%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO463^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n028.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 09:12:49 AM UTC 2026 % Result : Theorem 0.36s 0.63s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO463^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n028.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 00:11:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.36/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.63 % SZS status Theorem % 0.36/0.63 % SZS output start Proof % 0.36/0.63 ( % 0.36/0.63 (declare-sort $$unsorted 0) % 0.36/0.63 (declare-sort tptp.mu 0) % 0.36/0.63 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.q (-> $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.p (-> $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.36/0.63 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.36/0.63 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.36/0.63 (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)))))) % 0.36/0.63 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.36/0.63 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.63 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.36/0.63 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.63 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.36/0.63 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.36/0.63 (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))))))) % 0.36/0.63 (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))))))) % 0.36/0.63 (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)))))) % 0.36/0.63 (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)))))) % 0.36/0.63 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.36/0.63 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.36/0.63 (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)))))) % 0.36/0.63 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.63 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.63 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.63 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.36/0.63 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.36/0.63 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.36/0.63 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.36/0.63 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.36/0.63 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.36/0.63 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.36/0.63 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.36/0.63 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.36/0.63 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.36/0.63 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.36/0.63 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$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)))))))) % 0.36/0.63 (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))))) % 0.36/0.63 (define @t1 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ tptp.mbox_s4 (_ (_ tptp.mequiv tptp.p) tptp.q))) (_ tptp.mbox_s4 (_ (_ tptp.mequiv (_ tptp.mbox_s4 tptp.p)) (_ tptp.mbox_s4 tptp.q))))))) % 0.36/0.63 (define @t2 () (@var "Y" tptp.mu)) % 0.36/0.63 (define @t3 () (@var "X" tptp.mu)) % 0.36/0.63 (define @t4 () (@var "W" $$unsorted)) % 0.36/0.63 (define @t5 () (lambda (@list @t3 @t2 @t4) (= @t3 @t2))) % 0.36/0.63 (define @t6 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.63 (define @t7 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.63 (define @t8 () (lambda (@list @t7 @t6 @t4) (= (_ @t7 @t4) (_ @t6 @t4)))) % 0.36/0.63 (define @t9 () (@var "Phi" (-> $$unsorted Bool))) % 0.36/0.63 (define @t10 () (_ @t9 @t4)) % 0.36/0.63 (define @t11 () (not @t10)) % 0.36/0.63 (define @t12 () (@list @t9 @t4)) % 0.36/0.63 (define @t13 () (lambda @t12 @t11)) % 0.36/0.63 (define @t14 () (@var "Psi" (-> $$unsorted Bool))) % 0.36/0.63 (define @t15 () (_ @t14 @t4)) % 0.36/0.63 (define @t16 () (lambda (@list @t9 @t14 @t4) (or @t10 @t15))) % 0.36/0.63 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.63 (define @t18 () (_ tptp.mnot @t14)) % 