%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO574^7 : TPTP v9.2.1. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n026.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 0.37s 0.61s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO574^7 : TPTP v9.2.1. Released v5.5.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n026.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 00:21:40 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.37/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.61 % SZS status Theorem % 0.37/0.61 % SZS output start Proof % 0.37/0.61 ( % 0.37/0.61 (declare-sort $$unsorted 0) % 0.37/0.61 (declare-sort tptp.mu 0) % 0.37/0.61 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.p (-> $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.q (-> $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.37/0.61 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.37/0.61 (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)))))) % 0.37/0.61 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.61 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.37/0.61 (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))))))) % 0.37/0.61 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.37/0.61 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.61 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.61 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.61 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.37/0.61 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.61 (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)))))) % 0.37/0.61 (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)))))))) % 0.37/0.61 (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)))))) % 0.37/0.61 (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)))))) % 0.37/0.61 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.37/0.61 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.61 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.61 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.37/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.37/0.61 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.37/0.61 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.37/0.61 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.37/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.37/0.61 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.37/0.61 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.61 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.61 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.61 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.61 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$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)))))))) % 0.37/0.61 (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))))) % 0.37/0.61 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.61 (define @t2 () (@var "X" tptp.mu)) % 0.37/0.61 (define @t3 () (_ tptp.exists_in_world @t2)) % 0.37/0.61 (define @t4 () (_ @t3 @t1)) % 0.37/0.61 (define @t5 () (@list @t2)) % 0.37/0.61 (define @t6 () (@list @t1)) % 0.37/0.61 (define @t7 () (@var "W" $$unsorted)) % 0.37/0.61 (define @t8 () (_ @t3 @t7)) % 0.37/0.61 (define @t9 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mdia_s4 (_ (_ tptp.mimplies tptp.p) (_ tptp.mbox_s4 tptp.q)))) (_ (_ tptp.mimplies (_ tptp.mbox_s4 tptp.p)) (_ tptp.mdia_s4 tptp.q)))))) % 0.37/0.61 (define @t10 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.61 (define @t11 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.61 (define @t12 () (lambda (@list @t11 @t10 @t7) (= (_ @t11 @t7) (_ @t10 @t7)))) % 0.37/0.61 (define @t13 () (@var "Phi" (-> $$unsorted Bool))) % 0.37/0.61 (define @t14 () (_ @t13 @t7)) % 0.37/0.61 (define @t15 () (not @t14)) % 0.37/0.61 (define @t16 () (@list @t13 @t7)) % 0.37/0.61 (define @t17 () (lambda @t16 @t15)) % 0.37/0.61 (define @t18 () (@var "Psi" (-> $$unsorted Bool))) % 0.37/0.61 (define @t19 () (_ @t18 @t7)) % 0.37/0.61 (define @t20 () (lambda (@list @t13 @t18 @t7) (or @t14 @t19))) % 0.37/0.61 (define @t21 () (_ @t13 @t1)) % 0.37/0.61 (define @t22 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.61 (define @t23 () (lambda (@list @t22 @t13 @t7) (forall @t6 (or (not (_ (_ @t22 @t7) @t1)) @t21)))) % 0.37/0.61 (define @t24 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.61 (define @t25 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.37/0.61 (define @t26 () (_ @t25 @t24)) % 0.37/0.61 (define @t27 () (lambda (@list @t25 @t7) (forall (@list @t24) (_ @t26 @t7)))) % 0.37/0.61 (define @t28 () (@list @t7)) % 0.37/0.61 (define @t29 () (lambda @t28 true)) % 0.37/0.61 (define @t30 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.61 (define @t31 () (_ tptp.mnot @t18)) % 0.37/0.61 (define @t32 () (_ tptp.mnot @t13)) % 0.37/0.61 (define @t33 () (_ tptp.mor @t32)) % 0.37/0.61 (define @t34 () (@list @t13 @t18 @t30)) % 0.37/0.61 (define @t35 () (lambda @t34 (_ (_ tptp.mnot (_ @t33 @t31)) @t30))) % 0.37/0.61 (define @t36 () (lambda @t34 (_ (_ @t33 @t18) @t30))) % 0.37/0.61 (define @t37 () (lambda @t34 (_ (_ (_ tptp.mor @t31) @t13) @t30))) % 0.37/0.61 (define @t38 () (lambda @t34 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t13) @t18)) (_ (_ tptp.mimplies @t18) @t13)) @t30))) % 0.37/0.61 (define @t39 () (lambda @t34 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t13) @t18)) @t30))) % 0.37/0.61 (define @t40 () (lambda (@list @t22 @t13 @t30) (_ (_ tptp.mnot (_ (_ tptp.mbox @t22) @t32)) @t30))) % 0.37/0.61 (define @t41 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.37/0.61 (define @t42 () (_ @t41 @t2)) % 0.37/0.61 (define @t43 () (lambda (@list @t41 @t7) (forall @t5 (=> @t8 (_ @t42 @t7))))) % 0.37/0.61 (define @t44 () (lambda (@list @t41 @t30) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t2 @t30) (_ (_ tptp.mnot @t42) @t30)))) @t30))) % 0.37/0.61 (define @t45 () (lambda (@list @t25 @t30) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t24 @t30) (_ (_ tptp.mnot @t26) @t30)))) @t30))) % 0.37/0.61 (define @t46 () (@var "S" $$unsorted)) % 0.37/0.61 (define @t47 () (_ @t22 @t46)) % 0.37/0.61 (define @t48 () (_ @t47 @t46)) % 0.37/0.61 (define @t49 () (@list @t46)) % 0.37/0.61 (define @t50 () (forall @t49 @t48)) % 0.37/0.61 (define @t51 () (@list @t22)) % 0.37/0.61 (define @t52 () (lambda @t51 @t50)) % 0.37/0.61 (define @t53 () (@var "T" $$unsorted)) % 0.37/0.61 (define @t54 () (_ @t22 @t53)) % 0.37/0.61 (define @t55 () (_ @t47 @t53)) % 0.37/0.61 (define @t56 () (lambda @t51 (forall (@list @t46 @t53) (=> @t55 (_ @t54 @t46))))) % 0.37/0.61 (define @t57 () (@list @t53)) % 0.37/0.61 (define @t58 () (lambda @t51 (forall @t49 (exists @t57 @t55)))) % 0.37/0.61 (define @t59 () (@var "U" $$unsorted)) % 0.37/0.61 (define @t60 () (_ @t47 @t59)) % 0.37/0.61 (define @t61 () (_ @t54 @t59)) % 0.37/0.61 (define @t62 () (@list @t46 @t53 @t59)) % 0.37/0.61 (define @t63 () (lambda @t51 (forall @t62 (=> (and @t55 @t61) @t60)))) % 0.37/0.61 (define @t64 () (and @t55 @t60)) % 0.37/0.61 (define @t65 () (lambda @t51 (forall @t62 (=> @t64 @t61)))) % 0.37/0.61 (define @t66 () (= @t53 @t59)) % 0.37/0.61 (define @t67 () (lambda @t51 (forall @t62 (=> @t64 @t66)))) % 0.37/0.61 (define @t68 () (@list @t59)) % 0.37/0.61 (define @t69 () (lambda @t51 (forall @t49 (exists @t57 (and @t55 (forall @t68 (=> @t60 @t66))))))) % 0.37/0.61 (define @t70 () (_ @t22 @t59)) % 0.37/0.61 (define @t71 () (_ @t70 @t53)) % 0.37/0.61 (define @t72 () (lambda @t51 (forall @t62 (=> @t55 (exists @t68 (and @t60 @t71)))))) % 0.37/0.61 (define @t73 () (lambda @t51 (forall @t62 (=> @t64 (or @t61 @t66 @t71))))) % 0.37/0.61 (define @t74 () (lambda @t51 (forall @t62 (=> @t64 (exists @t6 (and (_ @t54 @t1) (_ @t70 @t1))))))) % 0.37/0.61 (define @t75 () (forall @t28 @t14)) % 0.37/0.61 (define @t76 () (@list @t13)) % 0.37/0.61 (define @t77 () (lambda @t76 @t75)) % 0.37/0.61 (define @t78 () (lambda @t76 (exists @t28 @t14))) % 0.37/0.61 (define @t79 () (lambda @t76 (exists @t28 @t15))) % 0.37/0.61 (define @t80 () (lambda @t76 (forall @t28 @t15))) % 0.37/0.61 (define @t81 () (_ (_ tptp.rel_s4 @t7) @t1)) % 0.37/0.61 (define @t82 () (not @t81)) % 0.37/0.61 (define @t83 () (or @t82 @t21)) % 0.37/0.61 (define @t84 () (forall @t6 @t83)) % 0.37/0.61 (define @t85 () (lambda @t16 @t84)) % 0.37/0.61 (define @t86 () (@list @t13 @t30)) % 0.37/0.61 (define @t87 () (lambda @t86 (_ (_ tptp.mnot (_ tptp.mbox_s4 @t32)) @t30))) % 0.37/0.61 (define @t88 () (forall @t49 (tptp.rel_s4 @t46 @t46))) % 0.37/0.61 (define @t89 () (_ @t22 @t46 @t46)) % 0.37/0.61 (define @t90 () (@var "BOUND_VARIABLE_8484" $$unsorted)) % 0.37/0.61 (define @t91 () (tptp.q @t90)) % 0.37/0.61 (define @t92 () (@var "BOUND_VARIABLE_8567" $$unsorted)) % 0.37/0.61 (define @t93 () (@list @t90)) % 0.37/0.61 (define @t94 () (and (tptp.p @t92) (not (forall @t93 (or (not (tptp.rel_s4 @t92 @t90)) @t91))))) % 0.37/0.61 (define @t95 () (not (tptp.rel_s4 @t7 @t92))) % 0.37/0.61 (define @t96 () (tptp.q @t1)) % 0.37/0.61 (define @t97 () (not @t96)) % 0.37/0.61 (define @t98 () (tptp.rel_s4 @t7 @t1)) % 