60 (define @t191 () (not @t190)) % 0.38/0.60 (define @t192 () (forall @t41 (or (not (tptp.rel_s4 @t189 @t38)) @t96))) % 0.38/0.60 (define @t193 () (not @t192)) % 0.38/0.60 (define @t194 () (or @t193 @t191 @t188)) % 0.38/0.60 (define @t195 () (@list true)) % 0.38/0.60 (define @t196 () (@list @t194)) % 0.38/0.60 (define @t197 () (@list @t186)) % 0.38/0.60 (define @t198 () (tptp.p @t186)) % 0.38/0.60 (define @t199 () (not @t198)) % 0.38/0.60 (define @t200 () (and (tptp.q @t186) @t199)) % 0.38/0.60 (define @t201 () (or @t191 @t200)) % 0.38/0.60 (define @t202 () (tptp.rel_s4 @t186 @t186)) % 0.38/0.60 (define @t203 () (not @t202)) % 0.38/0.60 (define @t204 () (or @t203 @t198)) % 0.38/0.60 (define @t205 () (@list true false)) % 0.38/0.60 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.38/0.60 (assume @p2 (_ tptp.mreflexive tptp.rel_s4)) % 0.38/0.60 (assume @p3 (_ tptp.mtransitive tptp.rel_s4)) % 0.38/0.60 (assume @p4 @t1) % 0.38/0.60 (assume @p5 true) % 0.38/0.60 (step @p6 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.38/0.60 (step @p7 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.38/0.60 (step @p8 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.38/0.60 (step @p9 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.38/0.60 (step @p10 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.38/0.60 (step @p11 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.38/0.60 (step @p12 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.38/0.60 (step @p13 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.38/0.60 (step @p14 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.38/0.60 (step @p15 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.38/0.60 (step @p16 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.38/0.60 (step @p17 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.38/0.60 (step @p18 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.38/0.60 (step @p19 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.38/0.60 (step @p20 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.38/0.60 (step @p21 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.38/0.60 (step @p22 (= tptp.mreflexive @t50) :rule refl :args (@t50)) % 0.38/0.60 (step @p23 (= tptp.msymmetric @t54) :rule refl :args (@t54)) % 0.38/0.60 (step @p24 (= tptp.mserial @t56) :rule refl :args (@t56)) % 0.38/0.60 (step @p25 (= tptp.mtransitive @t61) :rule refl :args (@t61)) % 0.38/0.60 (step @p26 (= tptp.meuclidean @t63) :rule refl :args (@t63)) % 0.38/0.60 (step @p27 (= tptp.mpartially_functional @t65) :rule refl :args (@t65)) % 0.38/0.60 (step @p28 (= tptp.mfunctional @t67) :rule refl :args (@t67)) % 0.38/0.60 (step @p29 (= tptp.mweakly_dense @t70) :rule refl :args (@t70)) % 0.38/0.60 (step @p30 (= tptp.mweakly_connected @t71) :rule refl :args (@t71)) % 0.38/0.60 (step @p31 (= tptp.mweakly_directed @t72) :rule refl :args (@t72)) % 0.38/0.60 (step @p32 (= tptp.mvalid @t75) :rule refl :args (@t75)) % 0.38/0.60 (step @p33 (= tptp.minvalid @t76) :rule refl :args (@t76)) % 0.38/0.60 (step @p34 (= tptp.msatisfiable @t77) :rule refl :args (@t77)) % 0.38/0.60 (step @p35 (= tptp.mcountersatisfiable @t78) :rule refl :args (@t78)) % 0.38/0.60 (step @p36 (= tptp.mbox_s4 @t83) :rule refl :args (@t83)) % 0.38/0.60 (step @p37 (= tptp.mdia_s4 @t85) :rule refl :args (@t85)) % 0.38/0.60 (step @p38 :rule beta-reduce :args ((= (_ (lambda @t49 (forall @t47 @t87)) tptp.rel_s4) @t86))) % 0.38/0.60 (step @p39 :rule refl :args (tptp.rel_s4)) % 0.38/0.60 (step @p40 :rule refl :args (@t87)) % 0.38/0.60 (step @p41 :rule refl :args (@t46)) % 0.38/0.60 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t46 @t87))) % 0.38/0.60 (step @p43 :rule symm :premises (@p42)) % 0.38/0.60 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.38/0.60 (step @p45 :rule cong :premises (@p44) :args (@t48)) % 0.38/0.60 (step @p46 :rule cong :premises (@p45) :args (@t50)) % 0.38/0.60 (step @p47 :rule trans :premises (@p22 @p46)) % 0.38/0.60 (step @p48 :rule ho_cong :premises (@p47 @p39)) % 0.38/0.60 (step @p49 :rule trans :premises (@p48 @p38)) % 0.38/0.60 (step @p50 :rule eq_resolve :premises (@p2 @p49)) % 0.38/0.60 (step @p51 :rule aci_norm :args ((= @t102 @t100))) % 0.38/0.60 (step @p52 :rule cong :premises (@p51) :args (@t104)) % 0.38/0.60 (step @p53 :rule quant-merge-prenex :args ((= (forall @t36 @t106) @t104))) % 0.38/0.60 (step @p54 :rule refl :args (@t99)) % 0.38/0.60 (step @p55 :rule alpha_equiv :args (@t107 (@list @t90) @t108)) % 0.38/0.60 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t109)) % 0.38/0.60 (step @p57 :rule quant-miniscope-or :args ((= @t106 @t109))) % 0.38/0.60 (step @p58 :rule trans :premises (@p57 @p56)) % 0.38/0.60 (step @p59 :rule symm :premises (@p58)) % 0.38/0.60 (step @p60 :rule cong :premises (@p59) :args ((forall @t36 @t112))) % 0.38/0.60 (step @p61 :rule trans :premises (@p60 @p53)) % 0.38/0.60 (step @p62 :rule trans :premises (@p61 @p52)) % 0.38/0.60 (step @p63 :rule beta-reduce :args ((= @t118 @t112))) % 0.38/0.60 (step @p64 :rule cong :premises (@p63) :args (@t119)) % 0.38/0.60 (step @p65 :rule trans :premises (@p64 @p62)) % 0.38/0.60 (step @p66 :rule beta-reduce :args ((= (_ @t121 @t117) @t119))) % 0.38/0.60 (step @p67 :rule trans :premises (@p66 @p65)) % 0.38/0.60 (step @p68 :rule beta-reduce :args ((= @t123 @t114))) % 0.38/0.60 (step @p69 :rule refl :args (@t115)) % 0.38/0.60 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t124)) % 0.38/0.60 (step @p71 :rule cong :premises (@p70) :args (@t125)) % 0.38/0.60 (step @p72 :rule beta-reduce :args ((= (_ (lambda @t127 (or @t115 @t126)) @t122) @t125))) % 0.38/0.60 (step @p73 :rule trans :premises (@p72 @p71)) % 0.38/0.60 (step @p74 :rule refl :args (@t94)) % 0.38/0.60 (step @p75 :rule refl :args (@t128)) % 0.38/0.60 (step @p76 :rule cong :premises (@p75 @p74) :args ((= @t128 @t94))) % 0.38/0.60 (step @p77 :rule symm :premises (@p76)) % 0.38/0.60 (step @p78 :rule eq_resolve :premises (@p75 @p77)) % 0.38/0.60 (step @p79 :rule cong :premises (@p78) :args (@t129)) % 0.38/0.60 (step @p80 :rule refl :args (@t95)) % 0.38/0.60 (step @p81 :rule refl :args (@t130)) % 0.38/0.60 (step @p82 :rule cong :premises (@p81 @p80) :args ((= @t130 @t95))) % 0.38/0.60 (step @p83 :rule symm :premises (@p82)) % 0.38/0.60 (step @p84 :rule eq_resolve :premises (@p81 @p83)) % 0.38/0.60 (step @p85 :rule nary_cong :premises (@p84 @p79) :args (@t131)) % 0.38/0.60 (step @p86 :rule refl :args (@t113)) % 0.38/0.60 (step @p87 :rule nary_cong :premises (@p86 @p85) :args (@t132)) % 0.38/0.60 (step @p88 :rule