%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO417^1 : 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 : n014.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 09:12:36 AM UTC 2026 % Result : Theorem 1.02s 1.23s % Output : Proof 1.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO417^1 : 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 : n014.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 00:07:28 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.50 %----Proving TH0 % 1.02/1.23 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.02/1.23 % SZS status Theorem % 1.02/1.23 % SZS output start Proof % 1.02/1.23 ( % 1.02/1.23 (declare-sort $$unsorted 0) % 1.02/1.23 (declare-sort tptp.mu 0) % 1.02/1.23 (declare-const tptp.rel_d (-> $$unsorted $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.p (-> $$unsorted Bool)) % 1.02/1.23 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 1.02/1.23 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 1.02/1.23 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 1.02/1.23 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 1.02/1.23 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 1.02/1.23 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 1.02/1.23 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 1.02/1.23 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 1.02/1.23 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 1.02/1.23 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 1.02/1.23 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 1.02/1.23 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 1.02/1.23 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 1.02/1.23 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 1.02/1.23 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 1.02/1.23 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 1.02/1.23 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 1.02/1.23 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 1.02/1.23 (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)))))))) % 1.02/1.23 (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)))))))) % 1.02/1.23 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 1.02/1.23 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 1.02/1.23 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 1.02/1.23 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 1.02/1.23 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 1.02/1.23 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 1.02/1.23 (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))))))))))))) % 1.02/1.23 (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)))))) % 1.02/1.23 (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))))))) % 1.02/1.23 (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)))))) % 1.02/1.23 (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))))))) % 1.02/1.23 (define tptp.mbox_d () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_d _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 1.02/1.23 (define tptp.mdia_d () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_d (_ tptp.mnot _let_2))) _let_1))))) % 1.02/1.23 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mbox_d (_ tptp.mbox_d tptp.p))) (_ tptp.mdia_d (_ tptp.mdia_d tptp.p)))))) % 1.02/1.23 (define @t2 () (@var "Y" tptp.mu)) % 1.02/1.23 (define @t3 () (@var "X" tptp.mu)) % 1.02/1.23 (define @t4 () (@var "W" $$unsorted)) % 1.02/1.23 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 1.02/1.23 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 1.02/1.23 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 1.02/1.23 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 1.02/1.23 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 1.02/1.23 (define @t10 () (_ @t9 @t4)) % 1.02/1.23 (define @t11 () (not @t10)) % 1.02/1.23 (define @t12 () (@list @t9 @t4)) % 1.02/1.23 (define @t13 () (lambda @t12 @t11)) % 1.02/1.23 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 1.02/1.23 (define @t15 () (_ @t14 @t4)) % 1.02/1.23 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 1.02/1.23 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 1.02/1.23 (define @t18 () (_ tptp.mnot @t14)) % 1.02/1.23 (define @t19 () (_ tptp.mnot @t9)) % 1.02/1.23 (define @t20 () (_ tptp.mor @t19)) % 1.02/1.23 (define @t21 () (@list @t9 @t14 @t17)) % 1.02/1.23 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 1.02/1.23 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 1.02/1.23 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 1.02/1.23 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 1.02/1.23 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 1.02/1.23 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 1.02/1.23 (define @t28 () (_ @t27 @t3)) % 1.02/1.23 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 1.02/1.23 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 1.02/1.23 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 1.02/1.23 (define @t32 () (_ @t31 @t30)) % 1.02/1.23 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 1.02/1.23 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 1.02/1.23 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 1.02/1.23 (define @t36 () (@list @t4)) % 1.02/1.23 (define @t37 () (lambda @t36 true)) % 1.02/1.23 (define @t38 () (@var "V" $$unsorted)) % 1.02/1.23 (define @t39 () (_ @t9 @t38)) % 1.02/1.23 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 1.02/1.23 (define @t41 () (@list @t38)) % 1.02/1.23 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 1.02/1.23 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 1.02/1.23 (define @t44 () (@var "S" $$unsorted)) % 1.02/1.23 (define @t45 () (_ @t40 @t44)) % 1.02/1.23 (define @t46 () (@list @t44)) % 1.02/1.23 (define @t47 () (@list @t40)) % 1.02/1.23 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 1.02/1.23 (define @t49 () (@var "T" $$unsorted)) % 1.02/1.23 (define @t50 () (_ @t40 @t49)) % 1.02/1.23 (define @t51 () (_ @t45 @t49)) % 1.02/1.23 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 1.02/1.23 (define @t53 () (@list @t49)) % 1.02/1.23 (define @t54 () (exists @t53 @t51)) % 1.02/1.23 (define @t55 () (forall @t46 @t54)) % 1.02/1.23 (define @t56 () (lambda @t47 @t55)) % 1.02/1.23 (define @t57 () (@var "U" $$unsorted)) % 1.02/1.23 (define @t58 () (_ @t45 @t57)) % 1.02/1.23 (define @t59 () (_ @t50 @t57)) % 1.02/1.23 (define @t60 () (@list @t44 @t49 @t57)) % 1.02/1.23 (define @t61 () (lambda @t47 (forall @t60 (=> (and @t51 @t59) @t58)))) % 1.02/1.23 (define @t62 () (and @t51 @t58)) % 1.02/1.23 (define @t63 () (lambda @t47 (forall @t60 (=> @t62 @t59)))) % 1.02/1.23 (define @t64 () (= @t49 @t57)) % 1.02/1.23 (define @t65 () (lambda @t47 (forall @t60 (=> @t62 @t64)))) % 1.02/1.23 (define @t66 () (@list @t57)) % 1.02/1.23 (define @t67 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t66 (=> @t58 @t64))))))) % 1.02/1.23 (define @t68 () (_ @t40 @t57)) % 1.02/1.23 (define @t69 () (_ @t68 @t49)) % 1.02/1.23 (define @t70 () (lambda @t47 (forall @t60 (=> @t51 (exists @t66 (and @t58 @t69)))))) % 1.02/1.23 (define @t71 () (lambda @t47 (forall @t60 (=> @t62 (or @t59 @t64 @t69))))) % 1.02/1.23 (define @t72 () (lambda @t47 (forall @t60 (=> @t62 (exists @t41 (and (_ @t50 @t38) (_ @t68 @t38))))))) % 1.02/1.23 (define @t73 () (forall @t36 @t10)) % 1.02/1.23 (define @t74 () (@list @t9)) % 1.02/1.23 (define @t75 () (lambda @t74 @t73)) % 1.02/1.23 (define @t76 () (lambda @t74 (forall @t36 @t11))) % 1.02/1.23 (define @t77 () (lambda @t74 (exists @t36 @t10))) % 1.02/1.23 (define @t78 () (lambda @t74 (exists @t36 @t11))) % 1.02/1.23 (define @t79 () (_ (_ tptp.rel_d @t4) @t38)) % 1.02/1.23 (define @t80 () (not @t79)) % 1.02/1.23 (define @t81 () (or @t80 @t39)) % 1.02/1.23 (define @t82 () (forall @t41 @t81)) % 1.02/1.23 (define @t83 () (lambda @t12 @t82)) % 1.02/1.23 (define @t84 () (@list @t9 @t17)) % 1.02/1.23 (define @t85 () (lambda @t84 (_ (_ tptp.mnot (_ tptp.mbox_d @t19)) @t17))) % 1.02/1.23 (define @t86 () (_ @t40 @t44 @t49)) % 1.02/1.23 (define @t87 () (not @t51)) % 1.02/1.23 (define @t88 () (forall @t53 @t87)) % 1.02/1.23 (define @t89 () (not @t88)) % 1.02/1.23 (define @t90 () (@var "BOUND_VARIABLE_8487" $$unsorted)) % 1.02/1.23 (define @t91 () (not (tptp.p @t90))) % 1.02/1.23 (define @t92 () (not (tptp.rel_d @t38 @t90))) % 1.02/1.23 (define @t93 () (tptp.rel_d @t4 @t38)) % 1.02/1.23 (define @t94 () (not @t93)) % 1.02/1.23 (define @t95 () (@list @t38 @t90)) % 1.02/1.23 (define @t96 () (@var "BOUND_VARIABLE_8432" $$unsorted)) % 1.02/1.23 (define @t97 () (tptp.p @t96)) % 1.02/1.23 (define @t98 () (not (tptp.rel_d @t38 @t96))) % 1.02/1.23 (define @t99 () (or @t94 @t98 @t97)) % 1.02/1.23 (define @t100 () (@list @t38 @t96)) % 1.02/1.23 (define @t101 () (forall @t100 @t99)) % 1.02/1.23 (define @t102 () (or (not @t101) (not (forall @t95 (or @t94 @t92 @t91))))) % 1.02/1.23 (define @t103 () (@quantifiers_skolemize (forall @t36 @t102) 0)) % 1.02/1.23 (define @t104 () (forall @t53 (not (tptp.rel_d @t103 @t49)))) % 1.02/1.23 (define @t105 () (@quantifiers_skolemize @t104 0)) % 1.02/1.23 (define @t106 () (tptp.rel_d @t103 @t105)) % 1.02/1.23 (define @t107 () (not @t104)) % 1.02/1.23 (define @t108 () (not @t106)) % 1.02/1.23 (define @t109 () (not @t108)) % 1.02/1.23 (define @t110 () (@list true)) % 1.02/1.23 (define @t111 () (forall @t53 (not (tptp.rel_d @t105 @t49)))) % 1.02/1.23 (define @t112 () (@quantifiers_skolemize @t111 0)) % 1.02/1.23 (define @t113 () (tptp.rel_d @t105 @t112)) % 1.02/1.23 (define @t114 () (not @t111)) % 1.02/1.23 (define @t115 () (not @t113)) % 1.02/1.23 (define @t116 () (not @t115)) % 1.02/1.23 (define @t117 () (not (tptp.rel_d @t17 @t38))) % 1.02/1.23 (define @t118 () (or @t117 @t92 @t91)) % 1.02/1.23 (define @t119 () (not (forall @t95 @t118))) % 1.02/1.23 (define @t120 () (forall @t100 (or @t117 @t98 @t97))) % 1.02/1.23 (define @t121 () (not @t120)) % 1.02/1.23 (define @t122 () (@list @t17)) % 1.02/1.23 (define @t123 () (lambda @t122 (or @t121 @t119))) % 1.02/1.24 (define @t124 () (_ @t123 @t4)) % 1.02/1.24 (define @t125 () (forall @t36 @t124)) % 1.02/1.24 (define @t126 () (_ @t9 @t4)) % 1.02/1.24 (define @t127 () (lambda @t74 (forall @t36 @t126))) % 1.02/1.24 (define @t128 () (lambda @t122 @t119)) % 1.02/1.24 (define @t129 () (_ @t128 @t17)) % 1.02/1.24 (define @t130 () (or @t121 @t129)) % 1.02/1.24 (define @t131 () (lambda @t122 @t130)) % 1.02/1.24 (define @t132 () (_ @t14 @t17)) % 1.02/1.24 (define @t133 () (@list @t14 @t17)) % 1.02/1.24 (define @t134 () (or @t92 @t91)) % 1.02/1.24 (define @t135 () (or @t117 @t134)) % 1.02/1.24 (define @t136 () (forall @t95 @t135)) % 1.02/1.24 (define @t137 () (@list @t90)) % 1.02/1.24 (define @t138 () (forall @t137 @t135)) % 1.02/1.24 (define @t139 () (forall @t137 @t134)) % 1.02/1.24 (define @t140 () (@var "BOUND_VARIABLE_8467" $$unsorted)) % 1.02/1.24 (define @t141 () (@list @t140)) % 1.02/1.24 (define @t142 () (or @t117 @t139)) % 1.02/1.24 (define @t143 () (not (tptp.p @t140))) % 1.02/1.24 (define @t144 () (@list @t140)) % 1.02/1.24 (define @t145 () (forall @t144 (or (not (tptp.rel_d @t38 @t140)) @t143))) % 1.02/1.24 (define @t146 () (tptp.p @t38)) % 1.02/1.24 (define @t147 () (forall @t41 (or @t117 (not @t146)))) % 1.02/1.24 (define @t148 () (@list @t38)) % 1.02/1.24 (define @t149 () (not @t147)) % 1.02/1.24 (define @t150 () (lambda @t122 @t149)) % 1.02/1.24 (define @t151 () (not (_ @t150 @t38))) % 1.02/1.24 (define @t152 () (or @t117 @t151)) % 1.02/1.24 (define @t153 () (forall @t41 @t152)) % 1.02/1.24 (define @t154 () (not @t153)) % 1.02/1.24 (define @t155 () (lambda @t122 @t154)) % 1.02/1.24 (define @t156 () (_ @t9 @t38)) % 1.02/1.24 (define @t157 () (not @t156)) % 1.02/1.24 (define @t158 () (not (forall @t41 (or @t117 @t157)))) % 1.02/1.24 (define @t159 () (lambda @t84 @t158)) % 1.02/1.24 (define @t160 () (_ @t159 tptp.p)) % 1.02/1.24 (define @t161 () (lambda @t36 @t101)) % 1.02/1.24 (define @t162 () (_ @t161 @t17)) % 1.02/1.24 (define @t163 () (not @t162)) % 1.02/1.24 (define @t164 () (or @t163 @t132)) % 1.02/1.24 (define @t165 () (lambda @t133 @t164)) % 1.02/1.24 (define @t166 () (or (not (_ @t9 @t17)) @t132)) % 1.02/1.24 (define @t167 () (lambda @t21 @t166)) % 1.02/1.24 (define @t168 () (or @t98 @t97)) % 1.02/1.24 (define @t169 () (or @t94 @t168)) % 1.02/1.24 (define @t170 () (forall @t100 @t169)) % 1.02/1.24 (define @t171 () (@list @t96)) % 1.02/1.24 (define @t172 () (forall @t171 @t169)) % 1.02/1.24 (define @t173 () (forall @t171 @t168)) % 1.02/1.24 (define @t174 () (@var "BOUND_VARIABLE_8416" $$unsorted)) % 1.02/1.24 (define @t175 () (@list @t174)) % 1.02/1.24 (define @t176 () (or @t94 @t173)) % 1.02/1.24 (define @t177 () (tptp.p @t174)) % 1.02/1.24 (define @t178 () (@list @t174)) % 1.02/1.24 (define @t179 () (forall @t178 (or (not (tptp.rel_d @t38 @t174)) @t177))) % 1.02/1.24 (define @t180 () (forall @t41 (or @t94 @t146))) % 1.02/1.24 (define @t181 () (lambda @t36 @t180)) % 1.02/1.24 (define @t182 () (or @t94 (_ @t181 @t38))) % 1.02/1.24 (define @t183 () (forall @t41 @t182)) % 1.02/1.24 (define @t184 () (lambda @t36 @t183)) % 1.02/1.24 (define @t185 () (lambda @t12 (forall @t41 (or @t94 @t156)))) % 1.02/1.24 (define @t186 () (_ @t185 tptp.p)) % 1.02/1.24 (define @t187 () (forall @t41 (or @t94 @t157))) % 1.02/1.24 (define @t188 () (lambda @t36 @t187)) % 1.02/1.24 (define @t189 () (_ @t188 @t4)) % 1.02/1.24 (define @t190 () (not @t189)) % 1.02/1.24 (define @t191 () (lambda @t36 @t190)) % 1.02/1.24 (define @t192 () (not @t39)) % 1.02/1.24 (define @t193 () (or @t94 @t192)) % 1.02/1.24 (define @t194 () (lambda @t36 @t11)) % 1.02/1.24 (define @t195 () (_ @t194 @t38)) % 1.02/1.24 (define @t196 () (or @t94 @t195)) % 1.02/1.24 (define @t197 () (forall @t41 @t196)) % 1.02/1.24 (define @t198 () (lambda @t36 @t197)) % 1.02/1.24 (define @t199 () (or @t11 @t15)) % 1.02/1.24 (define @t200 () (lambda @t36 @t199)) % 1.02/1.24 (define @t201 () (@list @t14 @t4)) % 1.02/1.24 (define @t202 () (_ @t194 @t4)) % 1.02/1.24 (define @t203 () (or @t202 @t15)) % 1.02/1.24 (define @t204 () (lambda @t201 @t203)) % 1.02/1.24 (define @t205 () (not (tptp.rel_d @t103 @t38))) % 1.02/1.24 (define @t206 () (forall @t95 (or @t205 @t92 @t91))) % 1.02/1.24 (define @t207 () (not @t206)) % 1.02/1.24 (define @t208 () (forall @t100 (or @t205 @t98 @t97))) % 1.02/1.24 (define @t209 () (not @t208)) % 1.02/1.24 (define @t210 () (or @t209 @t207)) % 1.02/1.24 (define @t211 () (@list @t210)) % 1.02/1.24 (define @t212 () (@list @t105 @t112)) % 1.02/1.24 (define @t213 () (tptp.p @t112)) % 1.02/1.24 (define @t214 () (or @t108 @t115 @t213)) % 1.02/1.24 (define @t215 () (not @t213)) % 1.02/1.24 (define @t216 () (or @t108 @t115 @t215)) % 1.02/1.24 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 1.02/1.24 (assume @p2 (_ tptp.mserial tptp.rel_d)) % 1.02/1.24 (assume @p3 @t1) % 1.02/1.24 (assume @p4 true) % 1.02/1.24 (step @p5 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 1.02/1.24 (step @p6 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 1.02/1.24 (step @p7 (= tptp.mnot @t13) :rule refl :args (@t13)) % 1.02/1.24 (step @p8 (= tptp.mor @t16) :rule refl :args (@t16)) % 1.02/1.24 (step @p9 (= tptp.mand @t22) :rule refl :args (@t22)) % 1.02/1.24 (step @p10 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 1.02/1.24 (step @p11 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 1.02/1.24 (step @p12 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 1.02/1.24 (step @p13 (= tptp.mxor @t26) :rule refl :args (@t26)) % 1.02/1.24 (step @p14 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 1.02/1.24 (step @p15 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 1.02/1.24 (step @p16 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 1.02/1.24 (step @p17 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 1.02/1.24 (step @p18 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 1.02/1.24 (step @p19 (= tptp.mbox @t42) :rule refl :args (@t42)) % 1.02/1.24 (step @p20 (= tptp.mdia @t43) :rule refl :args (@t43)) % 1.02/1.24 (step @p21 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 1.02/1.24 (step @p22 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 1.02/1.24 (step @p23 (= tptp.mserial @t56) :rule refl :args (@t56)) % 1.02/1.24 (step @p24 (= tptp.mtransitive @t61) :rule refl :args (@t61)) % 1.02/1.24 (step @p25 (= tptp.meuclidean @t63) :rule refl :args (@t63)) % 1.02/1.24 (step @p26 (= tptp.mpartially_functional @t65) :rule refl :args (@t65)) % 1.02/1.24 (step @p27 (= tptp.mfunctional @t67) :rule refl :args (@t67)) % 1.02/1.24 (step @p28 (= tptp.mweakly_dense @t70) :rule refl :args (@t70)) % 1.02/1.24 (step @p29 (= tptp.mweakly_connected @t71) :rule refl :args (@t71)) % 1.02/1.24 (step @p30 (= tptp.mweakly_directed @t72) :rule refl :args (@t72)) % 1.02/1.24 (step @p31 (= tptp.mvalid @t75) :rule refl :args (@t75)) % 1.02/1.24 (step @p32 (= tptp.minvalid @t76) :rule refl :args (@t76)) % 1.02/1.24 (step @p33 (= tptp.msatisfiable @t77) :rule refl :args (@t77)) % 1.02/1.24 (step @p34 (= tptp.mcountersatisfiable @t78) :rule