%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO576^7 : TPTP v9.2.1. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n011.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 09:13:09 AM UTC 2026 % Result : Theorem 0.83s 1.10s % Output : Proof 0.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO576^7 : TPTP v9.2.1. Released v5.5.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n011.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Wed Jun 3 00:21:05 EDT 2026 % 0.16/0.35 % CPUTime : % 0.31/0.51 %----Proving TH0 % 0.83/1.10 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.83/1.10 % SZS status Theorem % 0.83/1.10 % SZS output start Proof % 0.83/1.10 ( % 0.83/1.10 (declare-sort $$unsorted 0) % 0.83/1.10 (declare-sort tptp.mu 0) % 0.83/1.10 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 0.83/1.10 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.83/1.10 (declare-const tptp.p (-> $$unsorted Bool)) % 0.83/1.10 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.83/1.10 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.83/1.10 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.83/1.10 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.83/1.10 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.83/1.10 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.83/1.10 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.83/1.10 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.83/1.10 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.83/1.10 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.83/1.10 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.83/1.10 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.83/1.10 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.83/1.10 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.exists_in_world _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.83/1.10 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.83/1.10 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.83/1.10 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.83/1.10 (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)))))))) % 0.83/1.10 (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)))))))) % 0.83/1.10 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.83/1.10 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.83/1.10 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.83/1.10 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.83/1.10 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.83/1.10 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.83/1.10 (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))))))))))))) % 0.83/1.10 (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)))))) % 0.83/1.10 (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)))))) % 0.83/1.10 (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))))))) % 0.83/1.10 (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))))))) % 0.83/1.10 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.83/1.10 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.83/1.10 (define @t1 () (@var "V" $$unsorted)) % 0.83/1.10 (define @t2 () (@var "X" tptp.mu)) % 0.83/1.10 (define @t3 () (_ tptp.exists_in_world @t2)) % 0.83/1.10 (define @t4 () (_ @t3 @t1)) % 0.83/1.10 (define @t5 () (@list @t2)) % 0.83/1.10 (define @t6 () (@list @t1)) % 0.83/1.10 (define @t7 () (@var "W" $$unsorted)) % 0.83/1.10 (define @t8 () (_ @t3 @t7)) % 0.83/1.10 (define @t9 () (_ tptp.mdia_s4 (_ tptp.mbox_s4 tptp.p))) % 0.83/1.10 (define @t10 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mdia_s4 (_ tptp.mbox_s4 @t9))) @t9)))) % 0.83/1.10 (define @t11 () (@var "Y" (-> $$unsorted Bool))) % 0.83/1.10 (define @t12 () (@var "X" (-> $$unsorted Bool))) % 0.83/1.10 (define @t13 () (lambda (@list @t12 @t11 @t7) (= (_ @t12 @t7) (_ @t11 @t7)))) % 0.83/1.10 (define @t14 () (@var "Phi" (-> $$unsorted Bool))) % 0.83/1.10 (define @t15 () (_ @t14 @t7)) % 0.83/1.10 (define @t16 () (not @t15)) % 0.83/1.10 (define @t17 () (@list @t14 @t7)) % 0.83/1.10 (define @t18 () (lambda @t17 @t16)) % 0.83/1.10 (define @t19 () (@var "Psi" (-> $$unsorted Bool))) % 0.83/1.10 (define @t20 () (_ @t19 @t7)) % 0.83/1.10 (define @t21 () (lambda (@list @t14 @t19 @t7) (or @t15 @t20))) % 0.83/1.11 (define @t22 () (_ @t14 @t1)) % 0.83/1.11 (define @t23 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.83/1.11 (define @t24 () (lambda (@list @t23 @t14 @t7) (forall @t6 (or (not (_ (_ @t23 @t7) @t1)) @t22)))) % 0.83/1.11 (define @t25 () (@var "P" (-> $$unsorted Bool))) % 0.83/1.11 (define @t26 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.83/1.11 (define @t27 () (_ @t26 @t25)) % 0.83/1.11 (define @t28 () (lambda (@list @t26 @t7) (forall (@list @t25) (_ @t27 @t7)))) % 0.83/1.11 (define @t29 () (@list @t7)) % 0.83/1.11 (define @t30 () (lambda @t29 true)) % 0.83/1.11 (define @t31 () (@var "__flatten_var_0" $$unsorted)) % 0.83/1.11 (define @t32 () (_ tptp.mnot @t19)) % 0.83/1.11 (define @t33 () (_ tptp.mnot @t14)) % 0.83/1.11 (define @t34 () (_ tptp.mor @t33)) % 0.83/1.11 (define @t35 () (@list @t14 @t19 @t31)) % 0.83/1.11 (define @t36 () (lambda @t35 (_ (_ tptp.mnot (_ @t34 @t32)) @t31))) % 0.83/1.11 (define @t37 () (lambda @t35 (_ (_ @t34 @t19) @t31))) % 0.83/1.11 (define @t38 () (lambda @t35 (_ (_ (_ tptp.mor @t32) @t14) @t31))) % 0.83/1.11 (define @t39 () (lambda @t35 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t14) @t19)) (_ (_ tptp.mimplies @t19) @t14)) @t31))) % 0.83/1.11 (define @t40 () (lambda @t35 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t14) @t19)) @t31))) % 0.83/1.11 (define @t41 () (lambda (@list @t23 @t14 @t31) (_ (_ tptp.mnot (_ (_ tptp.mbox @t23) @t33)) @t31))) % 0.83/1.11 (define @t42 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.83/1.11 (define @t43 () (_ @t42 @t2)) % 0.83/1.11 (define @t44 () (lambda (@list @t42 @t7) (forall @t5 (=> @t8 (_ @t43 @t7))))) % 0.83/1.11 (define @t45 () (lambda (@list @t42 @t31) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t2 @t31) (_ (_ tptp.mnot @t43) @t31)))) @t31))) % 0.83/1.11 (define @t46 () (lambda (@list @t26 @t31) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t25 @t31) (_ (_ tptp.mnot @t27) @t31)))) @t31))) % 0.83/1.11 (define @t47 () (@var "S" $$unsorted)) % 0.83/1.11 (define @t48 () (_ @t23 @t47)) % 0.83/1.11 (define @t49 () (@list @t47)) % 0.83/1.11 (define @t50 () (@list @t23)) % 0.83/1.11 (define @t51 () (lambda @t50 (forall @t49 (_ @t48 @t47)))) % 0.83/1.11 (define @t52 () (@var "T" $$unsorted)) % 0.83/1.11 (define @t53 () (_ @t23 @t52)) % 0.83/1.11 (define @t54 () (_ @t48 @t52)) % 0.83/1.11 (define @t55 () (lambda @t50 (forall (@list @t47 @t52) (=> @t54 (_ @t53 @t47))))) % 0.83/1.11 (define @t56 () (@list @t52)) % 0.83/1.11 (define @t57 () (lambda @t50 (forall @t49 (exists @t56 @t54)))) % 0.83/1.11 (define @t58 () (@var "U" $$unsorted)) % 0.83/1.11 (define @t59 () (_ @t48 @t58)) % 0.83/1.11 (define @t60 () (_ @t53 @t58)) % 0.83/1.11 (define @t61 () (and @t54 @t60)) % 0.83/1.11 (define @t62 () (@list @t47 @t52 @t58)) % 0.83/1.11 (define @t63 () (forall @t62 (=> @t61 @t59))) % 0.83/1.11 (define @t64 () (lambda @t50 @t63)) % 0.83/1.11 (define @t65 () (and @t54 @t59)) % 0.83/1.11 (define @t66 () (lambda @t50 (forall @t62 (=> @t65 @t60)))) % 0.83/1.11 (define @t67 () (= @t52 @t58)) % 0.83/1.11 (define @t68 () (lambda @t50 (forall @t62 (=> @t65 @t67)))) % 0.83/1.11 (define @t69 () (@list @t58)) % 0.83/1.11 (define @t70 () (lambda @t50 (forall @t49 (exists @t56 (and @t54 (forall @t69 (=> @t59 @t67))))))) % 0.83/1.11 (define @t71 () (_ @t23 @t58)) % 0.83/1.11 (define @t72 () (_ @t71 @t52)) % 0.83/1.11 (define @t73 () (lambda @t50 (forall @t62 (=> @t54 (exists @t69 (and @t59 @t72)))))) % 0.83/1.11 (define @t74 () (lambda @t50 (forall @t62 (=> @t65 (or @t60 @t67 @t72))))) % 0.83/1.11 (define @t75 () (lambda @t50 (forall @t62 (=> @t65 (exists @t6 (and (_ @t53 @t1) (_ @t71 @t1))))))) % 0.83/1.11 (define @t76 () (forall @t29 @t15)) % 0.83/1.11 (define @t77 () (@list @t14)) % 0.83/1.11 (define @t78 () (lambda @t77 @t76)) % 0.83/1.11 (define @t79 () (lambda @t77 (exists @t29 @t15))) % 0.83/1.11 (define @t80 () (lambda @t77 (exists @t29 @t16))) % 0.83/1.11 (define @t81 () (lambda @t77 (forall @t29 @t16))) % 0.83/1.11 (define @t82 () (_ (_ tptp.rel_s4 @t7) @t1)) % 0.83/1.11 (define @t83 () (not @t82)) % 0.83/1.11 (define @t84 () (or @t83 @t22)) % 0.83/1.11 (define @t85 () (forall @t6 @t84)) % 0.83/1.11 (define @t86 () (lambda @t17 @t85)) % 0.83/1.11 (define @t87 () (@list @t14 @t31)) % 0.83/1.11 (define @t88 () (lambda @t87 (_ (_ tptp.mnot (_ tptp.mbox_s4 @t33)) @t31))) % 0.83/1.11 (define @t89 () (@var "BOUND_VARIABLE_8462" $$unsorted)) % 0.83/1.11 (define @t90 () (tptp.p @t89)) % 0.83/1.11 (define @t91 () (@var "BOUND_VARIABLE_8486" $$unsorted)) % 0.83/1.11 (define @t92 () (@list @t89)) % 0.83/1.11 (define @t93 () (not (forall @t92 (or (not (tptp.rel_s4 @t91 @t89)) @t90)))) % 0.83/1.11 (define @t94 () (@var "BOUND_VARIABLE_8516" $$unsorted)) % 0.83/1.11 (define @t95 () (@list @t91)) % 0.83/1.11 (define @t96 () (not (forall @t95 (or (not (tptp.rel_s4 @t94 @t91)) @t93)))) % 0.83/1.11 (define @t97 () (@var "BOUND_VARIABLE_8564" $$unsorted)) % 0.83/1.11 (define @t98 () (@list @t94)) % 0.83/1.11 (define @t99 () (not (forall @t98 (or (not (tptp.rel_s4 @t97 @t94)) @t96)))) % 0.83/1.11 (define @t100 () (not (tptp.rel_s4 @t7 @t97))) % 0.83/1.11 (define @t101 () (forall @t92 (or (not (tptp.rel_s4 @t1 @t89)) @t90))) % 0.83/1.11 (define @t102 () (not @t101)) % 0.83/1.11 (define @t103 () (tptp.rel_s4 @t7 @t1)) % 0.83/1.11 (define @t104 () (not @t103)) % 0.83/1.11 (define @t105 () (not (forall @t6 (or @t104 @t102)))) % 0.83/1.11 (define @t106 () (or @t105 @t100 @t99)) % 0.83/1.11 (define @t107 () (or @t100 @t99)) % 0.83/1.11 (define @t108 () (or @t107 @t105)) % 0.83/1.11 (define @t109 () (@list @t7 @t97)) % 0.83/1.11 (define @t110 () (forall @t109 @t108)) % 0.83/1.11 (define @t111 () (@list @t97)) % 0.83/1.11 (define @t112 () (forall @t111 @t108)) % 0.83/1.11 (define @t113 () (forall @t111 @t107)) % 0.83/1.11 (define @t114 () (@list @t1)) % 0.83/1.11 (define @t115 () (or @t113 @t105)) % 0.83/1.11 (define @t116 () (forall @t98 (or (not (tptp.rel_s4 @t1 @t94)) @t96))) % 0.83/1.11 (define @t117 () (not @t116)) % 0.83/1.11 (define @t118 () (or (forall @t6 (or @t104 @t117)) @t105)) % 0.83/1.11 (define @t119 () (not (tptp.rel_s4 @t31 @t1))) % 0.83/1.11 (define @t120 () (forall @t6 (or @t119 @t102))) % 0.83/1.11 (define @t121 () (not @t120)) % 0.83/1.11 (define @t122 () (forall @t6 (or @t119 @t117))) % 0.83/1.11 (define @t123 () (@list @t31)) % 0.83/1.11 (define @t124 () (lambda @t123 (or @t122 @t121))) % 0.83/1.11 (define @t125 () (_ @t124 @t7)) % 0.83/1.11 (define @t126 () (forall @t29 @t125)) % 0.83/1.11 (define @t127 () (_ @t14 @t7)) % 0.83/1.11 (define @t128 () (lambda @t77 (forall @t29 @t127))) % 0.83/1.11 (define @t129 () (lambda @t123 @t121)) % 0.83/1.11 (define @t130 () (_ @t129 @t31)) % 0.83/1.11 (define @t131 () (or @t122 @t130)) % 0.83/1.11 (define @t132 () (lambda @t123 @t131)) % 0.83/1.11 (define @t133 () (_ @t19 @t31)) % 0.83/1.11 (define @t134 () (@list @t19 @t31)) % 0.83/1.11 (define @t135 () (forall @t6 (or @t104 (tptp.p @t1)))) % 0.83/1.11 (define @t136 () (lambda @t29 @t135)) % 0.83/1.11 (define @t137 () (not (_ @t136 @t1))) % 0.83/1.11 (define @t138 () (or @t119 @t137)) % 0.83/1.11 (define @t139 () (forall @t6 @t138)) % 0.83/1.11 (define @t140 () (not @t139)) % 0.83/1.11 (define @t141 () (lambda @t123 @t140)) % 0.83/1.11 (define @t142 () (_ @t14 @t1)) % 0.83/1.11 (define @t143 () (not @t142)) % 0.83/1.11 (define @t144 () (not (forall @t6 (or @t119 @t143)))) % 0.83/1.11 (define @t145 () (lambda @t87 @t144)) % 0.83/1.11 (define @t146 () (lambda @t17 (forall @t6 (or @t104 @t142)))) % 0.83/1.11 (define @t147 () (_ @t146 tptp.p)) % 0.83/1.11 (define @t148 () (not @t122)) % 0.83/1.11 (define @t149 () (lambda @t123 @t148)) % 0.83/1.11 (define @t150 () (_ @t149 @t31)) % 0.83/1.11 (define @t151 () (not @t150)) % 0.83/1.11 (define @t152 () (or @t151 @t133)) % 0.83/1.11 (define @t153 () (lambda @t134 @t152)) % 0.83/1.11 (define @t154 () (or (not (_ @t14 @t31)) @t133)) % 0.83/1.11 (define @t155 () (lambda @t35 @t154)) % 0.83/1.11 (define @t156 () (not (forall @t95 (or (not (tptp.rel_s4 @t1 @t91)) @t93)))) % 0.83/1.11 (define @t157 () (forall @t6 (or @t104 @t156))) % 0.83/1.11 (define @t158 () (lambda @t29 @t157)) % 0.83/1.11 (define @t159 () (not (_ @t158 @t1))) % 0.83/1.11 (define @t160 () (or @t119 @t159)) % 0.83/1.11 (define @t161 () (forall @t6 @t160)) % 0.83/1.11 (define @t162 () (not @t161)) % 0.83/1.11 (define @t163 () (lambda @t123 @t162)) % 0.83/1.11 (define @t164 () (or @t104 (_ @t129 @t1))) % 0.83/1.11 (define @t165 () (forall @t6 @t164)) % 0.83/1.11 (define @t166 () (lambda @t29 @t165)) % 0.83/1.11 (define @t167 () (_ @t145 @t147)) % 0.83/1.11 (define @t168 () (forall @t6 (or @t104 @t143))) % 0.83/1.11 (define @t169 () (lambda @t29 @t168)) % 0.83/1.11 (define @t170 () (_ @t169 @t7)) % 0.83/1.11 (define @t171 () (not @t170)) % 0.83/1.11 (define @t172 () (lambda @t29 @t171)) % 0.83/1.11 (define @t173 () (not @t22)) % 0.83/1.11 (define @t174 () (or @t104 @t173)) % 0.83/1.11 (define @t175 () (lambda @t29 @t16)) % 0.83/1.11 (define @t176 () (_ @t175 @t1)) % 0.83/1.11 (define @t177 () (or @t104 @t176)) % 0.83/1.11 (define @t178 () (forall @t6 @t177)) % 0.83/1.11 (define @t179 () (lambda @t29 @t178)) % 0.83/1.11 (define @t180 () (or @t16 @t20)) % 0.83/1.11 (define @t181 () (lambda @t29 @t180)) % 0.83/1.11 (define @t182 () (@list @t19 @t7)) % 0.83/1.11 (define @t183 () (_ @t175 @t7)) % 0.83/1.11 (define @t184 () (or @t183 @t20)) % 0.83/1.11 (define @t185 () (lambda @t182 @t184)) % 0.83/1.11 (define @t186 () (forall @t109 @t106)) % 0.83/1.11 (define @t187 () (@quantifiers_skolemize @t186 0)) % 0.83/1.11 (define @t188 () (forall @t6 (or (not (tptp.rel_s4 @t187 @t1)) @t102))) % 0.83/1.11 (define @t189 () (@quantifiers_skolemize @t186 1)) % 0.83/1.11 (define @t190 () (forall @t98 (or (not (tptp.rel_s4 @t189 @t94)) @t96))) % 0.83/1.11 (define @t191 () (not @t190)) % 0.83/1.11 (define @t192 () (tptp.rel_s4 @t187 @t189)) % 0.83/1.11 (define @t193 () (not @t192)) % 0.83/1.11 (define @t194 () (not @t188)) % 0.83/1.11 (define @t195 () (or @t194 @t193 @t191)) % 0.83/1.11 (define @t196 () (@list true)) % 0.83/1.11 (define @t197 () (@list @t195)) % 0.83/1.11 (define @t198 () (_ @t23 @t47 @t58)) % 0.83/1.11 (define @t199 () (_ @t23 @t52 @t58)) % 0.83/1.11 (define @t200 () (_ @t23 @t47 @t52)) % 0.83/1.11 (define @t201 () (not @t60)) % 0.83/1.11 (define @t202 () (not @t54)) % 0.83/1.11 (define @t203 () (or @t202 @t201 @t59)) % 0.83/1.11 (define @t204 () (forall @t92 (or (not (tptp.rel_s4 @t189 @t89)) @t90))) % 0.83/1.11 (define @t205 () (@quantifiers_skolemize @t204 0)) % 0.83/1.11 (define @t206 () (forall @t95 (or (not (tptp.rel_s4 @t205 @t91)) @t93))) % 0.83/1.11 (define @t207 () (@quantifiers_skolemize @t206 0)) % 0.83/1.11 (define @t208 () (not @t204)) % 0.83/1.11 (define @t209 () (or @t193 @t208)) % 0.83/1.11 (define @t210 () (@list false false)) % 0.83/1.11 (define @t211 () (tptp.rel_s4 @t189 @t205)) % 0.83/1.11 (define @t212 () (not @t211)) % 0.83/1.11 (define @t213 () (or @t212 (tptp.p @t205))) % 0.83/1.11 (define @t214 () (not @t206)) % 0.83/1.11 (define @t215 () (or @t212 @t214)) % 0.83/1.11 (define @t216 () (tptp.rel_s4 @t205 @t207)) % 0.83/1.11 (define @t217 () (forall @t92 (or (not (tptp.rel_s4 @t207 @t89)) @t90))) % 0.83/1.11 (define @t218 () (not @t217)) % 0.83/1.11 (define @t219 () (not @t216)) % 0.83/1.11 (define @t220 () (or @t219 @t218)) % 0.83/1.11 (define @t221 () (@list @t220)) % 0.83/1.11 (define @t222 () (tptp.rel_s4 @t189 @t207)) % 0.83/1.11 (define @t223 () (or @t212 @t219 @t222)) % 0.83/1.11 (define @t224 () (@list false false false)) % 0.83/1.11 (define @t225 () (tptp.rel_s4 @t187 @t207)) % 0.83/1.11 (define @t226 () (not @t222)) % 0.83/1.11 (define @t227 () (or @t193 @t226 @t225)) % 0.83/1.11 (define @t228 () (not @t225)) % 0.83/1.11 (define @t229 () (or @t228 @t218)) % 0.83/1.11 (define @t230 () (not @t229)) % 0.83/1.11 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.83/1.11 (assume @p2 (forall @t6 (exists @t5 @t4))) % 0.83/1.11 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 0.83/1.11 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 0.83/1.11 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 0.83/1.11 (assume @p6 @t10) % 0.83/1.11 (assume @p7 true) % 0.83/1.11 (step @p8 (= tptp.meq_prop @t13) :rule refl :args (@t13)) % 0.83/1.11 (step @p9 (= tptp.mnot @t18) :rule refl :args (@t18)) % 0.83/1.11 (step @p10 (= tptp.mor @t21) :rule refl :args (@t21)) % 0.83/1.11 (step @p11 (= tptp.mbox @t24) :rule refl :args (@t24)) % 0.83/1.11 (step @p12 (= tptp.mforall_prop @t28) :rule refl :args (@t28)) % 0.83/1.11 (step @p13 (= tptp.mtrue @t30) :rule refl :args (@t30)) % 0.83/1.11 (step @p14 (= tptp.mand @t36) :rule refl :args (@t36)) % 0.83/1.11 (step @p15 (= tptp.mimplies @t37) :rule refl :args (@t37)) % 0.83/1.11 (step @p16 (= tptp.mimplied @t38) :rule refl :args (@t38)) % 0.83/1.11 (step @p17 (= tptp.mequiv @t39) :rule refl :args (@t39)) % 0.83/1.11 (step @p18 (= tptp.mxor @t40) :rule refl :args (@t40)) % 0.83/1.11 (step @p19 (= tptp.mdia @t41) :rule refl :args (@t41)) % 0.83/1.11 (step @p20 (= tptp.mforall_ind @t44) :rule refl :args (@t44)) % 0.83/1.11 (step @p21 (= tptp.mexists_ind @t45) :rule refl :args (@t45)) % 0.83/1.11 (step @p22 (= tptp.mexists_prop @t46) :rule refl :args (@t46)) % 0.83/1.11 (step @p23 (= tptp.mreflexive @t51) :rule refl :args (@t51)) % 0.83/1.11 (step @p24 (= tptp.msymmetric @t55) :rule refl :args (@t55)) % 0.83/1.11 (step @p25 (= tptp.mserial @t57) :rule refl :args (@t57)) % 0.83/1.11 (step @p26 (= tptp.mtransitive @t64) :rule refl :args (@t64)) % 0.83/1.11 (step @p27 (= tptp.meuclidean @t66) :rule refl :args (@t66)) % 0.83/1.11 (step @p28 (= tptp.mpartially_functional @t68) :rule refl :args (@t68)) % 0.83/1.11 (step @p29 (= tptp.mfunctional @t70) :rule refl :args (@t70)) % 0.83/1.11 (step @p30 (= tptp.mweakly_dense @t73) :rule refl :args (@t73)) % 0.83/1.11 (step @p31 (= tptp.mweakly_connected @t74) :rule refl :args (@t74)) % 0.83/1.11 (step @p32 (= tptp.mweakly_directed @t75) :rule refl :args (@t75)) % 0.83/1.11 (step @p33 (= tptp.mvalid @t78) :rule refl :args (@t78)) % 0.83/1.11 (step @p34 (= tptp.msatisfiable @t79) :rule refl :args (@t79)) % 0.83/1.11 (step @p35 (= tptp.mcountersatisfiable @t80) :rule refl :args (@t80)) % 0.83/1.11 (step @p36 (= tptp.minvalid @t81) :rule refl :args (@t81)) % 0.83/1.11 (step @p37 (= tptp.mbox_s4 @t86) :rule refl :args (@t86)) % 0.83/1.11 (step @p38 (= tptp.mdia_s4 @t88) :rule refl :args (@t88)) % 0.83/1.11 (step @p39 :rule aci_norm :args ((= @t108 @t106))) % 0.83/1.11 (step @p40 :rule cong :premises (@p39) :args (@t110)) % 0.83/1.11 (step @p41 :rule quant-merge-prenex :args ((= (forall @t29 @t112) @t110))) % 0.83/1.11 (step @p42 :rule refl :args (@t105)) % 0.83/1.11 (step @p43 :rule alpha_equiv :args (@t113 (@list @t97) @t114)) % 0.83/1.11 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t115)) % 0.83/1.11 (step @p45 :rule