%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO440^1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n007.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 09:12:39 AM UTC 2026 % Result : Theorem 0.85s 1.07s % Output : Proof 0.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO440^1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n007.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 00:06:56 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.85/1.07 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.85/1.07 % SZS status Theorem % 0.85/1.07 % SZS output start Proof % 0.85/1.07 ( % 0.85/1.07 (declare-sort $$unsorted 0) % 0.85/1.07 (declare-sort tptp.mu 0) % 0.85/1.07 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.85/1.07 (declare-const tptp.p (-> $$unsorted Bool)) % 0.85/1.07 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.85/1.07 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.85/1.07 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.85/1.07 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.85/1.07 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.85/1.07 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.85/1.07 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.85/1.07 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.85/1.07 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.85/1.07 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.85/1.07 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.85/1.07 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.85/1.07 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.85/1.07 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.85/1.07 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.85/1.07 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.85/1.07 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.85/1.07 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.85/1.07 (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)))))))) % 0.85/1.07 (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)))))))) % 0.85/1.07 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.85/1.07 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.85/1.07 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.85/1.07 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.85/1.07 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.85/1.07 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.85/1.07 (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))))))))))))) % 0.85/1.07 (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)))))) % 0.85/1.07 (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))))))) % 0.85/1.07 (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)))))) % 0.85/1.07 (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))))))) % 0.85/1.07 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.85/1.07 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.85/1.07 (define @t1 () (_ tptp.mdia_s4 (_ tptp.mbox_s4 tptp.p))) % 0.85/1.07 (define @t2 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mdia_s4 (_ tptp.mbox_s4 @t1))) @t1)))) % 0.85/1.07 (define @t3 () (@var "Y" tptp.mu)) % 0.85/1.07 (define @t4 () (@var "X" tptp.mu)) % 0.85/1.07 (define @t5 () (@var "W" $$unsorted)) % 0.85/1.07 (define @t6 () (lambda (@list @t4 @t3 @t5) (= @t4 @t3))) % 0.85/1.07 (define @t7 () (@var "Y" (-> $$unsorted Bool))) % 0.85/1.07 (define @t8 () (@var "X" (-> $$unsorted Bool))) % 0.85/1.07 (define @t9 () (lambda (@list @t8 @t7 @t5) (= (_ @t8 @t5) (_ @t7 @t5)))) % 0.85/1.07 (define @t10 () (@var "Phi" (-> $$unsorted Bool))) % 0.85/1.07 (define @t11 () (_ @t10 @t5)) % 0.85/1.07 (define @t12 () (not @t11)) % 0.85/1.07 (define @t13 () (@list @t10 @t5)) % 0.85/1.07 (define @t14 () (lambda @t13 @t12)) % 0.85/1.07 (define @t15 () (@var "Psi" (-> $$unsorted Bool))) % 0.85/1.07 (define @t16 () (_ @t15 @t5)) % 0.85/1.07 (define @t17 () (lambda (@list @t10 @t15 @t5) (or @t11 @t16))) % 0.85/1.07 (define @t18 () (@var "__flatten_var_0" $$unsorted)) % 0.85/1.07 (define @t19 () (_ tptp.mnot @t15)) % 0.85/1.07 (define @t20 () (_ tptp.mnot @t10)) % 0.85/1.07 (define @t21 () (_ tptp.mor @t20)) % 0.85/1.07 (define @t22 () (@list @t10 @t15 @t18)) % 0.85/1.07 (define @t23 () (lambda @t22 (_ (_ tptp.mnot (_ @t21 @t19)) @t18))) % 0.85/1.07 (define @t24 () (lambda @t22 (_ (_ @t21 @t15) @t18))) % 0.85/1.07 (define @t25 () (lambda @t22 (_ (_ (_ tptp.mor @t19) @t10) @t18))) % 0.85/1.07 (define @t26 () (lambda @t22 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t10) @t15)) (_ (_ tptp.mimplies @t15) @t10)) @t18))) % 0.85/1.07 (define @t27 () (lambda @t22 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t10) @t15)) @t18))) % 0.85/1.07 (define @t28 