refl :args (@t78)) % 1.02/1.24 (step @p35 (= tptp.mbox_d @t83) :rule refl :args (@t83)) % 1.02/1.24 (step @p36 (= tptp.mdia_d @t85) :rule refl :args (@t85)) % 1.02/1.24 (step @p37 :rule beta-reduce :args ((= (_ (lambda @t47 (forall @t46 (not (forall @t53 (not @t86))))) tptp.rel_d) (forall @t46 (not (forall @t53 (not (tptp.rel_d @t44 @t49)))))))) % 1.02/1.24 (step @p38 :rule refl :args (tptp.rel_d)) % 1.02/1.24 (step @p39 :rule refl :args (@t86)) % 1.02/1.24 (step @p40 :rule refl :args (@t51)) % 1.02/1.24 (step @p41 :rule cong :premises (@p40 @p39) :args ((= @t51 @t86))) % 1.02/1.24 (step @p42 :rule symm :premises (@p41)) % 1.02/1.24 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 1.02/1.24 (step @p44 :rule cong :premises (@p43) :args (@t87)) % 1.02/1.24 (step @p45 :rule cong :premises (@p44) :args (@t88)) % 1.02/1.24 (step @p46 :rule cong :premises (@p45) :args (@t89)) % 1.02/1.24 (step @p47 :rule exists-elim :args ((= @t54 @t89))) % 1.02/1.24 (step @p48 :rule trans :premises (@p47 @p46)) % 1.02/1.24 (step @p49 :rule cong :premises (@p48) :args (@t55)) % 1.02/1.24 (step @p50 :rule cong :premises (@p49) :args (@t56)) % 1.02/1.24 (step @p51 :rule trans :premises (@p23 @p50)) % 1.02/1.24 (step @p52 :rule ho_cong :premises (@p51 @p38)) % 1.02/1.24 (step @p53 :rule trans :premises (@p52 @p37)) % 1.02/1.24 (step @p54 :rule eq_resolve :premises (@p2 @p53)) % 1.02/1.24 (step @p55 :rule instantiate :premises (@p54) :args ((@list @t103))) % 1.02/1.24 (step @p56 :rule refl :args (@t106)) % 1.02/1.24 (step @p57 :rule bool-double-not-elim :args (@t104)) % 1.02/1.24 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or (not @t107) @t106))) % 1.02/1.24 (step @p59 :rule bool-double-not-elim :args (@t106)) % 1.02/1.24 (step @p60 :rule refl :args (@t107)) % 1.02/1.24 (step @p61 :rule cong :premises (@p60 @p59) :args ((=> @t107 @t109))) % 1.02/1.24 (assume-push @p284 @t107) % 1.02/1.24 (step @p63 :rule skolemize :premises (@p55)) % 1.02/1.24 (step-pop @p285 :rule scope :premises (@p63)) % 1.02/1.24 (step @p64 :rule process_scope :premises (@p285) :args (@t109)) % 1.02/1.24 (step @p66 :rule eq_resolve :premises (@p64 @p61)) % 1.02/1.24 (step @p67 :rule implies_elim :premises (@p66)) % 1.02/1.24 (step @p68 :rule eq_resolve :premises (@p67 @p58)) % 1.02/1.24 (step @p69 :rule chain_m_resolution :premises (@p68 @p55) :args (@t106 @t110 (@list @t104))) % 1.02/1.24 (step @p70 :rule instantiate :premises (@p54) :args ((@list @t105))) % 1.02/1.24 (step @p71 :rule refl :args (@t113)) % 1.02/1.24 (step @p72 :rule bool-double-not-elim :args (@t111)) % 1.02/1.24 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or (not @t114) @t113))) % 1.02/1.24 (step @p74 :rule bool-double-not-elim :args (@t113)) % 1.02/1.24 (step @p75 :rule refl :args (@t114)) % 1.02/1.24 (step @p76 :rule cong :premises (@p75 @p74) :args ((=> @t114 @t116))) % 1.02/1.24 (assume-push @p286 @t114) % 1.02/1.24 (step @p78 :rule skolemize :premises (@p70)) % 1.02/1.24 (step-pop @p287 :rule scope :premises (@p78)) % 1.02/1.24 (step @p79 :rule process_scope :premises (@p287) :args (@t116)) % 1.02/1.24 (step @p81 :rule eq_resolve :premises (@p79 @p76)) % 1.02/1.24 (step @p82 :rule implies_elim :premises (@p81)) % 1.02/1.24 (step @p83 :rule eq_resolve :premises (@p82 @p73)) % 1.02/1.24 (step @p84 :rule chain_m_resolution :premises (@p83 @p70) :args (@t113 @t110 (@list @t111))) % 1.02/1.24 (step @p85 :rule beta-reduce :args ((= @t124 @t102))) % 1.02/1.24 (step @p86 :rule cong :premises (@p85) :args (@t125)) % 1.02/1.24 (step @p87 :rule beta-reduce :args ((= (_ @t127 @t123) @t125))) % 1.02/1.24 (step @p88 :rule trans :premises (@p87 @p86)) % 1.02/1.24 (step @p89 :rule beta-reduce :args ((= @t129 @t119))) % 1.02/1.24 (step @p90 :rule refl :args (@t121)) % 1.02/1.24 (step @p91 :rule nary_cong :premises (@p90 @p89) :args (@t130)) % 1.02/1.24 (step @p92 :rule cong :premises (@p91) :args (@t131)) % 1.02/1.24 (step @p93 :rule beta-reduce :args ((= (_ (lambda @t133 (or @t121 @t132)) @t128) @t131))) % 1.02/1.24 (step @p94 :rule trans :premises (@p93 @p92)) % 1.02/1.24 (step @p95 :rule aci_norm :args ((= @t135 @t118))) % 1.02/1.24 (step @p96 :rule cong :premises (@p95) :args (@t136)) % 1.02/1.24 (step @p97 :rule quant-merge-prenex :args ((= (forall @t41 @t138) @t136))) % 1.02/1.24 (step @p98 :rule alpha_equiv :args (@t139 (@list @t90) @t141)) % 1.02/1.24 (step @p99 :rule refl :args (@t117)) % 1.02/1.24 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t142)) % 1.02/1.24 (step @p101 :rule quant-miniscope-or :args ((= @t138 @t142))) % 1.02/1.24 (step @p102 :rule trans :premises (@p101 @p100)) % 1.02/1.24 (step @p103 :rule symm :premises (@p102)) % 1.02/1.24 (step @p104 :rule cong :premises (@p103) :args ((forall @t41 (or @t117 @t145)))) % 1.02/1.24 (step @p105 :rule trans :premises (@p104 @p97)) % 1.02/1.24 (step @p106 :rule trans :premises (@p105 @p96)) % 1.02/1.24 (step @p107 :rule bool-double-not-elim :args (@t145)) % 1.02/1.24 (step @p108 :rule beta-reduce :args ((= (_ (lambda @t122 (not (forall @t144 (or (not (tptp.rel_d @t17 @t140)) @t143)))) @t38) (not @t145)))) % 1.02/1.24 (step @p109 :rule refl :args (@t38)) % 1.02/1.24 (step @p110 :rule alpha_equiv :args (@t147 @t148 @t141)) % 1.02/1.24 (step @p111 :rule cong :premises (@p110) :args (@t149)) % 1.02/1.24 (step @p112 :rule cong :premises (@p111) :args (@t150)) % 1.02/1.24 (step @p113 :rule ho_cong :premises (@p112 @p109)) % 1.02/1.24 (step @p114 :rule trans :premises (@p113 @p108)) % 1.02/1.24 (step @p115 :rule cong :premises (@p114) :args (@t151)) % 1.02/1.24 (step @p116 :rule trans :premises (@p115 @p107)) % 1.02/1.24 (step @p117 :rule refl :args (@t117)) % 1.02/1.24 (step @p118 :rule nary_cong :premises (@p117 @p116) :args (@t152)) % 1.02/1.24 (step @p119 :rule cong :premises (@p118) :args (@t153)) % 1.02/1.24 (step @p120 :rule trans :premises (@p119 @p106)) % 1.02/1.24 (step @p121 :rule cong :premises (@p120) :args (@t154)) % 1.02/1.24 (step @p122 :rule cong :premises (@p121) :args (@t155)) % 1.02/1.24 (step @p123 :rule beta-reduce :args ((= (_ @t159 @t150) @t155))) % 1.02/1.24 (step @p124 :rule trans :premises (@p123 @p122)) % 1.02/1.24 (step @p125 :rule beta-reduce :args ((= @t160 @t150))) % 1.02/1.24 (step @p126 :rule refl :args (@t159)) % 1.02/1.24 (step @p127 :rule ho_cong :premises (@p126 @p125)) % 1.02/1.24 (step @p128 :rule trans :premises (@p127 @p124)) % 1.02/1.24 (step @p129 :rule refl :args (@t132)) % 1.02/1.24 (step @p130 :rule beta-reduce :args ((= @t162 @t120))) % 1.02/1.24 (step @p131 :rule cong :premises (@p130) :args (@t163)) % 1.02/1.24 (step @p132 :rule nary_cong :premises (@p131 @p129) :args (@t164)) % 1.02/1.24 (step @p133 :rule cong :premises (@p132) :args (@t165)) % 1.02/1.24 (step @p134 :rule beta-reduce :args ((= (_ @t167 @t161) @t165))) % 1.02/1.24 (step @p135 :rule trans :premises (@p134 @p133)) % 1.02/1.24 (step @p136 :rule aci_norm :args ((= @t169 @t99))) % 1.02/1.24 (step @p137 :rule cong :premises (@p136) :args (@t170)) % 1.02/1.24 (step @p138 :rule quant-merge-prenex :args ((= (forall @t41 @t172) @t170))) % 1.02/1.24 (step @p139 :rule alpha_equiv :args (@t173 (@list @t96) @t175)) % 1.02/1.24 (step @p140 :rule refl :args (@t94)) % 1.02/1.24 (step @p141 :rule nary_cong :premises (@p140 @p139) :args (@t176)) % 1.02/1.24 (step @p142 :rule quant-miniscope-or :args ((= @t172 @t176))) % 1.02/1.24 (step @p143 :rule trans :premises (@p142 @p141)) % 1.02/1.24 (step @p144 :rule symm :premises (@p143)) % 1.02/1.24 (step @p145 :rule cong :premises (@p144) :args ((forall @t41 (or @t94 @t179)))) % 1.02/1.24 (step @p146 :rule trans :premises (@p145 @p138)) % 1.02/1.24 (step @p147 :rule trans :premises (@p146 @p137)) % 1.02/1.24 (step @p148 :rule beta-reduce :args ((= (_ (lambda @t36 (forall @t178 (or (not (tptp.rel_d @t4 @t174)) @t177))) @t38) @t179))) % 1.02/1.24 (step @p149 :rule alpha_equiv :args (@t180 @t148 @t175)) % 1.02/1.24 (step @p150 :rule cong :premises (@p149) :args (@t181)) % 1.02/1.24 (step @p151 :rule ho_cong :premises (@p150 @p109)) % 1.02/1.24 (step @p152 :rule trans :premises (@p151 @p148)) % 1.02/1.24 (step @p153 :rule refl :args (@t94)) % 1.02/1.24 (step @p154 :rule nary_cong :premises (@p153 @p152) :args (@t182)) % 1.02/1.24 (step @p155 :rule cong :premises (@p154) :args (@t183)) % 1.02/1.24 (step @p156 :rule trans :premises (@p155 @p147)) % 1.02/1.24 (step @p157 :rule cong :premises (@p156) :args (@t184)) % 1.02/1.24 (step @p158 :rule beta-reduce :args ((= (_ @t185 @t181) @t184))) % 1.02/1.24 (step @p159 :rule trans :premises (@p158 @p157)) % 