quant-miniscope-or :args ((= @t112 @t115))) % 0.83/1.11 (step @p46 :rule trans :premises (@p45 @p44)) % 0.83/1.11 (step @p47 :rule symm :premises (@p46)) % 0.83/1.11 (step @p48 :rule cong :premises (@p47) :args ((forall @t29 @t118))) % 0.83/1.11 (step @p49 :rule trans :premises (@p48 @p41)) % 0.83/1.11 (step @p50 :rule trans :premises (@p49 @p40)) % 0.83/1.11 (step @p51 :rule beta-reduce :args ((= @t125 @t118))) % 0.83/1.11 (step @p52 :rule cong :premises (@p51) :args (@t126)) % 0.83/1.11 (step @p53 :rule trans :premises (@p52 @p50)) % 0.83/1.11 (step @p54 :rule beta-reduce :args ((= (_ @t128 @t124) @t126))) % 0.83/1.11 (step @p55 :rule trans :premises (@p54 @p53)) % 0.83/1.11 (step @p56 :rule beta-reduce :args ((= @t130 @t121))) % 0.83/1.11 (step @p57 :rule refl :args (@t122)) % 0.83/1.11 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t131)) % 0.83/1.11 (step @p59 :rule cong :premises (@p58) :args (@t132)) % 0.83/1.11 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t134 (or @t122 @t133)) @t129) @t132))) % 0.83/1.11 (step @p61 :rule trans :premises (@p60 @p59)) % 0.83/1.11 (step @p62 :rule beta-reduce :args ((= (_ (lambda @t29 (forall @t92 (or (not (tptp.rel_s4 @t7 @t89)) @t90))) @t1) @t101))) % 0.83/1.11 (step @p63 :rule refl :args (@t1)) % 0.83/1.11 (step @p64 :rule alpha_equiv :args (@t135 @t114 (@list @t89))) % 0.83/1.11 (step @p65 :rule cong :premises (@p64) :args (@t136)) % 0.83/1.11 (step @p66 :rule ho_cong :premises (@p65 @p63)) % 0.83/1.11 (step @p67 :rule trans :premises (@p66 @p62)) % 0.83/1.11 (step @p68 :rule cong :premises (@p67) :args (@t137)) % 0.83/1.11 (step @p69 :rule refl :args (@t119)) % 0.83/1.11 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t138)) % 0.83/1.11 (step @p71 :rule cong :premises (@p70) :args (@t139)) % 0.83/1.11 (step @p72 :rule cong :premises (@p71) :args (@t140)) % 0.83/1.11 (step @p73 :rule cong :premises (@p72) :args (@t141)) % 0.83/1.11 (step @p74 :rule beta-reduce :args ((= (_ @t145 @t136) @t141))) % 0.83/1.11 (step @p75 :rule trans :premises (@p74 @p73)) % 0.83/1.11 (step @p76 :rule beta-reduce :args ((= @t147 @t136))) % 0.83/1.11 (step @p77 :rule refl :args (@t145)) % 0.83/1.11 (step @p78 :rule ho_cong :premises (@p77 @p76)) % 0.83/1.11 (step @p79 :rule trans :premises (@p78 @p75)) % 0.83/1.11 (step @p80 :rule refl :args (@t133)) % 0.83/1.11 (step @p81 :rule bool-double-not-elim :args (@t122)) % 0.83/1.11 (step @p82 :rule beta-reduce :args ((= @t150 @t148))) % 0.83/1.11 (step @p83 :rule cong :premises (@p82) :args (@t151)) % 0.83/1.11 (step @p84 :rule trans :premises (@p83 @p81)) % 0.83/1.11 (step @p85 :rule nary_cong :premises (@p84 @p80) :args (@t152)) % 0.83/1.11 (step @p86 :rule cong :premises (@p85) :args (@t153)) % 0.83/1.11 (step @p87 :rule beta-reduce :args ((= (_ @t155 @t149) @t153))) % 0.83/1.11 (step @p88 :rule trans :premises (@p87 @p86)) % 0.83/1.11 (step @p89 :rule beta-reduce :args ((= (_ (lambda @t29 (forall @t98 (or (not (tptp.rel_s4 @t7 @t94)) @t96))) @t1) @t116))) % 0.83/1.11 (step @p90 :rule alpha_equiv :args (@t157 @t114 (@list @t94))) % 0.83/1.11 (step @p91 :rule cong :premises (@p90) :args (@t158)) % 0.83/1.11 (step @p92 :rule ho_cong :premises (@p91 @p63)) % 0.83/1.11 (step @p93 :rule trans :premises (@p92 @p89)) % 0.83/1.11 (step @p94 :rule cong :premises (@p93) :args (@t159)) % 0.83/1.11 (step @p95 :rule nary_cong :premises (@p69 @p94) :args (@t160)) % 0.83/1.11 (step @p96 :rule cong :premises (@p95) :args (@t161)) % 0.83/1.11 (step @p97 :rule cong :premises (@p96) :args (@t162)) % 0.83/1.11 (step @p98 :rule cong :premises (@p97) :args (@t163)) % 0.83/1.11 (step @p99 :rule beta-reduce :args ((= (_ @t145 @t158) @t163))) % 0.83/1.11 (step @p100 :rule trans :premises (@p99 @p98)) % 0.83/1.11 (step @p101 :rule beta-reduce :args ((= (_ (lambda @t123 (not (forall @t95 (or (not (tptp.rel_s4 @t31 @t91)) @t93)))) @t1) @t156))) % 0.83/1.11 (step @p102 :rule alpha_equiv :args (@t120 @t114 (@list @t91))) % 0.83/1.11 (step @p103 :rule cong :premises (@p102) :args (@t121)) % 0.83/1.11 (step @p104 :rule cong :premises (@p103) :args (@t129)) % 0.83/1.11 (step @p105 :rule ho_cong :premises (@p104 @p63)) % 0.83/1.11 (step @p106 :rule trans :premises (@p105 @p101)) % 0.83/1.11 (step @p107 :rule refl :args (@t104)) % 0.83/1.11 (step @p108 :rule nary_cong :premises (@p107 @p106) :args (@t164)) % 0.83/1.11 (step @p109 :rule cong :premises (@p108) :args (@t165)) % 0.83/1.11 (step @p110 :rule cong :premises (@p109) :args (@t166)) % 0.83/1.11 (step @p111 :rule beta-reduce :args ((= (_ @t146 @t129) @t166))) % 0.83/1.11 (step @p112 :rule trans :premises (@p111 @p110)) % 0.83/1.11 (step @p113 :rule refl :args (@t146)) % 0.83/1.11 (step @p114 :rule ho_cong :premises (@p113 @p79)) % 0.83/1.11 (step @p115 :rule trans :premises (@p114 @p112)) % 