0.37/0.61 (define @t99 () (not @t98)) % 0.37/0.61 (define @t100 () (not (forall @t6 (or @t99 @t97)))) % 0.37/0.61 (define @t101 () (tptp.p @t1)) % 0.37/0.61 (define @t102 () (forall @t6 (or @t99 @t101))) % 0.37/0.61 (define @t103 () (not @t102)) % 0.37/0.61 (define @t104 () (or @t103 @t100 @t95 @t94)) % 0.37/0.61 (define @t105 () (or @t95 @t94)) % 0.37/0.61 (define @t106 () (or @t105 @t103 @t100)) % 0.37/0.61 (define @t107 () (@list @t7 @t92)) % 0.37/0.61 (define @t108 () (forall @t107 @t106)) % 0.37/0.61 (define @t109 () (@list @t92)) % 0.37/0.61 (define @t110 () (forall @t109 @t106)) % 0.37/0.61 (define @t111 () (forall @t109 @t105)) % 0.37/0.61 (define @t112 () (@list @t1)) % 0.37/0.61 (define @t113 () (or @t111 @t103 @t100)) % 0.37/0.61 (define @t114 () (forall @t93 (or (not (tptp.rel_s4 @t1 @t90)) @t91))) % 0.37/0.61 (define @t115 () (not @t114)) % 0.37/0.61 (define @t116 () (and @t101 @t115)) % 0.37/0.61 (define @t117 () (or (forall @t6 (or @t99 @t116)) @t103 @t100)) % 0.37/0.61 (define @t118 () (not (tptp.rel_s4 @t30 @t1))) % 0.37/0.61 (define @t119 () (not (forall @t6 (or @t118 @t97)))) % 0.37/0.61 (define @t120 () (forall @t6 (or @t118 @t101))) % 0.37/0.61 (define @t121 () (not @t120)) % 0.37/0.61 (define @t122 () (forall @t6 (or @t118 @t116))) % 0.37/0.61 (define @t123 () (or @t122 @t121 @t119)) % 0.37/0.61 (define @t124 () (@list @t30)) % 0.37/0.61 (define @t125 () (lambda @t124 @t123)) % 0.37/0.61 (define @t126 () (_ @t125 @t7)) % 0.37/0.61 (define @t127 () (forall @t28 @t126)) % 0.37/0.61 (define @t128 () (_ @t13 @t7)) % 0.37/0.61 (define @t129 () (lambda @t76 (forall @t28 @t128))) % 0.37/0.61 (define @t130 () (or @t121 @t119)) % 0.37/0.61 (define @t131 () (lambda @t124 @t130)) % 0.37/0.61 (define @t132 () (_ @t131 @t30)) % 0.37/0.61 (define @t133 () (or @t122 @t132)) % 0.37/0.61 (define @t134 () (lambda @t124 @t133)) % 0.37/0.61 (define @t135 () (_ @t18 @t30)) % 0.37/0.61 (define @t136 () (@list @t18 @t30)) % 0.37/0.61 (define @t137 () (lambda @t124 @t119)) % 0.37/0.61 (define @t138 () (_ @t137 @t30)) % 0.37/0.61 (define @t139 () (or @t121 @t138)) % 0.37/0.61 (define @t140 () (lambda @t124 @t139)) % 0.37/0.61 (define @t141 () (_ @t13 @t1)) % 0.37/0.61 (define @t142 () (not @t141)) % 0.37/0.61 (define @t143 () (not (forall @t6 (or @t118 @t142)))) % 0.37/0.61 (define @t144 () (lambda @t86 @t143)) % 0.37/0.61 (define @t145 () (_ @t144 tptp.q)) % 0.37/0.61 (define @t146 () (lambda @t28 @t102)) % 0.37/0.61 (define @t147 () (_ @t146 @t30)) % 0.37/0.61 (define @t148 () (not @t147)) % 0.37/0.61 (define @t149 () (or @t148 @t135)) % 0.37/0.61 (define @t150 () (lambda @t136 @t149)) % 0.37/0.61 (define @t151 () (or (not (_ @t13 @t30)) @t135)) % 0.37/0.61 (define @t152 () (lambda @t34 @t151)) % 0.37/0.61 (define @t153 () (lambda @t16 (forall @t6 (or @t99 @t141)))) % 0.37/0.61 (define @t154 () (_ @t153 tptp.p)) % 0.37/0.61 (define @t155 () (not @t122)) % 0.37/0.61 (define @t156 () (lambda @t124 @t155)) % 0.37/0.61 (define @t157 () (_ @t156 @t30)) % 0.37/0.61 (define @t158 () (not @t157)) % 0.37/0.61 (define @t159 () (or @t158 @t135)) % 0.37/0.61 (define @t160 () (lambda @t136 @t159)) % 0.37/0.61 (define @t161 () (_ tptp.p @t1)) % 0.37/0.61 (define @t162 () (and @t161 @t115)) % 0.37/0.61 (define @t163 () (or @t118 @t162)) % 0.37/0.61 (define @t164 () (not @t161)) % 0.37/0.61 (define @t165 () (or @t164 @t114)) % 0.37/0.61 (define @t166 () (or @t118 (not @t165))) % 0.37/0.61 (define @t167 () (not (_ tptp.p @t30))) % 0.37/0.61 (define @t168 () (forall @t6 (or @t118 @t96))) % 0.37/0.61 (define @t169 () (or @t167 @t168)) % 0.37/0.61 (define @t170 () (lambda @t124 @t169)) % 0.37/0.61 (define @t171 () (not (_ @t170 @t1))) % 0.37/0.61 (define @t172 () (or @t118 @t171)) % 0.37/0.61 (define @t173 () (forall @t6 @t172)) % 0.37/0.61 (define @t174 () (not @t173)) % 0.37/0.61 (define @t175 () (lambda @t124 @t174)) % 0.37/0.61 (define @t176 () (lambda @t28 (forall @t6 (or @t99 @t96)))) % 0.37/0.61 (define @t177 () (_ @t176 @t30)) % 0.37/0.61 (define @t178 () (or @t167 @t177)) % 0.37/0.61 (define @t179 () (lambda @t124 @t178)) % 0.37/0.61 (define @t180 () (lambda @t136 (or @t167 @t135))) % 0.37/0.61 (define @t181 () (_ @t153 tptp.q)) % 0.37/0.61 (define @t182 () (_ @t152 tptp.p)) % 0.37/0.61 (define @t183 () (forall @t6 (or @t99 @t142))) % 0.37/0.61 (define @t184 () (lambda @t28 @t183)) % 0.37/0.61 (define @t185 () (_ @t184 @t7)) % 0.37/0.61 (define @t186 () (not @t185)) % 0.37/0.61 (define @t187 () (lambda @t28 @t186)) % 0.37/0.61 (define @t188 () (not @t21)) % 0.37/0.61 (define @t189 () (or @t99 @t188)) % 0.37/0.61 (define @t190 () (lambda @t28 @t15)) % 0.37/0.61 (define @t191 () (_ @t190 @t1)) % 0.37/0.61 (define @t192 () (or @t99 @t191)) % 0.37/0.61 (define @t193 () (forall @t6 @t192)) % 0.37/0.61 (define @t194 () (lambda @t28 @t193)) % 0.37/0.61 (define @t195 () (or @t15 @t19)) % 0.37/0.61 (define @t196 () (lambda @t28 @t195)) % 0.37/0.61 (define @t197 () (@list @t18 @t7)) % 0.37/0.61 (define @t198 () (_ @t190 @t7)) % 0.37/0.61 (define @t199 () (or @t198 @t19)) % 0.37/0.61 (define @t200 () (lambda @t197 @t199)) % 0.37/0.61 (define @t201 () (forall @t107 @t104)) % 0.37/0.61 (define @t202 () (@quantifiers_skolemize @t201 0)) % 0.37/0.61 (define @t203 () (not (tptp.rel_s4 @t202 @t1))) % 0.37/0.61 (define @t204 () (forall @t6 (or @t203 @t101))) % 0.37/0.61 (define @t205 () (@quantifiers_skolemize @t201 1)) % 0.37/0.61 (define @t206 () (forall @t93 (or (not (tptp.rel_s4 @t205 @t90)) @t91))) % 0.37/0.61 (define @t207 () (not @t206)) % 0.37/0.61 (define @t208 () (tptp.p @t205)) % 0.37/0.61 (define @t209 () (and @t208 @t207)) % 0.37/0.61 (define @t210 () (tptp.rel_s4 @t202 @t205)) % 0.37/0.61 (define @t211 () (not @t210)) % 0.37/0.61 (define @t212 () (forall @t6 (or @t203 @t97))) % 0.37/0.61 (define @t213 () (not @t212)) % 0.37/0.61 (define @t214 () (not @t204)) % 0.37/0.61 (define @t215 () (or @t214 @t213 @t211 @t209)) % 0.37/0.61 (define @t216 () (@list true)) % 0.37/0.61 (define @t217 () (@list @t215)) % 0.37/0.61 (define @t218 () (@list @t205)) % 0.37/0.61 (define @t219 () (or @t211 @t208)) % 0.37/0.61 (define @t220 () (@list false false)) % 0.37/0.61 (define @t221 () (not @t208)) % 0.37/0.61 (define @t222 () (@list true false)) % 0.37/0.61 (define @t223 () (tptp.q @t205)) % 0.37/0.61 (define @t224 () (not @t223)) % 0.37/0.61 (define @t225 () (or @t211 @t224)) % 0.37/0.61 (define @t226 () (tptp.rel_s4 @t205 @t205)) % 0.37/0.61 (define @t227 () (not @t226)) % 0.37/0.61 (define @t228 () (or @t227 @t223)) % 0.37/0.61 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.37/0.61 (assume @p2 (forall @t6 (exists @t5 @t4))) % 0.37/0.61 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 0.37/0.61 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 0.37/0.61 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 0.37/0.61 (assume @p6 @t9) % 0.37/0.61 (assume @p7 true) % 0.37/0.61 (step @p8 (= tptp.meq_prop @t12) :rule refl :args (@t12)) % 0.37/0.61 (step @p9 (= tptp.mnot @t17) :rule refl :args (@t17)) % 0.37/0.61 (step @p10 (= tptp.mor @t20) :rule refl :args (@t20)) % 0.37/0.61 (step @p11 (= tptp.mbox @t23) :rule refl :args (@t23)) % 0.37/0.61 (step @p12 (= tptp.mforall_prop @t27) :rule refl :args (@t27)) % 0.37/0.61 (step @p13 (= tptp.mtrue @t29) :rule refl :args (@t29)) % 0.37/0.61 (step @p14 (= tptp.mand @t35) :rule refl :args (@t35)) % 0.37/0.61 (step @p15 (= tptp.mimplies @t36) :rule refl :args (@t36)) % 0.37/0.61 (step @p16 (= tptp.mimplied @t37) :rule refl :args (@t37)) % 0.37/0.61 (step @p17 (= tptp.mequiv @t38) :rule refl :args (@t38)) % 0.37/0.61 (step @p18 (= tptp.mxor @t39) :rule refl :args (@t39)) % 0.37/0.61 (step @p19 (= tptp.mdia @t40) :rule refl :args (@t40)) % 0.37/0.61 (step @p20 (= tptp.mforall_ind @t43) :rule refl :args (@t43)) % 0.37/0.61 (step @p21 (= tptp.mexists_ind @t44) :rule refl :args (@t44)) % 0.37/0.61 (step @p22 (= tptp.mexists_prop @t45) :rule refl :args (@t45)) % 0.37/0.61 (step @p23 (= tptp.mreflexive @t52) :rule refl :args (@t52)) % 0.37/0.61 (step @p24 (= tptp.msymmetric @t56) :rule refl :args (@t56)) % 0.37/0.61 (step @p25 (= tptp.mserial @t58) :rule refl :args (@t58)) % 0.37/0.61 (step @p26 (= tptp.mtransitive @t63) :rule refl :args (@t63)) % 0.37/0.61 (step @p27 (= tptp.meuclidean @t65) :rule refl :args (@t65)) % 0.37/0.61 (step @p28 (= tptp.mpartially_functional @t67) :rule refl :args (@t67)) % 0.37/0.61 (step @p29 (= tptp.mfunctional @t69) :rule refl :args (@t69)) % 0.37/0.61 (step @p30 (= tptp.mweakly_dense @t72) :rule refl :args (@t72)) % 0.37/0.61 (step @p31 (= tptp.mweakly_connected @t73) :rule refl :args (@t73)) % 0.37/0.61 (step @p32 (= tptp.mweakly_directed @t74) :rule refl :args (@t74)) % 0.37/0.61 (step @p33 (= tptp.mvalid @t77) :rule refl :args (@t77)) % 0.37/0.61 (step @p34 (= tptp.msatisfiable @t78) :rule refl :args (@t78)) % 0.37/0.61 (step @p35 (= tptp.mcountersatisfiable @t79) :rule refl :args (@t79)) % 0.37/0.61 (step @p36 (= tptp.minvalid @t80) :rule refl :args (@t80)) % 0.37/0.61 (step @p37 (= tptp.mbox_s4 @t85) :rule refl :args (@t85)) % 0.37/0.61 (step @p38 (= tptp.mdia_s4 @t87) :rule refl :args (@t87)) % 0.37/0.61 (step @p39 :rule beta-reduce :args ((= (_ (lambda @t51 (forall @t49 @t89)) tptp.rel_s4) @t88))) % 0.37/0.61 (step @p40 :rule refl :args (tptp.rel_s4)) % 0.37/0.61 (step @p41 :rule refl :args (@t89)) % 0.37/0.61 (step @p42 :rule refl :args (@t48)) % 0.37/0.61 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t48 @t89))) % 0.37/0.61 (step @p44 :rule symm :premises (@p43)) % 0.37/0.61 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.37/0.61 (step @p46 :rule cong :premises (@p45) :args (@t50)) % 0.37/0.61 (step @p47 :rule cong :premises (@p46) :args (@t52)) % 0.37/0.61 (step @p48 :rule trans :premises (@p23 @p47)) % 0.37/0.61 (step @p49 :rule ho_cong :premises (@p48 @p40)) % 0.37/0.61 (step @p50 :rule trans :premises (@p49 @p39)) % 0.37/0.61 (step @p51 :rule eq_resolve :premises (@p3 @p50)) % 0.37/0.61 (step @p52 :rule aci_norm :args ((= @t106 @t104))) % 0.37/0.61 (step @p53 :rule cong :premises (@p52) :args (@t108)) % 0.37/0.61 (step @p54 :rule quant-merge-prenex :args ((= (forall @t28 @t110) @t108))) % 0.37/0.61 (step @p55 :rule refl :args (@t100)) % 0.37/0.61 (step @p56 :rule refl :args (@t103)) % 0.37/0.61 (step @p57 :rule alpha_equiv :args (@t111 (@list @t92) @t112)) % 0.37/0.61 (step @p58 :rule nary_cong :premises (@p57 @p56 @p55) :args (@t113)) % 0.37/0.61 (step @p59 :rule quant-miniscope-or :args ((= @t110 @t113))) % 0.37/0.61 (step @p60 :rule trans :premises (@p59 @p58)) % 0.37/0.61 (step @p61 :rule symm :premises (@p60)) % 0.37/0.61 (step @p62 :rule cong :premises (@p61) :args ((forall @t28 @t117))) % 0.37/0.61 (step @p63 :rule trans :premises (@p62 @p54)) % 0.37/0.61 (step @p64 :rule trans :premises (@p63 @p53)) % 0.37/0.61 (step @p65 :rule beta-reduce :args ((= @t126 @t117))) % 0.37/0.61 (step @p66 :rule cong :premises (@p65) :args (@t127)) % 0.37/0.61 (step @p67 :rule trans :premises (@p66 @p64)) % 0.37/0.61 (step @p68 :rule beta-reduce :args ((= (_ @t129 @t125) @t127))) % 0.37/0.61 (step @p69 :rule trans :premises (@p68 @p67)) % 0.37/0.61 (step @p70 :rule aci_norm :args ((= (or @t122 @t130) @t123))) % 0.37/0.61 (step @p71 :rule beta-reduce :args ((= @t132 @t130))) % 0.37/0.61 (step @p72 :rule refl :args (@t122)) % 0.37/0.61 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t133)) % 0.37/0.61 (step @p74 :rule trans :premises (@p73 @p70)) % 0.37/0.61 (step @p75 :rule cong :premises (@p74) :args (@t134)) % 0.37/0.61 (step @p76 :rule beta-reduce :args ((= (_ (lambda @t136 (or @t122 @t135)) @t131) @t134))) % 0.37/0.61 (step @p77 :rule trans :premises (@p76 @p75)) % 0.37/0.61 (step @p78 :rule beta-reduce :args ((= @t138 @t119))) % 0.37/0.61 (step @p79 :rule refl :args (@t121)) % 0.37/0.61 (step @p80 :rule nary_cong :premises (@p79 @p78) :args (@t139)) % 0.37/0.61 (step @p81 :rule cong :premises (@p80) :args (@t140)) % 0.37/0.61 (step @p82 :rule beta-reduce :args ((= (_ (lambda @t136 (or @t121 @t135)) @t137) @t140))) % 0.37/0.61 (step @p83 :rule trans :premises (@p82 @p81)) % 0.37/0.61 (step @p84 :rule beta-reduce :args ((= @t145 @t137))) % 0.37/0.61 (step @p85 :rule refl :args (@t135)) % 0.37/0.61 (step @p86 :rule beta-reduce :args ((= @t147 @t120))) % 0.37/0.61 (step @p87 :rule cong :premises (@p86) :args (@t148)) % 0.37/0.61 (step @p88 :rule nary_cong :premises (@p87 @p85) :args (@t149)) % 0.37/0.61 (step @p89 :rule cong :premises (@p88) :args (@t150)) % 0.37/0.61 (step @p90 :rule beta-reduce :args ((= (_ @t152 @t146) @t150))) % 0.37/0.61 (step @p91 :rule trans :premises (@p90 @p89)) % 0.37/0.61 (step @p92 :rule beta-reduce :args ((= @t154 @t146))) % 0.37/0.61 (step @p93 :rule refl :args (@t152)) % 0.37/0.61 (step @p94 :rule ho_cong :premises (@p93 @p92)) % 0.37/0.61 (step @p95 :rule trans :premises (@p94 @p91)) % 0.37/0.61 (step @p96 :rule ho_cong :premises (@p95 @p84)) % 0.37/0.61 (step @p97 :rule trans :premises (@p96 @p83)) % 0.37/0.61 (step @p98 :rule bool-double-not-elim :args (@t122)) % 0.37/0.61 (step @p99 :rule beta-reduce :args ((= @t157 @t155))) % 0.37/0.61 (step @p100 :rule cong :premises (@p99) :args (@t158)) % 0.37/0.61 (step @p101 :rule trans :premises (@p100 @p98)) % 0.37/0.61 (step @p102 :rule nary_cong :premises (@p101 @p85) :args (@t159)) % 0.37/0.61 (step @p103 :rule cong :premises (@p102) :args (@t160)) % 0.37/0.61 (step @p104 :rule beta-reduce :args ((= (_ @t152 @t156) @t160))) % 0.37/0.61 (step @p105 :rule trans :premises (@p104 @p103)) % 0.37/0.61 (step @p106 :rule refl :args (@t115)) % 0.37/0.61 (step @p107 :rule refl :args (@t101)) % 0.37/0.61 (step @p108 :rule refl :args (@t161)) % 0.37/0.61 