cong :premises (@p87) :args ((forall @t41 @t132))) % 0.38/0.60 (step @p89 :rule refl :args (@t129)) % 0.38/0.60 (step @p90 :rule bool-double-not-elim :args (@t130)) % 0.38/0.60 (step @p91 :rule nary_cong :premises (@p90 @p89) :args ((and (not @t133) @t129))) % 0.38/0.60 (step @p92 :rule bool-or-de-morgan :args (@t133 @t128 false)) % 0.38/0.60 (step @p93 :rule trans :premises (@p92 @p91)) % 0.38/0.60 (step @p94 :rule nary_cong :premises (@p86 @p93) :args (@t135)) % 0.38/0.60 (step @p95 :rule cong :premises (@p94) :args ((forall @t41 @t135))) % 0.38/0.60 (step @p96 :rule trans :premises (@p95 @p88)) % 0.38/0.60 (step @p97 :rule beta-reduce :args ((= @t138 @t134))) % 0.38/0.60 (step @p98 :rule cong :premises (@p97) :args (@t139)) % 0.38/0.60 (step @p99 :rule refl :args (@t113)) % 0.38/0.60 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t140)) % 0.38/0.60 (step @p101 :rule cong :premises (@p100) :args (@t141)) % 0.38/0.60 (step @p102 :rule trans :premises (@p101 @p96)) % 0.38/0.60 (step @p103 :rule cong :premises (@p102) :args (@t142)) % 0.38/0.60 (step @p104 :rule cong :premises (@p103) :args (@t143)) % 0.38/0.60 (step @p105 :rule beta-reduce :args ((= (_ @t147 @t137) @t143))) % 0.38/0.60 (step @p106 :rule trans :premises (@p105 @p104)) % 0.38/0.60 (step @p107 :rule beta-reduce :args ((= (_ @t148 tptp.p) @t137))) % 0.38/0.60 (step @p108 :rule refl :args (tptp.p)) % 0.38/0.60 (step @p109 :rule beta-reduce :args ((= @t151 @t148))) % 0.38/0.60 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 0.38/0.60 (step @p111 :rule trans :premises (@p110 @p107)) % 0.38/0.60 (step @p112 :rule refl :args (@t147)) % 0.38/0.60 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 0.38/0.60 (step @p114 :rule trans :premises (@p113 @p106)) % 0.38/0.60 (step @p115 :rule refl :args (@t126)) % 0.38/0.60 (step @p116 :rule bool-double-not-elim :args (@t115)) % 0.38/0.60 (step @p117 :rule beta-reduce :args ((= @t154 @t152))) % 0.38/0.60 (step @p118 :rule cong :premises (@p117) :args (@t155)) % 0.38/0.60 (step @p119 :rule trans :premises (@p118 @p116)) % 0.38/0.60 (step @p120 :rule nary_cong :premises (@p119 @p115) :args (@t156)) % 0.38/0.60 (step @p121 :rule cong :premises (@p120) :args (@t157)) % 0.38/0.60 (step @p122 :rule beta-reduce :args ((= (_ @t150 @t153) @t157))) % 0.38/0.60 (step @p123 :rule trans :premises (@p122 @p121)) % 0.38/0.60 (step @p124 :rule beta-reduce :args ((= (_ (lambda @t36 (forall @t91 (or (not (tptp.rel_s4 @t4 @t88)) @t89))) @t38) @t110))) % 0.38/0.60 (step @p125 :rule refl :args (@t38)) % 0.38/0.60 (step @p126 :rule alpha_equiv :args (@t158 @t108 (@list @t88))) % 0.38/0.60 (step @p127 :rule cong :premises (@p126) :args (@t159)) % 0.38/0.60 (step @p128 :rule ho_cong :premises (@p127 @p125)) % 0.38/0.60 (step @p129 :rule trans :premises (@p128 @p124)) % 0.38/0.60 (step @p130 :rule cong :premises (@p129) :args (@t160)) % 0.38/0.60 (step @p131 :rule nary_cong :premises (@p99 @p130) :args (@t161)) % 0.38/0.60 (step @p132 :rule cong :premises (@p131) :args (@t162)) % 0.38/0.60 (step @p133 :rule cong :premises (@p132) :args (@t163)) % 0.38/0.60 (step @p134 :rule cong :premises (@p133) :args (@t164)) % 0.38/0.60 (step @p135 :rule beta-reduce :args ((= (_ @t147 @t159) @t164))) % 0.38/0.60 (step @p136 :rule trans :premises (@p135 @p134)) % 0.38/0.60 (step @p137 :rule beta-reduce :args ((= @t166 @t159))) % 0.38/0.60 (step @p138 :rule ho_cong :premises (@p112 @p137)) % 0.38/0.60 (step @p139 :rule trans :premises (@p138 @p136)) % 0.38/0.60 (step @p140 :rule refl :args (@t150)) % 0.38/0.60 (step @p141 :rule ho_cong :premises (@p140 @p139)) % 0.38/0.60 (step @p142 :rule trans :premises (@p141 @p123)) % 0.38/0.60 (step @p143 :rule ho_cong :premises (@p142 @p114)) % 0.38/0.60 (step @p144 :rule trans :premises (@p143 @p73)) % 0.38/0.60 (step @p145 :rule refl :args (@t121)) % 0.38/0.60 (step @p146 :rule ho_cong :premises (@p145 @p144)) % 0.38/0.60 (step @p147 :rule trans :premises (@p146 @p67)) % 0.38/0.60 (step @p148 :rule cong :premises (@p147) :args ((not (_ @t121 (_ (_ @t150 (_ @t147 @t166)) (_ @t147 (_ @t151 tptp.p))))))) % 0.38/0.60 (step @p149 :rule refl :args (tptp.q)) % 0.38/0.60 (step @p150 :rule beta-reduce :args ((= (_ @t168 @t17) @t149))) % 0.38/0.60 (step @p151 :rule refl :args (@t17)) % 0.38/0.60 (step @p152 :rule beta-reduce :args ((= (_ (lambda @t169 @t167) @t14) @t168))) % 0.38/0.60 (step @p153 :rule refl :args (@t14)) % 0.38/0.60 (step @p154 :rule refl :args (@t15)) % 0.38/0.60 (step @p155 :rule beta-reduce :args ((= @t171 @t11))) % 0.38/0.60 (step @p156 :rule nary_cong :premises (@p155 @p154) :args (@t172)) % 0.38/0.60 (step @p157 :rule cong :premises (@p156) :args (@t173)) % 0.38/0.60 (step @p158 :rule beta-reduce :args ((= (_ @t16 @t170) @t173))) % 0.38/0.60 (step @p159 :rule trans :premises (@p158 @p157)) % 0.38/0.60 (step @p160 :rule beta-reduce :args ((= (_ @t13 @t9) @t170))) % 0.38/0.60 (step @p161 :rule refl :args (@t16)) % 0.38/0.60 (step @p162 :rule ho_cong :premises (@p161 @p160)) % 0.38/0.60 (step @p163 :rule trans :premises (@p162 @p159)) % 0.38/0.60 (step @p164 :rule ho_cong :premises (@p163 @p153)) % 0.38/0.60 (step @p165 :rule trans :premises (@p164 @p152)) % 0.38/0.60 (step @p166 :rule ho_cong :premises (@p165 @p151)) % 0.38/0.60 (step @p167 :rule trans :premises (@p166 @p150)) % 0.38/0.60 (step @p168 :rule refl :args (@t9)) % 0.38/0.60 (step @p169 :rule ho_cong :premises (@p8 @p168)) % 0.38/0.60 (step @p170 :rule ho_cong :premises (@p9 @p169)) % 0.38/0.60 (step @p171 :rule ho_cong :premises (@p170 @p153)) % 0.38/0.60 (step @p172 :rule ho_cong :premises (@p171 @p151)) % 0.38/0.60 (step @p173 :rule trans :premises (@p172 @p167)) % 0.38/0.60 (step @p174 :rule cong :premises (@p173) :args (@t23)) % 0.38/0.60 (step @p175 :rule trans :premises (@p11 @p174)) % 0.38/0.60 (step @p176 :rule ho_cong :premises (@p175 @p149)) % 0.38/0.60 (step @p177 :rule ho_cong :premises (@p176 @p108)) % 0.38/0.60 (step @p178 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t174)) @t17) @t146))) % 0.38/0.60 (step @p179 :rule beta-reduce :args ((= @t176 @t174))) % 0.38/0.60 (step @p180 :rule cong :premises (@p179) :args (@t177)) % 0.38/0.60 (step @p181 :rule cong :premises (@p180) :args (@t178)) % 0.38/0.60 (step @p182 :rule beta-reduce :args ((= (_ @t13 @t175) @t178))) % 0.38/0.60 (step @p183 :rule trans :premises (@p182 @p181)) % 0.38/0.60 (step @p184 :rule refl :args (@t144)) % 0.38/0.60 (step @p185 :rule refl :args (@t39)) % 0.38/0.60 (step @p186 :rule cong :premises (@p185 @p184) :args ((= @t39 @t144))) % 0.38/0.60 (step @p187 :rule symm :premises (@p186)) % 0.38/0.60 (step @p188 :rule eq_resolve :premises (@p185 @p187)) % 0.38/0.60 (step @p189 :rule cong :premises (@p188) :args (@t179)) % 0.38/0.60 (step @p190 :rule refl :args (@t98)) % 0.38/0.60 (step @p191 :rule nary_cong :premises (@p190 @p189) :args (@t180)) % 0.38/0.60 (step @p192 :rule cong :premises (@p191) :args ((forall @t41 @t180))) % 0.38/0.60 (step @p193 :rule beta-reduce :args ((= @t181 @t179))) % 0.38/0.60 (step @p194 :rule refl :args (@t98)) % 0.38/0.60 (step @p195 :rule nary_cong :premises (@p194 @p193) :args (@t182)) % 0.38/0.60 (step @p196 :rule cong :premises (@p195) :args (@t183)) % 0.38/0.60 (step @p197 :rule trans :premises (@p196 @p192)) % 0.38/0.60 (step @p198 :rule cong :premises (@p197) :args (@t184)) % 0.38/0.60 (step @p199 :rule beta-reduce :args ((= (_ @t165 @t170) @t184))) % 0.38/0.60 (step @p200 :rule trans :premises (@p199 @p198)) % 0.38/0.60 (step @p201 :rule refl :args (@t165)) % 0.38/0.60 (step @p202 :rule ho_cong :premises (@p201 @p160)) % 0.38/0.60 (step @p203 :rule trans :premises (@p202 @p200)) % 0.38/0.60 (step @p204 :rule refl :args (@t13)) % 0.38/0.60 (step @p205 :rule ho_cong :premises (@p204 @p203)) % 0.38/0.60 (step @p206 :rule trans :premises (@p205 @p183)) % 0.38/0.60 (step @p207 :rule ho_cong :premises (@p206 @p151)) % 0.38/0.60 (step @p208 :rule trans :premises (@p207 @p178)) % 0.38/0.60 (step @p209 :rule refl :args (@t97)) % 0.38/0.60 (step @p210 :rule refl :args (@t79)) % 0.38/0.60 (step @p211 :rule cong :premises (@p210 @p209) :args ((= @t79 @t97))) % 0.38/0.60 (step @p212 :rule symm :premises (@p211)) % 0.38/0.60 (step @p213 :rule eq_resolve :premises (@p210 @p212)) % 0.38/0.60 (step @p214 :rule cong :premises (@p213) :args (@t80)) % 0.38/0.60 (step @p215 :rule nary_cong :premises (@p214 @p188) :args (@t81)) % 0.38/0.60 (step @p216 :rule cong :premises (@p215) :args (@t82)) % 0.38/0.60 (step @p217 :rule cong :premises (@p216) :args (@t83)) % 0.38/0.60 (step @p218 :rule trans :premises (@p36 @p217)) % 0.38/0.60 (step @p219 :rule ho_cong :premises (@p218 @p169)) % 0.38/0.60 (step @p220 :rule ho_cong :premises (@p8 @p219)) % 0.38/0.60 (step @p221 :rule ho_cong :premises (@p220 @p151)) % 0.38/0.60 (step @p222 :rule trans :premises (@p221 @p208)) % 0.38/0.60 (step @p223 :rule cong :premises (@p222) :args (@t85)) % 0.38/0.60 (step @p224 :rule trans :premises (@p37 @p223)) % 0.38/0.60 (step @p225 :rule ho_cong :premises (@p224 @p177)) % 0.38/0.60 (step @p226 :rule ho_cong :premises (@p218 @p108)) % 0.38/0.60 (step @p227 :rule ho_cong :premises (@p224 @p226)) % 0.38/0.60 (step @p228 :rule ho_cong :premises (@p175 @p227)) % 0.38/0.60 (step @p229 :rule ho_cong :premises (@p228 @p225)) % 0.38/0.60 (step @p230 :rule refl :args (@t120)) % 0.38/0.60 (step @p231 :rule refl :args (@t10)) % 0.38/0.60 (step @p232 :rule cong :premises (@p231 @p230) :args ((= @t10 @t120))) % 0.38/0.60 (step @p233 :rule symm :premises (@p232)) % 0.38/0.60 (step @p234 :rule eq_resolve :premises (@p231 @p233)) % 0.38/0.60 (step @p235 :rule cong :premises (@p234) :args (@t73)) % 0.38/0.60 (step @p236 :rule cong :premises (@p235) :args (@t75)) % 0.38/0.60 (step @p237 :rule trans :premises (@p32 @p236)) % 0.38/0.60 (step @p238 :rule ho_cong :premises (@p237 @p229)) % 