0.83/1.11 (step @p116 :rule ho_cong :premises (@p77 @p115)) % 0.83/1.11 (step @p117 :rule trans :premises (@p116 @p100)) % 0.83/1.11 (step @p118 :rule refl :args (@t155)) % 0.83/1.11 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 0.83/1.11 (step @p120 :rule trans :premises (@p119 @p88)) % 0.83/1.11 (step @p121 :rule ho_cong :premises (@p120 @p79)) % 0.83/1.11 (step @p122 :rule trans :premises (@p121 @p61)) % 0.83/1.11 (step @p123 :rule refl :args (@t128)) % 0.83/1.11 (step @p124 :rule ho_cong :premises (@p123 @p122)) % 0.83/1.11 (step @p125 :rule trans :premises (@p124 @p55)) % 0.83/1.11 (step @p126 :rule cong :premises (@p125) :args ((not (_ @t128 (_ (_ @t155 (_ @t145 (_ @t146 @t167))) @t167))))) % 0.83/1.11 (step @p127 :rule refl :args (tptp.p)) % 0.83/1.11 (step @p128 :rule refl :args (@t142)) % 0.83/1.11 (step @p129 :rule refl :args (@t22)) % 0.83/1.11 (step @p130 :rule cong :premises (@p129 @p128) :args ((= @t22 @t142))) % 0.83/1.11 (step @p131 :rule symm :premises (@p130)) % 0.83/1.11 (step @p132 :rule eq_resolve :premises (@p129 @p131)) % 0.83/1.11 (step @p133 :rule refl :args (@t103)) % 0.83/1.11 (step @p134 :rule refl :args (@t82)) % 0.83/1.11 (step @p135 :rule cong :premises (@p134 @p133) :args ((= @t82 @t103))) % 0.83/1.11 (step @p136 :rule symm :premises (@p135)) % 0.83/1.11 (step @p137 :rule eq_resolve :premises (@p134 @p136)) % 0.83/1.11 (step @p138 :rule cong :premises (@p137) :args (@t83)) % 0.83/1.11 (step @p139 :rule nary_cong :premises (@p138 @p132) :args (@t84)) % 0.83/1.11 (step @p140 :rule cong :premises (@p139) :args (@t85)) % 0.83/1.11 (step @p141 :rule cong :premises (@p140) :args (@t86)) % 0.83/1.11 (step @p142 :rule trans :premises (@p37 @p141)) % 0.83/1.11 (step @p143 :rule ho_cong :premises (@p142 @p127)) % 0.83/1.11 (step @p144 :rule beta-reduce :args ((= (_ (lambda @t29 (not @t168)) @t31) @t144))) % 0.83/1.11 (step @p145 :rule refl :args (@t31)) % 0.83/1.11 (step @p146 :rule beta-reduce :args ((= @t170 @t168))) % 0.83/1.11 (step @p147 :rule cong :premises (@p146) :args (@t171)) % 0.83/1.11 (step @p148 :rule cong :premises (@p147) :args (@t172)) % 0.83/1.11 (step @p149 :rule beta-reduce :args ((= (_ @t18 @t169) @t172))) % 0.83/1.11 (step @p150 :rule trans :premises (@p149 @p148)) % 0.83/1.11 (step @p151 :rule cong :premises (@p132) :args (@t173)) % 0.83/1.11 (step @p152 :rule refl :args (@t104)) % 0.83/1.11 (step @p153 :rule nary_cong :premises (@p152 @p151) :args (@t174)) % 0.83/1.11 (step @p154 :rule cong :premises (@p153) :args ((forall @t6 @t174))) % 0.83/1.11 (step @p155 :rule beta-reduce :args ((= @t176 @t173))) % 0.83/1.11 (step @p156 :rule nary_cong :premises (@p107 @p155) :args (@t177)) % 0.83/1.11 (step @p157 :rule cong :premises (@p156) :args (@t178)) % 0.83/1.11 (step @p158 :rule trans :premises (@p157 @p154)) % 0.83/1.11 (step @p159 :rule cong :premises (@p158) :args (@t179)) % 0.83/1.11 (step @p160 :rule beta-reduce :args ((= (_ @t146 @t175) @t179))) % 0.83/1.11 (step @p161 :rule trans :premises (@p160 @p159)) % 0.83/1.11 (step @p162 :rule beta-reduce :args ((= (_ @t18 @t14) @t175))) % 0.83/1.11 (step @p163 :rule ho_cong :premises (@p113 @p162)) % 0.83/1.11 (step @p164 :rule trans :premises (@p163 @p161)) % 0.83/1.11 (step @p165 :rule refl :args (@t18)) % 0.83/1.11 (step @p166 :rule ho_cong :premises (@p165 @p164)) % 0.83/1.11 (step @p167 :rule trans :premises (@p166 @p150)) % 0.83/1.11 (step @p168 :rule ho_cong :premises (@p167 @p145)) % 0.83/1.11 (step @p169 :rule trans :premises (@p168 @p144)) % 0.83/1.11 (step @p170 :rule refl :args (@t14)) % 0.83/1.11 (step @p171 :rule ho_cong :premises (@p9 @p170)) % 0.83/1.11 (step @p172 :rule ho_cong :premises (@p142 @p171)) % 0.83/1.11 (step @p173 :rule ho_cong :premises (@p9 @p172)) % 0.83/1.11 (step @p174 :rule ho_cong :premises (@p173 @p145)) % 0.83/1.11 (step @p175 :rule trans :premises (@p174 @p169)) % 0.83/1.11 (step @p176 :rule cong :premises (@p175) :args (@t88)) % 0.83/1.11 (step @p177 :rule trans :premises (@p38 @p176)) % 0.83/1.11 (step @p178 :rule ho_cong :premises (@p177 @p143)) % 0.83/1.11 (step @p179 :rule ho_cong :premises (@p142 @p178)) % 0.83/1.11 (step @p180 :rule ho_cong :premises (@p177 @p179)) % 0.83/1.11 (step @p181 :rule beta-reduce :args ((= (_ @t181 @t31) @t154))) % 0.83/1.11 (step @p182 :rule beta-reduce :args ((= (_ (lambda @t182 @t180) @t19) @t181))) % 0.83/1.11 (step @p183 :rule refl :args (@t19)) % 0.83/1.11 (step @p184 :rule refl :args (@t20)) % 0.83/1.11 (step @p185 :rule beta-reduce :args ((= @t183 @t16))) % 0.83/1.11 (step @p186 :rule nary_cong :premises (@p185 @p184) :args (@t184)) % 0.83/1.11 (step @p187 :rule cong :premises (@p186) :args (@t185)) % 0.83/1.11 (step @p188 :rule beta-reduce :args ((= (_ @t21 @t175) @t185))) % 0.83/1.11 (step @p189 :rule trans :premises (@p188 @p187)) % 0.83/1.11 (step @p190 :rule refl :args (@t21)) % 0.83/1.11 (step @p191 :rule ho_cong :premises (@p190 @p162)) % 0.83/1.11 (step @p192 :rule trans :premises (@p191 @p189)) % 0.83/1.11 (step @p193 :rule ho_cong :premises (@p192 @p183)) % 0.83/1.11 (step @p194 :rule trans :premises (@p193 @p182)) % 0.83/1.11 (step @p195 :rule ho_cong :premises (@p194 @p145)) % 0.83/1.11 (step @p196 :rule trans :premises (@p195 @p181)) % 0.83/1.11 (step @p197 :rule ho_cong :premises (@p10 @p171)) % 0.83/1.11 (step @p198 :rule ho_cong :premises (@p197 @p183)) % 0.83/1.11 (step @p199 :rule ho_cong :premises (@p198 @p145)) % 0.83/1.11 (step @p200 :rule trans :premises (@p199 @p196)) % 0.83/1.11 (step @p201 :rule cong :premises (@p200) :args (@t37)) % 0.83/1.11 (step @p202 :rule trans :premises (@p15 @p201)) % 0.83/1.11 (step @p203 :rule ho_cong :premises (@p202 @p180)) % 0.83/1.11 (step @p204 :rule ho_cong :premises (@p203 @p178)) % 0.83/1.11 (step @p205 :rule refl :args (@t127)) % 0.83/1.11 (step @p206 :rule refl :args (@t15)) % 0.83/1.11 (step @p207 :rule cong :premises (@p206 @p205) :args ((= @t15 @t127))) % 0.83/1.11 (step @p208 :rule symm :premises (@p207)) % 0.83/1.11 (step @p209 :rule eq_resolve :premises (@p206 @p208)) % 0.83/1.11 (step @p210 :rule cong :premises (@p209) :args (@t76)) % 0.83/1.11 (step @p211 :rule cong :premises (@p210) :args (@t78)) % 0.83/1.11 (step @p212 :rule trans :premises (@p33 @p211)) % 0.83/1.11 (step @p213 :rule ho_cong :premises (@p212 @p204)) % 0.83/1.11 (step @p214 :rule cong :premises (@p213) :args (@t10)) % 0.83/1.11 (step @p215 :rule trans :premises (@p214 @p126)) % 0.83/1.11 (step @p216 :rule eq_resolve :premises (@p6 @p215)) % 0.83/1.11 (step @p217 :rule skolemize :premises (@p216)) % 0.83/1.11 (step @p218 :rule bool-double-not-elim :args (@t188)) % 0.83/1.11 (step @p219 :rule refl :args (@t195)) % 0.83/1.11 (step @p220 :rule nary_cong :premises (@p219 @p218) :args ((or @t195 (not @t194)))) % 0.83/1.11 (step @p221 :rule cnf_or_neg :args (@t195 0)) % 0.83/1.11 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 0.83/1.11 (step @p223 :rule reordering :premises (@p222) :args ((or @t188 @t195))) % 0.83/1.11 (step @p224 :rule chain_m_resolution :premises (@p223 @p217) :args (@t188 @t196 @t197)) % 0.83/1.11 (step @p225 :rule beta-reduce :args ((= (_ (lambda @t50 (forall @t62 (or (not @t200) (not @t199) @t198))) tptp.rel_s4) (forall @t62 (or (not (tptp.rel_s4 @t47 @t52)) (not (tptp.rel_s4 @t52 @t58)) (tptp.rel_s4 @t47 @t58)))))) % 0.83/1.11 (step @p226 :rule refl :args (tptp.rel_s4)) % 0.83/1.11 (step @p227 :rule refl :args (@t198)) % 0.83/1.11 (step @p228 :rule refl :args (@t59)) % 0.83/1.11 (step @p229 :rule cong :premises (@p228 @p227) :args ((= @t59 @t198))) % 0.83/1.11 (step @p230 :rule symm :premises (@p229)) % 0.83/1.11 (step @p231 :rule eq_resolve :premises (@p228 @p230)) % 0.83/1.11 (step @p232 :rule refl :args (@t199)) % 0.83/1.11 (step @p233 :rule refl :args (@t60)) % 0.83/1.11 (step @p234 :rule cong :premises (@p233 @p232) :args ((= @t60 @t199))) % 0.83/1.11 (step @p235 :rule symm :premises (@p234)) % 0.83/1.11 (step @p236 :rule eq_resolve :premises (@p233 @p235)) % 0.83/1.11 (step @p237 :rule cong :premises (@p236) :args (@t201)) % 0.83/1.11 (step @p238 :rule refl :args (@t200)) % 0.83/1.11 (step @p239 :rule refl :args (@t54)) % 0.83/1.11 (step @p240 :rule cong :premises (@p239 @p238) :args ((= @t54 @t200))) % 0.83/1.11 (step @p241 :rule symm :premises (@p240)) % 0.83/1.11 (step @p242 :rule eq_resolve :premises (@p239 @p241)) % 0.83/1.11 (step @p243 :rule cong :premises (@p242) :args (@t202)) % 0.83/1.11 (step @p244 :rule nary_cong :premises (@p243 @p237 @p231) :args (@t203)) % 0.83/1.11 (step @p245 :rule cong :premises (@p244) :args ((forall @t62 @t203))) % 0.83/1.11 (step @p246 :rule aci_norm :args ((= (or (or @t202 @t201) @t59) @t203))) % 0.83/1.11 (step @p247 :rule bool-and-de-morgan :args (@t54 @t60 true)) % 0.83/1.11 (step @p248 :rule nary_cong :premises (@p247 @p228) :args ((or (not @t61) @t59))) % 0.83/1.11 (step @p249 :rule trans :premises (@p248 @p246)) % 0.83/1.11 (step @p250 :rule bool-impl-elim :args (@t61 @t59)) % 0.83/1.11 (step @p251 :rule trans :premises (@p250 @p249)) % 0.83/1.11 (step @p252 :rule cong :premises (@p251) :args (@t63)) % 0.83/1.11 (step @p253 :rule trans :premises (@p252 @p245)) % 0.83/1.11 (step @p254 :rule cong :premises (@p253) :args (@t64)) % 0.83/1.11 (step @p255 :rule trans :premises (@p26 @p254)) % 0.83/1.11 (step @p256 :rule ho_cong :premises (@p255 @p226)) % 0.83/1.11 (step @p257 :rule trans :premises (@p256 @p225)) % 0.83/1.11 (step @p258 :rule eq_resolve :premises (@p4 @p257)) % 0.83/1.11 (step @p259 :rule instantiate :premises (@p258) :args ((@list @t187 @t189 @t207))) % 0.83/1.11 (step @p260 :rule instantiate :premises (@p258) :args ((@list @t189 @t205 @t207))) % 0.83/1.11 (step @p261 :rule bool-double-not-elim :args (@t190)) % 0.83/1.11 (step @p262 :rule nary_cong :premises (@p219 @p261) :args ((or @t195 (not @t191)))) % 0.83/1.11 (step @p263 :rule cnf_or_neg :args (@t195 2)) % 0.83/1.11 (step @p264 :rule eq_resolve :premises (@p263 @p262)) % 0.83/1.11 (step @p265 :rule reordering :premises (@p264) :args ((or @t190 @t195))) % 0.83/1.11 (step @p266 :rule chain_m_resolution :premises (@p265 @p217) :args (@t190 @t196 @t197)) % 0.83/1.11 (step @p267 :rule instantiate :premises (@p266) :args ((@list @t205))) % 0.83/1.11 (step @p268 :rule instantiate :premises (@p224) :args ((@list @t189))) % 0.83/1.11 (step @p269 :rule bool-double-not-elim :args (@t192)) % 0.83/1.11 (step @p270 :rule nary_cong :premises (@p219 @p269) :args ((or @t195 (not @t193)))) % 0.83/1.11 (step @p271 :rule cnf_or_neg :args (@t195 1)) % 0.83/1.11 (step @p272 :rule eq_resolve :premises (@p271 @p270)) % 0.83/1.11 (step @p273 :rule reordering :premises (@p272) :args ((or @t192 @t195))) % 0.83/1.11 (step @p274 :rule chain_m_resolution :premises (@p273 @p217) :args (@t192 @t196 @t197)) % 0.83/1.11 (step @p275 :rule cnf_or_pos :args (@t209)) % 0.83/1.11 (step @p276 :rule reordering :premises (@p275) :args ((or @t193 @t208 (not @t209)))) % 0.83/1.11 (step @p277 :rule chain_m_resolution :premises (@p276 @p274 @p268) :args (@t208 @t210 (@list @t192 @t209))) % 0.83/1.11 (step @p278 :rule skolemize :premises (@p277)) % 0.83/1.11 (step @p279 :rule bool-double-not-elim :args (@t211)) % 0.83/1.11 (step @p280 :rule refl :args (@t213)) % 0.83/1.11 (step @p281 :rule nary_cong :premises (@p280 @p279) :args ((or @t213 (not @t212)))) % 0.83/1.11 (step @p282 :rule cnf_or_neg :args (@t213 0)) % 0.83/1.11 (step @p283 :rule eq_resolve :premises (@p282 @p281)) % 0.83/1.11 (step @p284 :rule reordering :premises (@p283) :args ((or @t211 @t213))) % 0.83/1.11 (step @p285 :rule chain_m_resolution :premises (@p284 @p278) :args (@t211 @t196 (@list @t213))) % 0.83/1.11 (step @p286 :rule cnf_or_pos :args (@t215)) % 0.83/1.11 (step @p287 :rule reordering :premises (@p286) :args ((or @t212 @t214 (not @t215)))) % 0.83/1.11 (step @p288 :rule chain_m_resolution :premises (@p287 @p285 @p267) :args (@t214 @t210 (@list @t211 @t215))) % 0.83/1.11 (step @p289 :rule skolemize :premises (@p288)) % 0.83/1.11 (step @p290 :rule bool-double-not-elim :args (@t216)) % 0.83/1.11 (step @p291 :rule refl :args (@t220)) % 0.83/1.11 (step @p292 :rule nary_cong :premises (@p291 @p290) :args ((or @t220 (not @t219)))) % 0.83/1.11 (step @p293 :rule cnf_or_neg :args (@t220 0)) % 0.83/1.11 (step @p294 :rule eq_resolve :premises (@p293 @p292)) % 0.83/1.11 (step @p295 :rule reordering :premises (@p294) :args ((or @t216 @t220))) % 0.83/1.11 (step @p296 :rule chain_m_resolution :premises (@p295 @p289) :args (@t216 @t196 @t221)) % 0.83/1.11 (step @p297 :rule cnf_or_pos :args (@t223)) % 0.83/1.11 (step @p298 :rule reordering :premises (@p297) :args ((or @t212 @t219 @t222 (not @t223)))) % 0.83/1.11 (step @p299 :rule chain_m_resolution :premises (@p298 @p285 @p296 @p260) :args (@t222 @t224 (@list @t211 @t216 @t223))) % 0.83/1.11 (step @p300 :rule cnf_or_pos :args (@t227)) % 0.83/1.11 (step @p301 :rule reordering :premises (@p300) :args ((or @t193 @t226 @t225 (not @t227)))) % 0.83/1.11 (step @p302 :rule chain_m_resolution :premises (@p301 @p274 @p299 @p259) :args (@t225 @t224 (@list @t192 @t222 @t227))) % 0.83/1.11 (step @p303 :rule bool-double-not-elim :args (@t217)) % 0.83/1.11 (step @p304 :rule nary_cong :premises (@p291 @p303) :args ((or @t220 (not @t218)))) % 0.83/1.11 (step @p305 :rule cnf_or_neg :args (@t220 1)) % 0.83/1.11 (step @p306 :rule eq_resolve :premises (@p305 @p304)) % 0.83/1.11 (step @p307 :rule reordering :premises (@p306) :args ((or @t217 @t220))) % 0.83/1.11 (step @p308 :rule chain_m_resolution :premises (@p307 @p289) :args (@t217 @t196 @t221)) % 0.83/1.11 (step @p309 :rule cnf_or_pos :args (@t229)) % 0.83/1.11 (step @p310 :rule reordering :premises (@p309) :args ((or @t218 @t228 @t230))) % 0.83/1.11 (step @p311 :rule chain_m_resolution :premises (@p310 @p308 @p302) :args (@t230 @t210 (@list @t217 @t225))) % 0.83/1.11 (assume-push @p318 @t188) % 0.83/1.11 (step @p313 :rule instantiate :premises (@p224) :args ((@list @t207))) % 0.83/1.11 (step-pop @p319 :rule scope :premises (@p313)) % 0.83/1.11 (step @p314 :rule process_scope :premises (@p319) :args (@t229)) % 0.83/1.11 (step @p316 :rule implies_elim :premises (@p314)) % 0.83/1.11 (step @p317 false :rule chain_m_resolution :premises (@p316 @p311 @p224) :args (false (@list true false) (@list @t229 @t188))) % 0.83/1.11 ) % 0.83/1.11 % SZS output end Proof % 0.83/1.11 % cvc5 exiting %------------------------------------------------------------------------------