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t161 @t101))) % 0.37/0.61 (step @p110 :rule symm :premises (@p109)) % 0.37/0.61 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 0.37/0.61 (step @p112 :rule nary_cong :premises (@p111 @p106) :args (@t162)) % 0.37/0.61 (step @p113 :rule refl :args (@t118)) % 0.37/0.61 (step @p114 :rule nary_cong :premises (@p113 @p112) :args (@t163)) % 0.37/0.61 (step @p115 :rule cong :premises (@p114) :args ((forall @t6 @t163))) % 0.37/0.61 (step @p116 :rule bool-double-not-elim :args (@t161)) % 0.37/0.61 (step @p117 :rule nary_cong :premises (@p116 @p106) :args ((and (not @t164) @t115))) % 0.37/0.61 (step @p118 :rule bool-or-de-morgan :args (@t164 @t114 false)) % 0.37/0.61 (step @p119 :rule trans :premises (@p118 @p117)) % 0.37/0.61 (step @p120 :rule nary_cong :premises (@p113 @p119) :args (@t166)) % 0.37/0.61 (step @p121 :rule cong :premises (@p120) :args ((forall @t6 @t166))) % 0.37/0.61 (step @p122 :rule trans :premises (@p121 @p115)) % 0.37/0.61 (step @p123 :rule beta-reduce :args ((= (_ (lambda @t124 (or @t167 (forall @t93 (or (not (tptp.rel_s4 @t30 @t90)) @t91)))) @t1) @t165))) % 0.37/0.61 (step @p124 :rule refl :args (@t1)) % 0.37/0.61 (step @p125 :rule alpha_equiv :args (@t168 @t112 (@list @t90))) % 0.37/0.61 (step @p126 :rule refl :args (@t167)) % 0.37/0.61 (step @p127 :rule nary_cong :premises (@p126 @p125) :args (@t169)) % 0.37/0.61 (step @p128 :rule cong :premises (@p127) :args (@t170)) % 0.37/0.61 (step @p129 :rule ho_cong :premises (@p128 @p124)) % 0.37/0.61 (step @p130 :rule trans :premises (@p129 @p123)) % 0.37/0.61 (step @p131 :rule cong :premises (@p130) :args (@t171)) % 0.37/0.61 (step @p132 :rule refl :args (@t118)) % 0.37/0.61 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t172)) % 0.37/0.61 (step @p134 :rule cong :premises (@p133) :args (@t173)) % 0.37/0.61 (step @p135 :rule trans :premises (@p134 @p122)) % 0.37/0.61 (step @p136 :rule cong :premises (@p135) :args (@t174)) % 0.37/0.61 (step @p137 :rule cong :premises (@p136) :args (@t175)) % 0.37/0.61 (step @p138 :rule beta-reduce :args ((= (_ @t144 @t170) @t175))) % 0.37/0.61 (step @p139 :rule trans :premises (@p138 @p137)) % 0.37/0.61 (step @p140 :rule beta-reduce :args ((= @t177 @t168))) % 0.37/0.61 (step @p141 :rule refl :args (@t167)) % 0.37/0.61 (step @p142 :rule nary_cong :premises (@p141 @p140) :args (@t178)) % 0.37/0.61 (step @p143 :rule cong :premises (@p142) :args (@t179)) % 0.37/0.61 (step @p144 :rule beta-reduce :args ((= (_ @t180 @t176) @t179))) % 0.37/0.61 (step @p145 :rule trans :premises (@p144 @p143)) % 0.37/0.61 (step @p146 :rule beta-reduce :args ((= @t181 @t176))) % 0.37/0.61 (step @p147 :rule beta-reduce :args ((= @t182 @t180))) % 0.37/0.61 (step @p148 :rule ho_cong :premises (@p147 @p146)) % 0.37/0.61 (step @p149 :rule trans :premises (@p148 @p145)) % 0.37/0.61 (step @p150 :rule refl :args (@t144)) % 0.37/0.61 (step @p151 :rule ho_cong :premises (@p150 @p149)) % 0.37/0.61 (step @p152 :rule trans :premises (@p151 @p139)) % 0.37/0.61 (step @p153 :rule ho_cong :premises (@p93 @p152)) % 0.37/0.61 (step @p154 :rule trans :premises (@p153 @p105)) % 0.37/0.61 (step @p155 :rule ho_cong :premises (@p154 @p97)) % 0.37/0.61 (step @p156 :rule trans :premises (@p155 @p77)) % 0.37/0.61 (step @p157 :rule refl :args (@t129)) % 0.37/0.61 (step @p158 :rule ho_cong :premises (@p157 @p156)) % 0.37/0.61 (step @p159 :rule trans :premises (@p158 @p69)) % 0.37/0.61 (step @p160 :rule cong :premises (@p159) :args ((not (_ @t129 (_ (_ @t152 (_ @t144 (_ @t182 @t181))) (_ (_ @t152 @t154) @t145)))))) % 0.37/0.61 (step @p161 :rule refl :args (tptp.q)) % 0.37/0.61 (step @p162 :rule beta-reduce :args ((= (_ (lambda @t28 (not @t183)) @t30) @t143))) % 0.37/0.61 (step @p163 :rule refl :args (@t30)) % 0.37/0.61 (step @p164 :rule beta-reduce :args ((= @t185 @t183))) % 0.37/0.61 (step @p165 :rule cong :premises (@p164) :args (@t186)) % 0.37/0.61 (step @p166 :rule cong :premises (@p165) :args (@t187)) % 0.37/0.61 (step @p167 :rule beta-reduce :args ((= (_ @t17 @t184) @t187))) % 0.37/0.61 (step @p168 :rule trans :premises (@p167 @p166)) % 0.37/0.61 (step @p169 :rule refl :args (@t141)) % 0.37/0.61 (step @p170 :rule refl :args (@t21)) % 0.37/0.61 (step @p171 :rule cong :premises (@p170 @p169) :args ((= @t21 @t141))) % 0.37/0.61 (step @p172 :rule symm :premises (@p171)) % 0.37/0.61 (step @p173 :rule eq_resolve :premises (@p170 @p172)) % 0.37/0.61 (step @p174 :rule cong :premises (@p173) :args (@t188)) % 0.37/0.61 (step @p175 :rule refl :args (@t99)) % 0.37/0.61 (step @p176 :rule nary_cong :premises (@p175 @p174) :args (@t189)) % 0.37/0.61 (step @p177 :rule cong :premises (@p176) :args ((forall @t6 @t189))) % 0.37/0.61 (step @p178 :rule beta-reduce :args ((= @t191 @t188))) % 0.37/0.61 (step @p179 :rule refl :args (@t99)) % 0.37/0.61 (step @p180 :rule nary_cong :premises (@p179 @p178) :args (@t192)) % 0.37/0.61 (step @p181 :rule cong :premises (@p180) :args (@t193)) % 0.37/0.61 (step @p182 :rule trans :premises (@p181 @p177)) % 0.37/0.61 (step @p183 :rule cong :premises (@p182) :args (@t194)) % 0.37/0.61 (step @p184 :rule beta-reduce :args ((= (_ @t153 @t190) @t194))) % 0.37/0.61 (step @p185 :rule trans :premises (@p184 @p183)) % 0.37/0.61 (step @p186 :rule beta-reduce :args ((= (_ @t17 @t13) @t190))) % 0.37/0.61 (step @p187 :rule refl :args (@t153)) % 0.37/0.61 (step @p188 :rule ho_cong :premises (@p187 @p186)) % 0.37/0.61 (step @p189 :rule trans :premises (@p188 @p185)) % 0.37/0.61 (step @p190 :rule refl :args (@t17)) % 0.37/0.61 (step @p191 :rule ho_cong :premises (@p190 @p189)) % 0.37/0.61 (step @p192 :rule trans :premises (@p191 @p168)) % 0.37/0.61 (step @p193 :rule ho_cong :premises (@p192 @p163)) % 0.37/0.61 (step @p194 :rule trans :premises (@p193 @p162)) % 0.37/0.61 (step @p195 :rule refl :args (@t13)) % 0.37/0.61 (step @p196 :rule ho_cong :premises (@p9 @p195)) % 0.37/0.61 (step @p197 :rule refl :args (@t98)) % 0.37/0.61 (step @p198 :rule refl :args (@t81)) % 0.37/0.61 (step @p199 :rule cong :premises (@p198 @p197) :args ((= @t81 @t98))) % 0.37/0.61 (step @p200 :rule symm :premises (@p199)) % 0.37/0.61 (step @p201 :rule eq_resolve :premises (@p198 @p200)) % 0.37/0.61 (step @p202 :rule cong :premises (@p201) :args (@t82)) % 0.37/0.61 (step @p203 :rule nary_cong :premises (@p202 @p173) :args (@t83)) % 0.37/0.61 (step @p204 :rule cong :premises (@p203) :args (@t84)) % 0.37/0.61 (step @p205 :rule cong :premises (@p204) :args (@t85)) % 0.37/0.61 (step @p206 :rule trans :premises (@p37 @p205)) % 0.37/0.61 (step @p207 :rule ho_cong :premises (@p206 @p196)) % 0.37/0.61 (step @p208 :rule ho_cong :premises (@p9 @p207)) % 0.37/0.61 (step @p209 :rule ho_cong :premises (@p208 @p163)) % 0.37/0.61 (step @p210 :rule trans :premises (@p209 @p194)) % 0.37/0.61 (step @p211 :rule cong :premises (@p210) :args (@t87)) % 0.37/0.61 (step @p212 :rule trans :premises (@p38 @p211)) % 0.37/0.61 (step @p213 :rule ho_cong :premises (@p212 @p161)) % 0.37/0.61 (step @p214 :rule refl :args (tptp.p)) % 0.37/0.61 (step @p215 :rule ho_cong :premises (@p206 @p214)) % 0.37/0.61 (step @p216 :rule beta-reduce :args ((= (_ @t196 @t30) @t151))) % 0.37/0.61 (step @p217 :rule beta-reduce :args ((= (_ (lambda @t197 @t195) @t18) @t196))) % 0.37/0.61 (step @p218 :rule refl :args (@t18)) % 0.37/0.61 (step @p219 :rule refl :args (@t19)) % 0.37/0.61 (step @p220 :rule beta-reduce :args ((= @t198 @t15))) % 0.37/0.61 (step @p221 :rule nary_cong :premises (@p220 @p219) :args (@t199)) % 0.37/0.61 (step @p222 :rule cong :premises (@p221) :args (@t200)) % 0.37/0.61 (step @p223 :rule beta-reduce :args ((= (_ @t20 @t190) @t200))) % 0.37/0.61 (step @p224 :rule trans :premises (@p223 @p222)) % 0.37/0.61 (step @p225 :rule refl :args (@t20)) % 0.37/0.61 (step @p226 :rule ho_cong :premises (@p225 @p186)) % 0.37/0.61 (step @p227 :rule trans :premises (@p226 @p224)) % 0.37/0.61 (step @p228 :rule ho_cong :premises (@p227 @p218)) % 0.37/0.61 (step @p229 :rule trans :premises (@p228 @p217)) % 0.37/0.61 (step @p230 :rule ho_cong :premises (@p229 @p163)) % 0.37/0.61 (step @p231 :rule trans :premises (@p230 @p216)) % 0.37/0.61 (step @p232 :rule ho_cong :premises (@p10 @p196)) % 0.37/0.61 (step @p233 :rule ho_cong :premises (@p232 @p218)) % 0.37/0.61 (step @p234 :rule ho_cong :premises (@p233 @p163)) % 0.37/0.61 (step @p235 :rule trans :premises (@p234 @p231)) % 0.37/0.61 (step @p236 :rule cong :premises (@p235) :args (@t36)) % 0.37/0.61 (step @p237 :rule trans :premises (@p15 @p236)) % 0.37/0.61 (step @p238 :rule ho_cong :premises (@p237 @p215)) % 0.37/0.61 (step @p239 :rule ho_cong :premises (@p238 @p213)) % 0.37/0.61 (step @p240 :rule ho_cong :premises (@p206 @p161)) % 0.37/0.61 (step @p241 :rule ho_cong :premises (@p237 @p214)) % 0.37/0.61 (step @p242 :rule ho_cong :premises (@p241 @p240)) % 0.37/0.61 (step @p243 :rule ho_cong :premises (@p212 @p242)) % 0.37/0.61 (step @p244 :rule ho_cong :premises (@p237 @p243)) % 0.37/0.61 (step @p245 :rule ho_cong :premises (@p244 @p239)) % 0.37/0.61 (step @p246 :rule refl :args (@t128)) % 0.37/0.61 (step @p247 :rule refl :args (@t14)) % 0.37/0.61 (step @p248 :rule cong :premises (@p247 @p246) :args ((= @t14 @t128))) % 0.37/0.61 (step @p249 :rule symm :premises (@p248)) % 0.37/0.62 (step @p250 :rule eq_resolve :premises (@p247 @p249)) % 0.37/0.62 (step @p251 :rule cong :premises (@p250) :args (@t75)) % 0.37/0.62 (step @p252 :rule cong :premises (@p251) :args (@t77)) % 0.37/0.62 (step @p253 :rule trans :premises (@p33 @p252)) % 0.37/0.62 (step @p254 :rule ho_cong :premises (@p253 @p245)) % 0.37/0.62 (step @p255 :rule cong :premises (@p254) :args (@t9)) % 0.37/0.62 (step @p256 :rule trans :premises (@p255 @p160)) % 0.37/0.62 (step @p257 :rule eq_resolve :premises (@p6 @p256)) % 0.37/0.62 (step @p258 :rule skolemize :premises (@p257)) % 0.37/0.62 (step @p259 :rule bool-double-not-elim :args (@t204)) % 0.37/0.62 (step @p260 :rule refl :args (@t215)) % 0.37/0.62 (step @p261 :rule nary_cong :premises (@p260 @p259) :args ((or @t215 (not @t214)))) % 0.37/0.62 (step @p262 :rule cnf_or_neg :args (@t215 0)) % 0.37/0.62 (step @p263 :rule eq_resolve :premises (@p262 @p261)) % 0.37/0.62 (step @p264 :rule reordering :premises (@p263) :args ((or @t204 @t215))) % 0.37/0.62 (step @p265 :rule chain_m_resolution :premises (@p264 @p258) :args (@t204 @t216 @t217)) % 0.37/0.62 (step @p266 :rule instantiate :premises (@p265) :args (@t218)) % 0.37/0.62 (step @p267 :rule bool-double-not-elim :args (@t210)) % 0.37/0.62 (step @p268 :rule nary_cong :premises (@p260 @p267) :args ((or @t215 (not @t211)))) % 0.37/0.62 (step @p269 :rule cnf_or_neg :args (@t215 2)) % 0.37/0.62 (step @p270 :rule eq_resolve :premises (@p269 @p268)) % 0.37/0.62 (step @p271 :rule reordering :premises (@p270) :args ((or @t210 @t215))) % 0.37/0.62 (step @p272 :rule chain_m_resolution :premises (@p271 @p258) :args (@t210 @t216 @t217)) % 0.37/0.62 (step @p273 :rule cnf_or_pos :args (@t219)) % 0.37/0.62 (step @p274 :rule reordering :premises (@p273) :args ((or @t211 @t208 (not @t219)))) % 0.37/0.62 (step @p275 :rule chain_m_resolution :premises (@p274 @p272 @p266) :args (@t208 @t220 (@list @t210 @t219))) % 0.37/0.62 (step @p276 :rule cnf_or_neg :args (@t215 3)) % 0.37/0.62 (step @p277 :rule chain_m_resolution :premises (@p276 @p258) :args ((not @t209) @t216 @t217)) % 0.37/0.62 (step @p278 :rule bool-double-not-elim :args (@t206)) % 0.37/0.62 (step @p279 :rule refl :args (@t221)) % 0.37/0.62 (step @p280 :rule refl :args (@t209)) % 0.37/0.62 (step @p281 :rule nary_cong :premises (@p280 @p279 @p278) :args ((or @t209 @t221 (not @t207)))) % 0.37/0.62 (step @p282 :rule cnf_and_neg :args (@t209)) % 0.37/0.62 (step @p283 :rule eq_resolve :premises (@p282 @p281)) % 0.37/0.62 (step @p284 :rule reordering :premises (@p283) :args ((or @t206 @t209 @t221))) % 0.37/0.62 (step @p285 :rule chain_m_resolution :premises (@p284 @p277 @p275) :args (@t206 @t222 (@list @t209 @t208))) % 0.37/0.62 (step @p286 :rule instantiate :premises (@p285) :args (@t218)) % 0.37/0.62 (step @p287 :rule bool-double-not-elim :args (@t212)) % 0.37/0.62 (step @p288 :rule nary_cong :premises (@p260 @p287) :args ((or @t215 (not @t213)))) % 0.37/0.62 (step @p289 :rule cnf_or_neg :args (@t215 1)) % 0.37/0.62 (step @p290 :rule eq_resolve :premises (@p289 @p288)) % 0.37/0.62 (step @p291 :rule reordering :premises (@p290) :args ((or @t212 @t215))) % 0.37/0.62 (step @p292 :rule chain_m_resolution :premises (@p291 @p258) :args (@t212 @t216 @t217)) % 0.37/0.62 (step @p293 :rule instantiate :premises (@p292) :args (@t218)) % 0.37/0.62 (step @p294 :rule cnf_or_pos :args (@t225)) % 0.37/0.62 (step @p295 :rule reordering :premises (@p294) :args ((or @t211 @t224 (not @t225)))) % 0.37/0.62 (step @p296 :rule chain_m_resolution :premises (@p295 @p272 @p293) :args (@t224 @t220 (@list @t210 @t225))) % 0.37/0.62 (step @p297 :rule cnf_or_pos :args (@t228)) % 0.37/0.62 (step @p298 :rule reordering :premises (@p297) :args ((or @t223 @t227 (not @t228)))) % 0.37/0.62 (step @p299 :rule chain_m_resolution :premises (@p298 @p296 @p286) :args (@t227 @t222 (@list @t223 @t228))) % 0.37/0.62 (assume-push @p306 @t88) % 0.37/0.62 (step @p301 :rule instantiate :premises (@p51) :args (@t218)) % 0.37/0.62 (step-pop @p307 :rule scope :premises (@p301)) % 0.37/0.62 (step @p302 :rule process_scope :premises (@p307) :args (@t226)) % 0.37/0.62 (step @p304 :rule implies_elim :premises (@p302)) % 0.37/0.62 (step @p305 false :rule chain_m_resolution :premises (@p304 @p299 @p51) :args (false @t222 (@list @t226 @t88))) % 0.37/0.62 ) % 0.37/0.62 % SZS output end Proof % 0.37/0.62 % cvc5 exiting %------------------------------------------------------------------------------