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.85/1.07 (define @t29 () (_ @t28 @t4)) % 0.85/1.07 (define @t30 () (lambda (@list @t28 @t5) (forall (@list @t4) (_ @t29 @t5)))) % 0.85/1.07 (define @t31 () (@var "P" (-> $$unsorted Bool))) % 0.85/1.07 (define @t32 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.85/1.07 (define @t33 () (_ @t32 @t31)) % 0.85/1.07 (define @t34 () (lambda (@list @t32 @t5) (forall (@list @t31) (_ @t33 @t5)))) % 0.85/1.07 (define @t35 () (lambda (@list @t28 @t18) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t4 @t18) (_ (_ tptp.mnot @t29) @t18)))) @t18))) % 0.85/1.07 (define @t36 () (lambda (@list @t32 @t18) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t31 @t18) (_ (_ tptp.mnot @t33) @t18)))) @t18))) % 0.85/1.07 (define @t37 () (@list @t5)) % 0.85/1.07 (define @t38 () (lambda @t37 true)) % 0.85/1.07 (define @t39 () (@var "V" $$unsorted)) % 0.85/1.07 (define @t40 () (_ @t10 @t39)) % 0.85/1.07 (define @t41 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.85/1.07 (define @t42 () (@list @t39)) % 0.85/1.07 (define @t43 () (lambda (@list @t41 @t10 @t5) (forall @t42 (or (not (_ (_ @t41 @t5) @t39)) @t40)))) % 0.85/1.07 (define @t44 () (lambda (@list @t41 @t10 @t18) (_ (_ tptp.mnot (_ (_ tptp.mbox @t41) @t20)) @t18))) % 0.85/1.07 (define @t45 () (@var "S" $$unsorted)) % 0.85/1.07 (define @t46 () (_ @t41 @t45)) % 0.85/1.07 (define @t47 () (@list @t45)) % 0.85/1.07 (define @t48 () (@list @t41)) % 0.85/1.07 (define @t49 () (lambda @t48 (forall @t47 (_ @t46 @t45)))) % 0.85/1.07 (define @t50 () (@var "T" $$unsorted)) % 0.85/1.07 (define @t51 () (_ @t41 @t50)) % 0.85/1.07 (define @t52 () (_ @t46 @t50)) % 0.85/1.07 (define @t53 () (lambda @t48 (forall (@list @t45 @t50) (=> @t52 (_ @t51 @t45))))) % 0.85/1.07 (define @t54 () (@list @t50)) % 0.85/1.07 (define @t55 () (lambda @t48 (forall @t47 (exists @t54 @t52)))) % 0.85/1.07 (define @t56 () (@var "U" $$unsorted)) % 0.85/1.07 (define @t57 () (_ @t46 @t56)) % 0.85/1.07 (define @t58 () (_ @t51 @t56)) % 0.85/1.07 (define @t59 () (and @t52 @t58)) % 0.85/1.07 (define @t60 () (@list @t45 @t50 @t56)) % 0.85/1.07 (define @t61 () (forall @t60 (=> @t59 @t57))) % 0.85/1.07 (define @t62 () (lambda @t48 @t61)) % 0.85/1.07 (define @t63 () (and @t52 @t57)) % 0.85/1.07 (define @t64 () (lambda @t48 (forall @t60 (=> @t63 @t58)))) % 0.85/1.07 (define @t65 () (= @t50 @t56)) % 0.85/1.07 (define @t66 () (lambda @t48 (forall @t60 (=> @t63 @t65)))) % 0.85/1.07 (define @t67 () (@list @t56)) % 0.85/1.07 (define @t68 () (lambda @t48 (forall @t47 (exists @t54 (and @t52 (forall @t67 (=> @t57 @t65))))))) % 0.85/1.07 (define @t69 () (_ @t41 @t56)) % 0.85/1.07 (define @t70 () (_ @t69 @t50)) % 0.85/1.07 (define @t71 () (lambda @t48 (forall @t60 (=> @t52 (exists @t67 (and @t57 @t70)))))) % 0.85/1.07 (define @t72 () (lambda @t48 (forall @t60 (=> @t63 (or @t58 @t65 @t70))))) % 0.85/1.07 (define @t73 () (lambda @t48 (forall @t60 (=> @t63 (exists @t42 (and (_ @t51 @t39) (_ @t69 @t39))))))) % 0.85/1.07 (define @t74 () (forall @t37 @t11)) % 0.85/1.07 (define @t75 () (@list @t10)) % 0.85/1.07 (define @t76 () (lambda @t75 @t74)) % 0.85/1.07 (define @t77 () (lambda @t75 (forall @t37 @t12))) % 0.85/1.07 (define @t78 () (lambda @t75 (exists @t37 @t11))) % 0.85/1.07 (define @t79 () (lambda @t75 (exists @t37 @t12))) % 0.85/1.07 (define @t80 () (_ (_ tptp.rel_s4 @t5) @t39)) % 0.85/1.07 (define @t81 () (not @t80)) % 0.85/1.07 (define @t82 () (or @t81 @t40)) % 0.85/1.07 (define @t83 () (forall @t42 @t82)) % 0.85/1.07 (define @t84 () (lambda @t13 @t83)) % 0.85/1.07 (define @t85 () (@list @t10 @t18)) % 0.85/1.07 (define @t86 () (lambda @t85 (_ (_ tptp.mnot (_ tptp.mbox_s4 @t20)) @t18))) % 0.85/1.07 (define @t87 () (@var "BOUND_VARIABLE_8426" $$unsorted)) % 0.85/1.07 (define @t88 () (tptp.p @t87)) % 0.85/1.07 (define @t89 () (@var "BOUND_VARIABLE_8450" $$unsorted)) % 0.85/1.07 (define @t90 () (@list @t87)) % 0.85/1.07 (define @t91 () (not (forall @t90 (or (not (tptp.rel_s4 @t89 @t87)) @t88)))) % 0.85/1.07 (define @t92 () (@var "BOUND_VARIABLE_8480" $$unsorted)) % 0.85/1.07 (define @t93 () (@list @t89)) % 0.85/1.07 (define @t94 () (not (forall @t93 (or (not (tptp.rel_s4 @t92 @t89)) @t91)))) % 0.85/1.07 (define @t95 () (@var "BOUND_VARIABLE_8528" $$unsorted)) % 0.85/1.07 (define @t96 () (@list @t92)) % 0.85/1.07 (define @t97 () (not (forall @t96 (or (not (tptp.rel_s4 @t95 @t92)) @t94)))) % 0.85/1.07 (define @t98 () (not (tptp.rel_s4 @t5 @t95))) % 0.85/1.07 (define @t99 () (forall @t90 (or (not (tptp.rel_s4 @t39 @t87)) @t88))) % 0.85/1.07 (define @t100 () (not @t99)) % 0.85/1.07 (define @t101 () (tptp.rel_s4 @t5 @t39)) % 0.85/1.07 (define @t102 () (not @t101)) % 0.85/1.07 (define @t103 () (not (forall @t42 (or @t102 @t100)))) % 0.85/1.07 (define @t104 () (or @t103 @t98 @t97)) % 0.85/1.07 (define @t105 () (or @t98 @t97)) % 0.85/1.07 (define @t106 () (or @t105 @t103)) % 0.85/1.07 (define @t107 () (@list @t5 @t95)) % 0.85/1.07 (define @t108 () (forall @t107 @t106)) % 0.85/1.07 (define @t109 () (@list @t95)) % 0.85/1.07 (define @t110 () (forall @t109 @t106)) % 0.85/1.07 (define @t111 () (forall @t109 @t105)) % 0.85/1.07 (define @t112 () (@list @t39)) % 0.85/1.07 (define @t113 () (or @t111 @t103)) % 0.85/1.07 (define @t114 () (forall @t96 (or (not (tptp.rel_s4 @t39 @t92)) @t94))) % 0.85/1.07 (define @t115 () (not @t114)) % 0.85/1.07 (define @t116 () (or (forall @t42 (or @t102 @t115)) @t103)) % 0.85/1.07 (define @t117 () (not (tptp.rel_s4 @t18 @t39))) % 0.85/1.07 (define @t118 () (forall @t42 (or @t117 @t100))) % 0.85/1.07 (define @t119 () (not @t118)) % 0.85/1.07 (define @t120 () (forall @t42 (or @t117 @t115))) % 0.85/1.07 (define @t121 () (@list @t18)) % 0.85/1.07 (define @t122 () (lambda @t121 (or @t120 @t119))) % 0.85/1.07 (define @t123 () (_ @t122 @t5)) % 0.85/1.07 (define @t124 () (forall @t37 @t123)) % 0.85/1.07 (define @t125 () (_ @t10 @t5)) % 0.85/1.07 (define @t126 () (lambda @t75 (forall @t37 @t125))) % 0.85/1.07 (define @t127 () (lambda @t121 @t119)) % 0.85/1.07 (define @t128 () (_ @t127 @t18)) % 0.85/1.07 (define @t129 () (or @t120 @t128)) % 0.85/1.07 (define @t130 () (lambda @t121 @t129)) % 0.85/1.07 (define @t131 () (_ @t15 @t18)) % 0.85/1.07 (define @t132 () (@list @t15 @t18)) % 0.85/1.07 (define @t133 () (forall @t42 (or @t102 (tptp.p @t39)))) % 0.85/1.07 (define @t134 () (lambda @t37 @t133)) % 0.85/1.07 (define @t135 () (not (_ @t134 @t39))) % 0.85/1.07 (define @t136 () (or @t117 @t135)) % 0.85/1.07 (define @t137 () (forall @t42 @t136)) % 0.85/1.07 (define @t138 () (not @t137)) % 0.85/1.07 (define @t139 () (lambda @t121 @t138)) % 0.85/1.07 (define @t140 () (_ @t10 @t39)) % 0.85/1.07 (define @t141 () (not @t140)) % 0.85/1.07 (define @t142 () (not (forall @t42 (or @t117 @t141)))) % 0.85/1.07 (define @t143 () (lambda @t85 @t142)) % 0.85/1.07 (define @t144 () (lambda @t13 (forall @t42 (or @t102 @t140)))) % 0.85/1.07 (define @t145 () (_ @t144 tptp.p)) % 0.85/1.07 (define @t146 () (not @t120)) % 0.85/1.07 (define @t147 () (lambda @t121 @t146)) % 0.85/1.07 (define @t148 () (_ @t147 @t18)) % 0.85/1.07 (define @t149 () (not @t148)) % 0.85/1.07 (define @t150 () (or @t149 @t131)) % 0.85/1.07 (define @t151 () (lambda @t132 @t150)) % 0.85/1.07 (define @t152 () (or (not (_ @t10 @t18)) @t131)) % 0.85/1.07 (define @t153 () (lambda @t22 @t152)) % 0.85/1.07 (define @t154 () (not (forall @t93 (or (not (tptp.rel_s4 @t39 @t89)) @t91)))) % 0.85/1.07 (define @t155 () (forall @t42 (or @t102 @t154))) % 0.85/1.07 (define @t156 () (lambda @t37 @t155)) % 0.85/1.07 (define @t157 () (not (_ @t156 @t39))) % 0.85/1.07 (define @t158 () (or @t117 @t157)) % 0.85/1.07 (define @t159 () (forall @t42 @t158)) % 0.85/1.07 (define @t160 () (not @t159)) % 0.85/1.07 (define @t161 () (lambda @t121 @t160)) % 0.85/1.07 (define @t162 () (or @t102 (_ @t127 @t39))) % 0.85/1.07 (define @t163 () (forall @t42 @t162)) % 0.85/1.07 (define @t164 () (lambda @t37 @t163)) % 0.85/1.07 (define @t165 () (_ @t143 @t145)) % 0.85/1.07 (define @t166 () (forall @t42 (or @t102 @t141))) % 0.85/1.07 (define @t167 () (lambda @t37 @t166)) % 0.85/1.07 (define @t168 () (_ @t167 @t5)) % 0.85/1.07 (define @t169 () (not @t168)) % 0.85/1.07 (define @t170 () (lambda @t37 @t169)) % 0.85/1.07 (define @t171 () (not @t40)) % 0.85/1.07 (define @t172 () (or @t102 @t171)) % 0.85/1.07 (define @t173 () (lambda @t37 @t12)) % 0.85/1.07 (define @t174 () (_ @t173 @t39)) % 0.85/1.07 (define @t175 () (or @t102 @t174)) % 0.85/1.07 (define @t176 () (forall @t42 @t175)) % 0.85/1.07 (define @t177 () (lambda @t37 @t176)) % 0.85/1.07 (define @t178 () (or @t12 @t16)) % 0.85/1.07 (define @t179 () (lambda @t37 @t178)) % 0.85/1.07 (define @t180 () (@list @t15 @t5)) % 0.85/1.07 (define @t181 () (_ @t173 @t5)) % 0.85/1.07 (define @t182 () (or @t181 @t16)) % 0.85/1.07 (define @t183 () (lambda @t180 @t182)) % 0.85/1.07 (define @t184 () (forall @t107 @t104)) % 0.85/1.07 (define @t185 () (@quantifiers_skolemize @t184 0)) % 0.85/1.07 (define @t186 () (forall @t42 (or (not (tptp.rel_s4 @t185 @t39)) @t100))) % 0.85/1.07 (define @t187 () (@quantifiers_skolemize @t184 1)) % 0.85/1.07 (define @t188 () (forall @t96 (or (not (tptp.rel_s4 @t187 @t92)) @t94))) % 0.85/1.07 (define @t189 () (not @t188)) % 0.85/1.07 (define @t190 () (tptp.rel_s4 @t185 @t187)) % 0.85/1.07 (define @t191 () (not @t190)) % 0.85/1.07 (define @t192 () (not @t186)) % 0.85/1.07 (define @t193 () (or @t192 @t191 @t189)) % 0.85/1.07 (define @t194 () (@list true)) % 0.85/1.07 (define @t195 () (@list @t193)) % 0.85/1.07 (define @t196 () (_ @t41 @t45 @t56)) % 0.85/1.07 (define @t197 () (_ @t41 @t50 @t56)) % 0.85/1.07 (define @t198 () (_ @t41 @t45 @t50)) % 0.85/1.07 (define @t199 () (not @t58)) % 0.85/1.07 (define @t200 () (not @t52)) % 0.85/1.07 (define @t201 () (or @t200 @t199 @t57)) % 0.85/1.07 (define @t202 () (forall @t90 (or (not (tptp.rel_s4 @t187 @t87)) @t88))) % 0.85/1.07 (define @t203 () (@quantifiers_skolemize @t202 0)) % 0.85/1.07 (define @t204 () (forall @t93 (or (not (tptp.rel_s4 @t203 @t89)) @t91))) % 0.85/1.07 (define @t205 () (@quantifiers_skolemize @t204 0)) % 0.85/1.07 (define @t206 () (not @t202)) % 0.85/1.07 (define @t207 () (or @t191 @t206)) % 0.85/1.07 (define @t208 () (@list false false)) % 0.85/1.07 (define @t209 () (tptp.rel_s4 @t187 @t203)) % 0.85/1.07 (define @t210 () (not @t209)) % 0.85/1.07 (define @t211 () (or @t210 (tptp.p @t203))) % 0.85/1.07 (define @t212 () (not @t204)) % 0.85/1.07 (define @t213 () (or @t210 @t212)) % 0.85/1.07 (define @t214 () (tptp.rel_s4 @t203 @t205)) % 0.85/1.07 (define @t215 () (forall @t90 (or (not (tptp.rel_s4 @t205 @t87)) @t88))) % 0.85/1.07 (define @t216 () (not @t215)) % 0.85/1.07 (define @t217 () (not @t214)) % 0.85/1.07 (define @t218 () (or @t217 @t216)) % 0.85/1.07 (define @t219 () (@list @t218)) % 0.85/1.07 (define @t220 () (tptp.rel_s4 @t187 @t205)) % 0.85/1.07 (define @t221 () (or @t210 @t217 @t220)) % 0.85/1.07 (define @t222 () (@list false false false)) % 0.85/1.07 (define @t223 () (tptp.rel_s4 @t185 @t205)) % 0.85/1.07 (define @t224 () (not @t220)) % 0.85/1.07 (define @t225 () (or @t191 @t224 @t223)) % 0.85/1.07 (define @t226 () (not @t223)) % 0.85/1.07 (define @t227 () (or @t226 @t216)) % 0.85/1.07 (define @t228 () (not @t227)) % 0.85/1.07 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.85/1.07 (assume @p2 (_ tptp.mreflexive tptp.rel_s4)) % 0.85/1.07 (assume @p3 (_ tptp.mtransitive tptp.rel_s4)) % 0.85/1.07 (assume @p4 @t2) % 0.85/1.07 (assume @p5 true) % 0.85/1.07 (step @p6 (= tptp.meq_ind @t6) :rule refl :args (@t6)) % 0.85/1.07 (step @p7 (= tptp.meq_prop @t9) :rule refl :args (@t9)) % 0.85/1.07 (step @p8 (= tptp.mnot @t14) :rule refl :args (@t14)) % 0.85/1.07 (step @p9 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.85/1.07 (step @p10 (= tptp.mand @t23) :rule refl :args (@t23)) % 0.85/1.07 (step @p11 (= tptp.mimplies @t24) :rule refl :args (@t24)) % 0.85/1.07 (step @p12 (= tptp.mimplied @t25) :rule refl :args (@t25)) % 0.85/1.07 (step @p13 (= tptp.mequiv @t26) :rule refl :args (@t26)) % 0.85/1.07 (step @p14 (= tptp.mxor @t27) :rule refl :args (@t27)) % 0.85/1.07 (step @p15 (= tptp.mforall_ind @t30) :rule refl :args (@t30)) % 0.85/1.07 (step @p16 (= tptp.mforall_prop @t34) :rule refl :args (@t34)) % 0.85/1.07 (step @p17 (= tptp.mexists_ind @t35) :rule refl :args (@t35)) % 0.85/1.07 (step @p18 (= tptp.mexists_prop @t36) :rule refl :args (@t36)) % 0.85/1.07 (step @p19 (= tptp.mtrue @t38) :rule refl :args (@t38)) % 0.85/1.07 (step @p20 (= tptp.mbox @t43) :rule refl :args (@t43)) % 0.85/1.07 (step @p21 (= tptp.mdia @t44) :rule refl :args (@t44)) % 0.85/1.07 (step @p22 (= tptp.mreflexive @t49) :rule refl :args (@t49)) % 0.85/1.07 (step @p23 (= tptp.msymmetric @t53) :rule refl :args (@t53)) % 0.85/1.07 (step @p24 (= tptp.mserial @t55) :rule refl :args (@t55)) % 0.85/1.07 (step @p25 (= tptp.mtransitive @t62) :rule refl :args (@t62)) % 0.85/1.07 (step @p26 (= tptp.meuclidean @t64) :rule refl :args (@t64)) % 0.85/1.07 (step @p27 (= tptp.mpartially_functional @t66) :rule refl :args (@t66)) % 0.85/1.07 (step @p28 (= tptp.mfunctional @t68) :rule refl :args (@t68)) % 0.85/1.07 (step @p29 (= tptp.mweakly_dense @t71) :rule refl :args (@t71)) % 0.85/1.07 (step @p30 (= tptp.mweakly_connected @t72) :rule refl :args (@t72)) % 0.85/1.07 (step @p31 (= tptp.mweakly_directed @t73) :rule refl :args (@t73)) % 0.85/1.07 (step @p32 (= tptp.mvalid @t76) :rule refl :args (@t76)) % 0.85/1.07 (step @p33 (= tptp.minvalid @t77) :rule refl :args (@t77)) % 0.85/1.07 (step @p34 (= tptp.msatisfiable @t78) :rule refl :args (@t78)) % 0.85/1.07 (step @p35 (= tptp.mcountersatisfiable @t79) :rule refl :args (@t79)) % 0.85/1.07 (step @p36 (= tptp.mbox_s4 @t84) :rule refl :args (@t84)) % 0.85/1.07 (step @p37 (= tptp.mdia_s4 @t86) :rule refl :args (@t86)) % 0.85/1.07 (step @p38 :rule aci_norm :args ((= @t106 @t104))) % 0.85/1.07 (step @p39 :rule cong :premises (@p38) :args (@t108)) % 0.85/1.07 (step @p40 :rule quant-merge-prenex :args ((= (forall @t37 @t110) @t108))) % 0.85/1.07 (step @p41 :rule refl :args (@t103)) % 0.85/1.07 (step @p42 :rule alpha_equiv :args (@t111 (@list @t95) @t112)) % 0.85/1.07 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t113)) % 0.85/1.07 (step @p44 :rule quant-miniscope-or :args ((= @t110 @t113))) % 0.85/1.07 (step @p45 :rule trans :premises (@p44 @p43)) % 0.85/1.07 (step @p46 :rule symm :premises (@p45)) % 0.85/1.07 (step @p47 :rule cong :premises (@p46) :args ((forall @t37 @t116))) % 0.85/1.07 (step @p48 :rule trans :premises (@p47 @p40)) % 0.85/1.07 (step @p49 :rule trans :premises (@p48 @p39)) % 0.85/1.07 (step @p50 :rule beta-reduce :args ((= @t123 @t116))) % 0.85/1.07 (step @p51 :rule cong :premises (@p50) :args (@t124)) % 0.85/1.07 (step @p52 :rule trans :premises (@p51 @p49)) % 0.85/1.07 (step @p53 :rule beta-reduce :args ((= (_ @t126 @t122) @t124))) % 0.85/1.07 (step @p54 :rule trans :premises (@p53 @p52)) % 0.85/1.07 (step @p55 :rule beta-reduce :args ((= @t128 @t119))) % 0.85/1.07 (step @p56 :rule refl :args (@t120)) % 0.85/1.07 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t129)) % 0.85/1.07 (step @p58 :rule cong :premises (@p57) :args (@t130)) % 0.85/1.07 (step @p59 :rule beta-reduce :args ((= (_ (lambda @t132 (or @t120 @t131)) @t127) @t130))) % 0.85/1.07 (step @p60 :rule trans :premises (@p59 @p58)) % 0.85/1.07 (step @p61 :rule beta-reduce :args ((= (_ (lambda @t37 (forall @t90 (or (not (tptp.rel_s4 @t5 @t87)) @t88))) @t39) @t99))) % 0.85/1.07 (step @p62 :rule refl :args (@t39)) % 0.85/1.07 (step @p63 :rule alpha_equiv :args (@t133 @t112 (@list @t87))) % 0.85/1.07 (step @p64 :rule cong :premises (@p63) :args (@t134)) % 0.85/1.07 (step @p65 :rule ho_cong :premises (@p64 @p62)) % 0.85/1.07 (step @p66 :rule trans :premises (@p65 @p61)) % 0.85/1.07 (step @p67 :rule cong :premises (@p66) :args (@t135)) % 0.85/1.07 (step @p68 :rule refl :args (@t117)) % 0.85/1.07 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t136)) % 0.85/1.07 (step @p70 :rule cong :premises (@p69) :args (@t137)) % 0.85/1.07 (step @p71 :rule cong :premises (@p70) :args (@t138)) % 0.85/1.07 (step @p72 :rule cong :premises (@p71) :args (@t139)) % 0.85/1.07 (step @p73 :rule beta-reduce :args ((= (_ @t143 @t134) @t139))) % 0.85/1.07 (step @p74 :rule trans :premises (@p73 @p72)) % 0.85/1.07 (step @p75 :rule beta-reduce :args ((= @t145 @t134))) % 0.85/1.07 (step @p76 :rule refl :args (@t143)) % 0.85/1.07 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 0.85/1.07 (step @p78 :rule trans :premises (@p77 @p74)) % 0.85/1.07 (step @p79 :rule refl :args (@t131)) % 0.85/1.07 (step @p80 :rule bool-double-not-elim :args (@t120)) % 0.85/1.07 (step @p81 :rule beta-reduce :args ((= @t148 @t146))) % 0.85/1.07 (step @p82 :rule cong :premises (@p81) :args (@t149)) % 0.85/1.07 (step @p83 :rule trans :premises (@p82 @p80)) % 0.85/1.07 (step @p84 :rule nary_cong :premises (@p83 @p79) :args (@t150)) % 0.85/1.07 (step @p85 :rule cong :premises (@p84) :args (@t151)) % 0.85/1.07 (step @p86 :rule beta-reduce :args ((= (_ @t153 @t147) @t151))) % 0.85/1.07 (step @p87 :rule trans :premises (@p86 @p85)) % 0.85/1.07 (step @p88 :rule beta-reduce :args ((= (_ (lambda @t37 (forall @t96 (or (not (tptp.rel_s4 @t5 @t92)) @t94))) @t39) @t114))) % 0.85/1.07 (step @p89 :rule alpha_equiv :args (@t155 @t112 (@list @t92))) % 0.85/1.07 (step @p90 :rule cong :premises (@p89) :args (@t156)) % 0.85/1.07 (step @p91 :rule ho_cong :premises (@p90 @p62)) % 0.85/1.07 (step @p92 :rule trans :premises (@p91 @p88)) % 0.85/1.07 (step @p93 :rule cong :premises (@p92) :args (@t157)) % 0.85/1.07 (step @p94 :rule nary_cong :premises (@p68 @p93) :args (@t158)) % 0.85/1.07 (step @p95 :rule cong :premises (@p94) :args (@t159)) % 0.85/1.07 (step @p96 :rule cong :premises (@p95) :args (@t160)) % 0.85/1.07 (step @p97 :rule cong :premises (@p96) :args (@t161)) % 0.85/1.07 (step @p98 :rule beta-reduce :args ((= (_ @t143 @t156) @t161))) % 0.85/1.07 (step @p99 :rule trans :premises (@p98 @p97)) % 0.85/1.07 (step @p100 :rule beta-reduce :args ((= (_ (lambda @t121 (not (forall @t93 (or (not (tptp.rel_s4 @t18 @t89)) @t91)))) @t39) @t154))) % 0.85/1.07 (step @p101 :rule alpha_equiv :args (@t118 @t112 (@list @t89))) % 0.85/1.07 (step @p102 :rule cong :premises (@p101) :args (@t119)) % 0.85/1.07 (step @p103 :rule cong :premises (@p102) :args (@t127)) % 0.85/1.07 (step @p104 :rule ho_cong :premises (@p103 @p62)) % 0.85/1.07 (step @p105 :rule trans :premises (@p104 @p100)) % 0.85/1.07 (step @p106 :rule refl :args (@t102)) % 0.85/1.07 (step @p107 :rule nary_cong :premises (@p106 @p105) :args (@t162)) % 0.85/1.07 (step @p108 :rule cong :premises (@p107) :args (@t163)) % 0.85/1.07 (step @p109 :rule cong :premises (@p108) :args (@t164)) % 0.85/1.07 (step @p110 :rule beta-reduce :args ((= (_ @t144 @t127) @t164))) % 0.85/1.07 (step @p111 :rule trans :premises (@p110 @p109)) % 0.85/1.07 (step @p112 :rule refl :args (@t144)) % 0.85/1.07 (step @p113 :rule ho_cong :premises (@p112 @p78)) % 0.85/1.07 (step @p114 :rule trans :premises (@p113 @p111)) % 0.85/1.07 (step @p115 :rule ho_cong :premises (@p76 @p114)) % 0.85/1.07 (step @p116 :rule trans :premises (@p115 @p99)) % 0.85/1.07 (step @p117 :rule refl :args (@t153)) % 0.85/1.07 (step @p118 :rule ho_cong :premises (@p117 @p116)) % 0.85/1.07 (step @p119 :rule trans :premises (@p118 @p87)) % 0.85/1.07 (step @p120 :rule ho_cong :premises (@p119 @p78)) % 0.85/1.07 (step @p121 :rule trans :premises (@p120 @p60)) % 0.85/1.07 (step @p122 :rule refl :args (@t126)) % 0.85/1.07 (step @p123 :rule ho_cong :premises (@p122 @p121)) % 0.85/1.07 (step @p124 :rule trans :premises (@p123 @p54)) % 0.85/1.07 (step @p125 :rule cong :premises (@p124) :args ((not (_ @t126 (_ (_ @t153 (_ @t143 (_ @t144 @t165))) @t165))))) % 0.85/1.07 (step @p126 :rule refl :args (tptp.p)) % 0.85/1.07 (step @p127 :rule refl :args (@t140)) % 0.85/1.07 (step @p128 :rule refl :args (@t40)) % 0.85/1.07 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t40 @t140))) % 0.85/1.07 (step @p130 :rule symm :premises (@p129)) % 0.85/1.07 (step @p131 :rule eq_resolve :premises (@p128 @p130)) % 0.85/1.07 (step @p132 :rule refl :args (@t101)) % 0.85/1.07 (step @p133 :rule refl :args (@t80)) % 0.85/1.07 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t80 @t101))) % 0.85/1.07 (step @p135 :rule symm :premises (@p134)) % 0.85/1.07 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 0.85/1.07 (step @p137 :rule cong :premises (@p136) :args (@t81)) % 0.85/1.07 (step @p138 :rule nary_cong :premises (@p137 @p131) :args (@t82)) % 0.85/1.07 (step @p139 :rule cong :premises (@p138) :args (@t83)) % 0.85/1.07 (step @p140 :rule cong :premises (@p139) :args (@t84)) % 0.85/1.07 (step @p141 :rule trans :premises (@p36 @p140)) % 0.85/1.07 (step @p142 :rule ho_cong :premises (@p141 @p126)) % 0.85/1.07 (step @p143 :rule beta-reduce :args ((= (_ (lambda @t37 (not @t166)) @t18) @t142))) % 0.85/1.07 (step @p144 :rule refl :args (@t18)) % 0.85/1.07 (step @p145 :rule beta-reduce :args ((= @t168 @t166))) % 0.85/1.07 (step @p146 :rule cong :premises (@p145) :args (@t169)) % 0.85/1.07 (step @p147 :rule cong :premises (@p146) :args (@t170)) % 0.85/1.07 (step @p148 :rule beta-reduce :args ((= (_ @t14 @t167) @t170))) % 0.85/1.07 (step @p149 :rule trans :premises (@p148 @p147)) % 0.85/1.07 (step @p150 :rule cong :premises (@p131) :args (@t171)) % 0.85/1.07 (step @p151 :rule refl :args (@t102)) % 0.85/1.07 (step @p152 :rule nary_cong :premises (@p151 @p150) :args (@t172)) % 0.85/1.07 (step @p153 :rule cong :premises (@p152) :args ((forall @t42 @t172))) % 0.85/1.07 (step @p154 :rule beta-reduce :args ((= @t174 @t171))) % 0.85/1.07 (step @p155 :rule nary_cong :premises (@p106 @p154) :args (@t175)) % 0.85/1.07 (step @p156 :rule cong :premises (@p155) :args (@t176)) % 0.85/1.07 (step @p157 :rule trans :premises (@p156 @p153)) % 0.85/1.07 (step @p158 :rule cong :premises (@p157) :args (@t177)) % 0.85/1.07 (step @p159 :rule beta-reduce :args ((= (_ @t144 @t173) @t177))) % 0.85/1.07 (step @p160 :rule trans :premises (@p159 @p158)) % 0.85/1.07 (step @p161 :rule beta-reduce :args ((= (_ @t14 @t10) @t173))) % 0.85/1.07 (step @p162 :rule ho_cong :premises (@p112 @p161)) % 0.85/1.07 (step @p163 :rule trans :premises (@p162 @p160)) % 0.85/1.07 (step @p164 :rule refl :args (@t14)) % 0.85/1.07 (step @p165 :rule ho_cong :premises (@p164 @p163)) % 0.85/1.07 (step @p166 :rule trans :premises (@p165 @p149)) % 0.85/1.07 (step @p167 :rule ho_cong :premises (@p166 @p144)) % 0.85/1.07 (step @p168 :rule trans :premises (@p167 @p143)) % 0.85/1.07 (step @p169 :rule refl :args (@t10)) % 0.85/1.07 (step @p170 :rule ho_cong :premises (@p8 @p169)) % 0.85/1.07 (step @p171 :rule ho_cong :premises (@p141 @p170)) % 0.85/1.07 (step @p172 :rule ho_cong :premises (@p8 @p171)) % 0.85/1.07 (step @p173 :rule ho_cong :premises (@p172 @p144)) % 0.85/1.07 (step @p174 :rule trans :premises (@p173 @p168)) % 0.85/1.07 (step @p175 :rule cong :premises (@p174) :args (@t86)) % 0.85/1.07 (step @p176 :rule trans :premises (@p37 @p175)) % 0.85/1.07 (step @p177 :rule ho_cong :premises (@p176 @p142)) % 0.85/1.07 (step @p178 :rule ho_cong :premises (@p141 @p177)) % 0.85/1.07 (step @p179 :rule ho_cong :premises (@p176 @p178)) % 0.85/1.07 (step @p180 :rule beta-reduce :args ((= (_ @t179 @t18) @t152))) % 0.85/1.07 (step @p181 :rule beta-reduce :args ((= (_ (lambda @t180 @t178) @t15) @t179))) % 0.85/1.07 (step @p182 :rule refl :args (@t15)) % 0.85/1.07 (step @p183 :rule refl :args (@t16)) % 0.85/1.07 (step @p184 :rule beta-reduce :args ((= @t181 @t12))) % 0.85/1.07 (step @p185 :rule nary_cong :premises (@p184 @p183) :args (@t182)) % 0.85/1.07 (step @p186 :rule cong :premises (@p185) :args (@t183)) % 0.85/1.07 (step @p187 :rule beta-reduce :args ((= (_ @t17 @t173) @t183))) % 0.85/1.07 (step @p188 :rule trans :premises (@p187 @p186)) % 0.85/1.07 (step @p189 :rule refl :args (@t17)) % 0.85/1.07 (step @p190 :rule ho_cong :premises (@p189 @p161)) % 0.85/1.07 (step @p191 :rule trans :premises (@p190 @p188)) % 0.85/1.07 (step @p192 :rule ho_cong :premises (@p191 @p182)) % 0.85/1.07 (step @p193 :rule trans :premises (@p192 @p181)) % 0.85/1.07 (step @p194 :rule ho_cong :premises (@p193 @p144)) % 0.85/1.07 (step @p195 :rule trans :premises (@p194 @p180)) % 0.85/1.07 (step @p196 :rule ho_cong :premises (@p9 @p170)) % 0.85/1.07 (step @p197 :rule ho_cong :premises (@p196 @p182)) % 0.85/1.07 (step @p198 :rule ho_cong :premises (@p197 @p144)) % 0.85/1.07 (step @p199 :rule trans :premises (@p198 @p195)) % 0.85/1.07 (step @p200 :rule cong :premises (@p199) :args (@t24)) % 0.85/1.07 (step @p201 :rule trans :premises (@p11 @p200)) % 0.85/1.07 (step @p202 :rule ho_cong :premises (@p201 @p179)) % 0.85/1.07 (step @p203 :rule ho_cong :premises (@p202 @p177)) % 0.85/1.07 (step @p204 :rule refl :args (@t125)) % 0.85/1.07 (step @p205 :rule refl :args (@t11)) % 0.85/1.07 (step @p206 :rule cong :premises (@p205 @p204) :args ((= @t11 @t125))) % 0.85/1.07 (step @p207 :rule symm :premises (@p206)) % 0.85/1.07 (step @p208 :rule eq_resolve :premises (@p205 @p207)) % 0.85/1.07 (step @p209 :rule cong :premises (@p208) :args (@t74)) % 0.85/1.07 (step @p210 :rule cong :premises (@p209) :args (@t76)) % 0.85/1.07 (step @p211 :rule trans :premises (@p32 @p210)) % 0.85/1.07 (step @p212 :rule ho_cong :premises (@p211 @p203)) % 0.85/1.07 (step @p213 :rule cong :premises (@p212) :args (@t2)) % 0.85/1.07 (step @p214 :rule trans :premises (@p213 @p125)) % 0.85/1.07 (step @p215 :rule eq_resolve :premises (@p4 @p214)) % 0.85/1.07 (step @p216 :rule skolemize :premises (@p215)) % 0.85/1.07 (step @p217 :rule bool-double-not-elim :args (@t186)) % 0.85/1.07 (step @p218 :rule refl :args (@t193)) % 0.85/1.07 (step @p219 :rule nary_cong :premises (@p218 @p217) :args ((or @t193 (not @t192)))) % 0.85/1.07 (step @p220 :rule cnf_or_neg :args (@t193 0)) % 0.85/1.07 (step @p221 :rule eq_resolve :premises (@p220 @p219)) % 0.85/1.07 (step @p222 :rule reordering :premises (@p221) :args ((or @t186 @t193))) % 0.85/1.07 (step @p223 :rule chain_m_resolution :premises (@p222 @p216) :args (@t186 @t194 @t195)) % 0.85/1.07 (step @p224 :rule beta-reduce :args ((= (_ (lambda @t48 (forall @t60 (or (not @t198) (not @t197) @t196))) tptp.rel_s4) (forall @t60 (or (not (tptp.rel_s4 @t45 @t50)) (not (tptp.rel_s4 @t50 @t56)) (tptp.rel_s4 @t45 @t56)))))) % 0.85/1.07 (step @p225 :rule refl :args (tptp.rel_s4)) % 0.85/1.07 (step @p226 :rule refl :args (@t196)) % 0.85/1.07 (step @p227 :rule refl :args (@t57)) % 0.85/1.07 (step @p228 :rule cong :premises (@p227 @p226) :args ((= @t57 @t196))) % 0.85/1.07 (step @p229 :rule symm :premises (@p228)) % 0.85/1.07 (step @p230 :rule eq_resolve :premises (@p227 @p229)) % 0.85/1.07 (step @p231 :rule refl :args (@t197)) % 0.85/1.07 (step @p232 :rule refl :args (@t58)) % 0.85/1.07 (step @p233 :rule cong :premises (@p232 @p231) :args ((= @t58 @t197))) % 0.85/1.07 (step @p234 :rule symm :premises (@p233)) % 0.85/1.07 (step @p235 :rule eq_resolve :premises (@p232 @p234)) % 0.85/1.07 (step @p236 :rule cong :premises (@p235) :args (@t199)) % 0.85/1.07 (step @p237 :rule refl :args (@t198)) % 0.85/1.07 (step @p238 :rule refl :args (@t52)) % 0.85/1.07 (step @p239 :rule cong :premises (@p238 @p237) :args ((= @t52 @t198))) % 0.85/1.07 (step @p240 :rule symm :premises (@p239)) % 0.85/1.07 (step @p241 :rule eq_resolve :premises (@p238 @p240)) % 0.85/1.07 (step @p242 :rule cong :premises (@p241) :args (@t200)) % 0.85/1.07 (step @p243 :rule nary_cong :premises (@p242 @p236 @p230) :args (@t201)) % 0.85/1.07 (step @p244 :rule cong :premises (@p243) :args ((forall @t60 @t201))) % 0.85/1.07 (step @p245 :rule aci_norm :args ((= (or (or @t200 @t199) @t57) @t201))) % 0.85/1.07 (step @p246 :rule bool-and-de-morgan :args (@t52 @t58 true)) % 0.85/1.07 (step @p247 :rule nary_cong :premises (@p246 @p227) :args ((or (not @t59) @t57))) % 0.85/1.07 (step @p248 :rule trans :premises (@p247 @p245)) % 0.85/1.07 (step @p249 :rule bool-impl-elim :args (@t59 @t57)) % 0.85/1.07 (step @p250 :rule trans :premises (@p249 @p248)) % 0.85/1.07 (step @p251 :rule cong :premises (@p250) :args (@t61)) % 0.85/1.07 (step @p252 :rule trans :premises (@p251 @p244)) % 0.85/1.07 (step @p253 :rule cong :premises (@p252) :args (@t62)) % 0.85/1.07 (step @p254 :rule trans :premises (@p25 @p253)) % 0.85/1.07 (step @p255 :rule ho_cong :premises (@p254 @p225)) % 0.85/1.07 (step @p256 :rule trans :premises (@p255 @p224)) % 0.85/1.07 (step @p257 :rule eq_resolve :premises (@p3 @p256)) % 0.85/1.07 (step @p258 :rule instantiate :premises (@p257) :args ((@list @t185 @t187 @t205))) % 0.85/1.07 (step @p259 :rule instantiate :premises (@p257) :args ((@list @t187 @t203 @t205))) % 0.85/1.07 (step @p260 :rule bool-double-not-elim :args (@t188)) % 0.85/1.07 (step @p261 :rule nary_cong :premises (@p218 @p260) :args ((or @t193 (not @t189)))) % 0.85/1.07 (step @p262 :rule cnf_or_neg :args (@t193 2)) % 0.85/1.07 (step @p263 :rule eq_resolve :premises (@p262 @p261)) % 0.85/1.07 (step @p264 :rule reordering :premises (@p263) :args ((or @t188 @t193))) % 0.85/1.07 (step @p265 :rule chain_m_resolution :premises (@p264 @p216) :args (@t188 @t194 @t195)) % 0.85/1.07 (step @p266 :rule instantiate :premises (@p265) :args ((@list @t203))) % 0.85/1.07 (step @p267 :rule instantiate :premises (@p223) :args ((@list @t187))) % 0.85/1.07 (step @p268 :rule bool-double-not-elim :args (@t190)) % 0.85/1.07 (step @p269 :rule nary_cong :premises (@p218 @p268) :args ((or @t193 (not @t191)))) % 0.85/1.07 (step @p270 :rule cnf_or_neg :args (@t193 1)) % 0.85/1.07 (step @p271 :rule eq_resolve :premises (@p270 @p269)) % 0.85/1.07 (step @p272 :rule reordering :premises (@p271) :args ((or @t190 @t193))) % 0.85/1.07 (step @p273 :rule chain_m_resolution :premises (@p272 @p216) :args (@t190 @t194 @t195)) % 0.85/1.07 (step @p274 :rule cnf_or_pos :args (@t207)) % 0.85/1.07 (step @p275 :rule reordering :premises (@p274) :args ((or @t191 @t206 (not @t207)))) % 0.85/1.07 (step @p276 :rule chain_m_resolution :premises (@p275 @p273 @p267) :args (@t206 @t208 (@list @t190 @t207))) % 0.85/1.07 (step @p277 :rule skolemize :premises (@p276)) % 0.85/1.07 (step @p278 :rule bool-double-not-elim :args (@t209)) % 0.85/1.07 (step @p279 :rule refl :args (@t211)) % 0.85/1.07 (step @p280 :rule nary_cong :premises (@p279 @p278) :args ((or @t211 (not @t210)))) % 0.85/1.07 (step @p281 :rule cnf_or_neg :args (@t211 0)) % 0.85/1.07 (step @p282 :rule eq_resolve :premises (@p281 @p280)) % 0.85/1.07 (step @p283 :rule reordering :premises (@p282) :args ((or @t209 @t211))) % 0.85/1.07 (step @p284 :rule chain_m_resolution :premises (@p283 @p277) :args (@t209 @t194 (@list @t211))) % 0.85/1.07 (step @p285 :rule cnf_or_pos :args (@t213)) % 0.85/1.07 (step @p286 :rule reordering :premises (@p285) :args ((or @t210 @t212 (not @t213)))) % 0.85/1.07 (step @p287 :rule chain_m_resolution :premises (@p286 @p284 @p266) :args (@t212 @t208 (@list @t209 @t213))) % 0.85/1.07 (step @p288 :rule skolemize :premises (@p287)) % 0.85/1.07 (step @p289 :rule bool-double-not-elim :args (@t214)) % 0.85/1.07 (step @p290 :rule refl :args (@t218)) % 0.85/1.07 (step @p291 :rule nary_cong :premises (@p290 @p289) :args ((or @t218 (not @t217)))) % 0.85/1.07 (step @p292 :rule cnf_or_neg :args (@t218 0)) % 0.85/1.07 (step @p293 :rule eq_resolve :premises (@p292 @p291)) % 0.85/1.07 (step @p294 :rule reordering :premises (@p293) :args ((or @t214 @t218))) % 0.85/1.07 (step @p295 :rule chain_m_resolution :premises (@p294 @p288) :args (@t214 @t194 @t219)) % 0.85/1.07 (step @p296 :rule cnf_or_pos :args (@t221)) % 0.85/1.07 (step @p297 :rule reordering :premises (@p296) :args ((or @t210 @t217 @t220 (not @t221)))) % 0.85/1.07 (step @p298 :rule chain_m_resolution :premises (@p297 @p284 @p295 @p259) :args (@t220 @t222 (@list @t209 @t214 @t221))) % 0.85/1.07 (step @p299 :rule cnf_or_pos :args (@t225)) % 0.85/1.07 (step @p300 :rule reordering :premises (@p299) :args ((or @t191 @t224 @t223 (not @t225)))) % 0.85/1.07 (step @p301 :rule chain_m_resolution :premises (@p300 @p273 @p298 @p258) :args (@t223 @t222 (@list @t190 @t220 @t225))) % 0.85/1.07 (step @p302 :rule bool-double-not-elim :args (@t215)) % 0.85/1.08 (step @p303 :rule nary_cong :premises (@p290 @p302) :args ((or @t218 (not @t216)))) % 0.85/1.08 (step @p304 :rule cnf_or_neg :args (@t218 1)) % 0.85/1.08 (step @p305 :rule eq_resolve :premises (@p304 @p303)) % 0.85/1.08 (step @p306 :rule reordering :premises (@p305) :args ((or @t215 @t218))) % 0.85/1.08 (step @p307 :rule chain_m_resolution :premises (@p306 @p288) :args (@t215 @t194 @t219)) % 0.85/1.08 (step @p308 :rule cnf_or_pos :args (@t227)) % 0.85/1.08 (step @p309 :rule reordering :premises (@p308) :args ((or @t216 @t226 @t228))) % 0.85/1.08 (step @p310 :rule chain_m_resolution :premises (@p309 @p307 @p301) :args (@t228 @t208 (@list @t215 @t223))) % 0.85/1.08 (assume-push @p317 @t186) % 0.85/1.08 (step @p312 :rule instantiate :premises (@p223) :args ((@list @t205))) % 0.85/1.08 (step-pop @p318 :rule scope :premises (@p312)) % 0.85/1.08 (step @p313 :rule process_scope :premises (@p318) :args (@t227)) % 0.85/1.08 (step @p315 :rule implies_elim :premises (@p313)) % 0.85/1.08 (step @p316 false :rule chain_m_resolution :premises (@p315 @p310 @p223) :args (false (@list true false) (@list @t227 @t186))) % 0.85/1.08 ) % 0.85/1.08 % SZS output end Proof % 0.85/1.08 % cvc5 exiting %------------------------------------------------------------------------------