0.38/0.60 (step @p239 :rule cong :premises (@p238) :args (@t1)) % 0.38/0.60 (step @p240 :rule trans :premises (@p239 @p148)) % 0.38/0.60 (step @p241 :rule eq_resolve :premises (@p4 @p240)) % 0.38/0.60 (step @p242 :rule skolemize :premises (@p241)) % 0.38/0.60 (step @p243 :rule bool-double-not-elim :args (@t187)) % 0.38/0.60 (step @p244 :rule refl :args (@t194)) % 0.38/0.60 (step @p245 :rule nary_cong :premises (@p244 @p243) :args ((or @t194 (not @t188)))) % 0.38/0.60 (step @p246 :rule cnf_or_neg :args (@t194 2)) % 0.38/0.60 (step @p247 :rule eq_resolve :premises (@p246 @p245)) % 0.38/0.60 (step @p248 :rule reordering :premises (@p247) :args ((or @t187 @t194))) % 0.38/0.60 (step @p249 :rule chain_m_resolution :premises (@p248 @p242) :args (@t187 @t195 @t196)) % 0.38/0.60 (step @p250 :rule instantiate :premises (@p249) :args (@t197)) % 0.38/0.60 (step @p251 :rule bool-double-not-elim :args (@t192)) % 0.38/0.60 (step @p252 :rule nary_cong :premises (@p244 @p251) :args ((or @t194 (not @t193)))) % 0.38/0.60 (step @p253 :rule cnf_or_neg :args (@t194 0)) % 0.38/0.60 (step @p254 :rule eq_resolve :premises (@p253 @p252)) % 0.38/0.60 (step @p255 :rule reordering :premises (@p254) :args ((or @t192 @t194))) % 0.38/0.60 (step @p256 :rule chain_m_resolution :premises (@p255 @p242) :args (@t192 @t195 @t196)) % 0.38/0.60 (step @p257 :rule instantiate :premises (@p256) :args (@t197)) % 0.38/0.60 (step @p258 :rule bool-double-not-elim :args (@t190)) % 0.38/0.60 (step @p259 :rule nary_cong :premises (@p244 @p258) :args ((or @t194 (not @t191)))) % 0.38/0.60 (step @p260 :rule cnf_or_neg :args (@t194 1)) % 0.38/0.60 (step @p261 :rule eq_resolve :premises (@p260 @p259)) % 0.38/0.60 (step @p262 :rule reordering :premises (@p261) :args ((or @t190 @t194))) % 0.38/0.60 (step @p263 :rule chain_m_resolution :premises (@p262 @p242) :args (@t190 @t195 @t196)) % 0.38/0.60 (step @p264 :rule cnf_or_pos :args (@t201)) % 0.38/0.60 (step @p265 :rule reordering :premises (@p264) :args ((or @t191 @t200 (not @t201)))) % 0.38/0.60 (step @p266 :rule chain_m_resolution :premises (@p265 @p263 @p257) :args (@t200 (@list false false) (@list @t190 @t201))) % 0.38/0.60 (step @p267 :rule cnf_and_pos :args (@t200 1)) % 0.38/0.60 (step @p268 :rule reordering :premises (@p267) :args ((or @t199 (not @t200)))) % 0.38/0.60 (step @p269 :rule chain_m_resolution :premises (@p268 @p266) :args (@t199 (@list false) (@list @t200))) % 0.38/0.60 (step @p270 :rule cnf_or_pos :args (@t204)) % 0.38/0.60 (step @p271 :rule reordering :premises (@p270) :args ((or @t198 @t203 (not @t204)))) % 0.38/0.60 (step @p272 :rule chain_m_resolution :premises (@p271 @p269 @p250) :args (@t203 @t205 (@list @t198 @t204))) % 0.38/0.60 (assume-push @p279 @t86) % 0.38/0.60 (step @p274 :rule instantiate :premises (@p50) :args (@t197)) % 0.38/0.60 (step-pop @p280 :rule scope :premises (@p274)) % 0.38/0.60 (step @p275 :rule process_scope :premises (@p280) :args (@t202)) % 0.38/0.60 (step @p277 :rule implies_elim :premises (@p275)) % 0.38/0.60 (step @p278 false :rule chain_m_resolution :premises (@p277 @p272 @p50) :args (false @t205 (@list @t202 @t86))) % 0.38/0.60 ) % 0.38/0.60 % SZS output end Proof % 0.38/0.60 % cvc5 exiting %------------------------------------------------------------------------------