1.02/1.24 (step @p160 :rule beta-reduce :args ((= @t186 @t181))) % 1.02/1.24 (step @p161 :rule refl :args (@t185)) % 1.02/1.24 (step @p162 :rule ho_cong :premises (@p161 @p160)) % 1.02/1.24 (step @p163 :rule trans :premises (@p162 @p159)) % 1.02/1.24 (step @p164 :rule refl :args (@t167)) % 1.02/1.24 (step @p165 :rule ho_cong :premises (@p164 @p163)) % 1.02/1.24 (step @p166 :rule trans :premises (@p165 @p135)) % 1.02/1.24 (step @p167 :rule ho_cong :premises (@p166 @p128)) % 1.02/1.24 (step @p168 :rule trans :premises (@p167 @p94)) % 1.02/1.24 (step @p169 :rule refl :args (@t127)) % 1.02/1.24 (step @p170 :rule ho_cong :premises (@p169 @p168)) % 1.02/1.24 (step @p171 :rule trans :premises (@p170 @p88)) % 1.02/1.24 (step @p172 :rule cong :premises (@p171) :args ((not (_ @t127 (_ (_ @t167 (_ @t185 @t186)) (_ @t159 @t160)))))) % 1.02/1.24 (step @p173 :rule refl :args (tptp.p)) % 1.02/1.24 (step @p174 :rule beta-reduce :args ((= (_ (lambda @t36 (not @t187)) @t17) @t158))) % 1.02/1.24 (step @p175 :rule refl :args (@t17)) % 1.02/1.24 (step @p176 :rule beta-reduce :args ((= @t189 @t187))) % 1.02/1.24 (step @p177 :rule cong :premises (@p176) :args (@t190)) % 1.02/1.24 (step @p178 :rule cong :premises (@p177) :args (@t191)) % 1.02/1.24 (step @p179 :rule beta-reduce :args ((= (_ @t13 @t188) @t191))) % 1.02/1.24 (step @p180 :rule trans :premises (@p179 @p178)) % 1.02/1.24 (step @p181 :rule refl :args (@t156)) % 1.02/1.24 (step @p182 :rule refl :args (@t39)) % 1.02/1.24 (step @p183 :rule cong :premises (@p182 @p181) :args ((= @t39 @t156))) % 1.02/1.24 (step @p184 :rule symm :premises (@p183)) % 1.02/1.24 (step @p185 :rule eq_resolve :premises (@p182 @p184)) % 1.02/1.24 (step @p186 :rule cong :premises (@p185) :args (@t192)) % 1.02/1.24 (step @p187 :rule nary_cong :premises (@p140 @p186) :args (@t193)) % 1.02/1.24 (step @p188 :rule cong :premises (@p187) :args ((forall @t41 @t193))) % 1.02/1.24 (step @p189 :rule beta-reduce :args ((= @t195 @t192))) % 1.02/1.24 (step @p190 :rule nary_cong :premises (@p153 @p189) :args (@t196)) % 1.02/1.24 (step @p191 :rule cong :premises (@p190) :args (@t197)) % 1.02/1.24 (step @p192 :rule trans :premises (@p191 @p188)) % 1.02/1.24 (step @p193 :rule cong :premises (@p192) :args (@t198)) % 1.02/1.24 (step @p194 :rule beta-reduce :args ((= (_ @t185 @t194) @t198))) % 1.02/1.24 (step @p195 :rule trans :premises (@p194 @p193)) % 1.02/1.24 (step @p196 :rule beta-reduce :args ((= (_ @t13 @t9) @t194))) % 1.02/1.24 (step @p197 :rule ho_cong :premises (@p161 @p196)) % 1.02/1.24 (step @p198 :rule trans :premises (@p197 @p195)) % 1.02/1.24 (step @p199 :rule refl :args (@t13)) % 1.02/1.24 (step @p200 :rule ho_cong :premises (@p199 @p198)) % 1.02/1.24 (step @p201 :rule trans :premises (@p200 @p180)) % 1.02/1.24 (step @p202 :rule ho_cong :premises (@p201 @p175)) % 1.02/1.24 (step @p203 :rule trans :premises (@p202 @p174)) % 1.02/1.24 (step @p204 :rule refl :args (@t9)) % 1.02/1.24 (step @p205 :rule ho_cong :premises (@p7 @p204)) % 1.02/1.24 (step @p206 :rule refl :args (@t93)) % 1.02/1.24 (step @p207 :rule refl :args (@t79)) % 1.02/1.24 (step @p208 :rule cong :premises (@p207 @p206) :args ((= @t79 @t93))) % 1.02/1.24 (step @p209 :rule symm :premises (@p208)) % 1.02/1.24 (step @p210 :rule eq_resolve :premises (@p207 @p209)) % 1.02/1.24 (step @p211 :rule cong :premises (@p210) :args (@t80)) % 1.02/1.24 (step @p212 :rule nary_cong :premises (@p211 @p185) :args (@t81)) % 1.02/1.24 (step @p213 :rule cong :premises (@p212) :args (@t82)) % 1.02/1.24 (step @p214 :rule cong :premises (@p213) :args (@t83)) % 1.02/1.24 (step @p215 :rule trans :premises (@p35 @p214)) % 1.02/1.24 (step @p216 :rule ho_cong :premises (@p215 @p205)) % 1.02/1.24 (step @p217 :rule ho_cong :premises (@p7 @p216)) % 1.02/1.24 (step @p218 :rule ho_cong :premises (@p217 @p175)) % 1.02/1.24 (step @p219 :rule trans :premises (@p218 @p203)) % 1.02/1.24 (step @p220 :rule cong :premises (@p219) :args (@t85)) % 1.02/1.24 (step @p221 :rule trans :premises (@p36 @p220)) % 1.02/1.24 (step @p222 :rule ho_cong :premises (@p221 @p173)) % 1.02/1.24 (step @p223 :rule ho_cong :premises (@p221 @p222)) % 1.02/1.24 (step @p224 :rule ho_cong :premises (@p215 @p173)) % 1.02/1.24 (step @p225 :rule ho_cong :premises (@p215 @p224)) % 1.02/1.24 (step @p226 :rule beta-reduce :args ((= (_ @t200 @t17) @t166))) % 1.02/1.24 (step @p227 :rule beta-reduce :args ((= (_ (lambda @t201 @t199) @t14) @t200))) % 1.02/1.24 (step @p228 :rule refl :args (@t14)) % 1.02/1.24 (step @p229 :rule refl :args (@t15)) % 1.02/1.24 (step @p230 :rule beta-reduce :args ((= @t202 @t11))) % 1.02/1.24 (step @p231 :rule nary_cong :premises (@p230 @p229) :args (@t203)) % 1.02/1.24 (step @p232 :rule cong :premises (@p231) :args (@t204)) % 1.02/1.24 (step @p233 :rule beta-reduce :args ((= (_ @t16 @t194) @t204))) % 1.02/1.24 (step @p234 :rule trans :premises (@p233 @p232)) % 1.02/1.24 (step @p235 :rule refl :args (@t16)) % 1.02/1.24 (step @p236 :rule ho_cong :premises (@p235 @p196)) % 1.02/1.24 (step @p237 :rule trans :premises (@p236 @p234)) % 1.02/1.24 (step @p238 :rule ho_cong :premises (@p237 @p228)) % 1.02/1.24 (step @p239 :rule trans :premises (@p238 @p227)) % 1.02/1.24 (step @p240 :rule ho_cong :premises (@p239 @p175)) % 1.02/1.24 (step @p241 :rule trans :premises (@p240 @p226)) % 1.02/1.24 (step @p242 :rule ho_cong :premises (@p8 @p205)) % 1.02/1.24 (step @p243 :rule ho_cong :premises (@p242 @p228)) % 1.02/1.24 (step @p244 :rule ho_cong :premises (@p243 @p175)) % 1.02/1.24 (step @p245 :rule trans :premises (@p244 @p241)) % 1.02/1.24 (step @p246 :rule cong :premises (@p245) :args (@t23)) % 1.02/1.24 (step @p247 :rule trans :premises (@p10 @p246)) % 1.02/1.24 (step @p248 :rule ho_cong :premises (@p247 @p225)) % 1.02/1.24 (step @p249 :rule ho_cong :premises (@p248 @p223)) % 1.02/1.24 (step @p250 :rule refl :args (@t126)) % 1.02/1.24 (step @p251 :rule refl :args (@t10)) % 1.02/1.24 (step @p252 :rule cong :premises (@p251 @p250) :args ((= @t10 @t126))) % 1.02/1.24 (step @p253 :rule symm :premises (@p252)) % 1.02/1.24 (step @p254 :rule eq_resolve :premises (@p251 @p253)) % 1.02/1.24 (step @p255 :rule cong :premises (@p254) :args (@t73)) % 1.02/1.24 (step @p256 :rule cong :premises (@p255) :args (@t75)) % 1.02/1.24 (step @p257 :rule trans :premises (@p31 @p256)) % 1.02/1.24 (step @p258 :rule ho_cong :premises (@p257 @p249)) % 1.02/1.24 (step @p259 :rule cong :premises (@p258) :args (@t1)) % 1.02/1.24 (step @p260 :rule trans :premises (@p259 @p172)) % 1.02/1.24 (step @p261 :rule eq_resolve :premises (@p3 @p260)) % 1.02/1.24 (step @p262 :rule skolemize :premises (@p261)) % 1.02/1.24 (step @p263 :rule bool-double-not-elim :args (@t206)) % 1.02/1.24 (step @p264 :rule refl :args (@t210)) % 1.02/1.24 (step @p265 :rule nary_cong :premises (@p264 @p263) :args ((or @t210 (not @t207)))) % 1.02/1.24 (step @p266 :rule cnf_or_neg :args (@t210 1)) % 1.02/1.24 (step @p267 :rule eq_resolve :premises (@p266 @p265)) % 1.02/1.24 (step @p268 :rule reordering :premises (@p267) :args ((or @t206 @t210))) % 1.02/1.24 (step @p269 :rule chain_m_resolution :premises (@p268 @p262) :args (@t206 @t110 @t211)) % 1.02/1.24 (step @p270 :rule instantiate :premises (@p269) :args (@t212)) % 1.02/1.24 (step @p271 :rule bool-double-not-elim :args (@t208)) % 1.02/1.24 (step @p272 :rule nary_cong :premises (@p264 @p271) :args ((or @t210 (not @t209)))) % 1.02/1.24 (step @p273 :rule cnf_or_neg :args (@t210 0)) % 1.02/1.24 (step @p274 :rule eq_resolve :premises (@p273 @p272)) % 1.02/1.24 (step @p275 :rule reordering :premises (@p274) :args ((or @t208 @t210))) % 1.02/1.24 (step @p276 :rule chain_m_resolution :premises (@p275 @p262) :args (@t208 @t110 @t211)) % 1.02/1.24 (step @p277 :rule instantiate :premises (@p276) :args (@t212)) % 1.02/1.24 (step @p278 :rule cnf_or_pos :args (@t214)) % 1.02/1.24 (step @p279 :rule reordering :premises (@p278) :args ((or @t108 @t115 @t213 (not @t214)))) % 1.02/1.24 (step @p280 :rule chain_m_resolution :premises (@p279 @p69 @p84 @p277) :args (@t213 (@list false false false) (@list @t106 @t113 @t214))) % 1.02/1.24 (step @p281 :rule cnf_or_pos :args (@t216)) % 1.02/1.24 (step @p282 :rule reordering :premises (@p281) :args ((or @t108 @t115 @t215 (not @t216)))) % 1.02/1.24 (step @p283 false :rule chain_m_resolution :premises (@p282 @p280 @p270 @p84 @p69) :args (false (@list false false false false) (@list @t213 @t216 @t113 @t106))) % 1.02/1.24 ) % 1.02/1.24 % SZS output end Proof % 1.02/1.24 % cvc5 exiting %------------------------------------------------------------------------------