0.36/0.63 (define @t19 () (_ tptp.mnot @t9)) % 0.36/0.63 (define @t20 () (_ tptp.mor @t19)) % 0.36/0.63 (define @t21 () (@list @t9 @t14 @t17)) % 0.36/0.63 (define @t22 () (lambda @t21 (_ (_ tptp.mnot (_ @t20 @t18)) @t17))) % 0.36/0.63 (define @t23 () (lambda @t21 (_ (_ @t20 @t14) @t17))) % 0.36/0.63 (define @t24 () (lambda @t21 (_ (_ (_ tptp.mor @t18) @t9) @t17))) % 0.36/0.63 (define @t25 () (lambda @t21 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t9) @t14)) (_ (_ tptp.mimplies @t14) @t9)) @t17))) % 0.36/0.63 (define @t26 () (lambda @t21 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t9) @t14)) @t17))) % 0.36/0.63 (define @t27 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.36/0.63 (define @t28 () (_ @t27 @t3)) % 0.36/0.63 (define @t29 () (lambda (@list @t27 @t4) (forall (@list @t3) (_ @t28 @t4)))) % 0.36/0.63 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.63 (define @t31 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.36/0.63 (define @t32 () (_ @t31 @t30)) % 0.36/0.63 (define @t33 () (lambda (@list @t31 @t4) (forall (@list @t30) (_ @t32 @t4)))) % 0.36/0.63 (define @t34 () (lambda (@list @t27 @t17) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t3 @t17) (_ (_ tptp.mnot @t28) @t17)))) @t17))) % 0.36/0.63 (define @t35 () (lambda (@list @t31 @t17) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t30 @t17) (_ (_ tptp.mnot @t32) @t17)))) @t17))) % 0.36/0.63 (define @t36 () (@list @t4)) % 0.36/0.63 (define @t37 () (lambda @t36 true)) % 0.36/0.63 (define @t38 () (@var "V" $$unsorted)) % 0.36/0.63 (define @t39 () (_ @t9 @t38)) % 0.36/0.63 (define @t40 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t41 () (@list @t38)) % 0.36/0.63 (define @t42 () (lambda (@list @t40 @t9 @t4) (forall @t41 (or (not (_ (_ @t40 @t4) @t38)) @t39)))) % 0.36/0.63 (define @t43 () (lambda (@list @t40 @t9 @t17) (_ (_ tptp.mnot (_ (_ tptp.mbox @t40) @t19)) @t17))) % 0.36/0.63 (define @t44 () (@var "S" $$unsorted)) % 0.36/0.63 (define @t45 () (_ @t40 @t44)) % 0.36/0.63 (define @t46 () (@list @t44)) % 0.36/0.63 (define @t47 () (@list @t40)) % 0.36/0.63 (define @t48 () (lambda @t47 (forall @t46 (_ @t45 @t44)))) % 0.36/0.63 (define @t49 () (@var "T" $$unsorted)) % 0.36/0.63 (define @t50 () (_ @t40 @t49)) % 0.36/0.63 (define @t51 () (_ @t45 @t49)) % 0.36/0.63 (define @t52 () (lambda @t47 (forall (@list @t44 @t49) (=> @t51 (_ @t50 @t44))))) % 0.36/0.63 (define @t53 () (@list @t49)) % 0.36/0.63 (define @t54 () (lambda @t47 (forall @t46 (exists @t53 @t51)))) % 0.36/0.63 (define @t55 () (@var "U" $$unsorted)) % 0.36/0.63 (define @t56 () (_ @t45 @t55)) % 0.36/0.63 (define @t57 () (_ @t50 @t55)) % 0.36/0.63 (define @t58 () (and @t51 @t57)) % 0.36/0.63 (define @t59 () (@list @t44 @t49 @t55)) % 0.36/0.63 (define @t60 () (forall @t59 (=> @t58 @t56))) % 0.36/0.63 (define @t61 () (lambda @t47 @t60)) % 0.36/0.63 (define @t62 () (and @t51 @t56)) % 0.36/0.63 (define @t63 () (lambda @t47 (forall @t59 (=> @t62 @t57)))) % 0.36/0.63 (define @t64 () (= @t49 @t55)) % 0.36/0.63 (define @t65 () (lambda @t47 (forall @t59 (=> @t62 @t64)))) % 0.36/0.63 (define @t66 () (@list @t55)) % 0.36/0.63 (define @t67 () (lambda @t47 (forall @t46 (exists @t53 (and @t51 (forall @t66 (=> @t56 @t64))))))) % 0.36/0.63 (define @t68 () (_ @t40 @t55)) % 0.36/0.63 (define @t69 () (_ @t68 @t49)) % 0.36/0.63 (define @t70 () (lambda @t47 (forall @t59 (=> @t51 (exists @t66 (and @t56 @t69)))))) % 0.36/0.63 (define @t71 () (lambda @t47 (forall @t59 (=> @t62 (or @t57 @t64 @t69))))) % 0.36/0.63 (define @t72 () (lambda @t47 (forall @t59 (=> @t62 (exists @t41 (and (_ @t50 @t38) (_ @t68 @t38))))))) % 0.36/0.63 (define @t73 () (forall @t36 @t10)) % 0.36/0.63 (define @t74 () (@list @t9)) % 0.36/0.63 (define @t75 () (lambda @t74 @t73)) % 0.36/0.63 (define @t76 () (lambda @t74 (forall @t36 @t11))) % 0.36/0.63 (define @t77 () (lambda @t74 (exists @t36 @t10))) % 0.36/0.63 (define @t78 () (lambda @t74 (exists @t36 @t11))) % 0.36/0.63 (define @t79 () (_ (_ tptp.rel_s4 @t4) @t38)) % 0.36/0.63 (define @t80 () (not @t79)) % 0.36/0.63 (define @t81 () (or @t80 @t39)) % 0.36/0.63 (define @t82 () (forall @t41 @t81)) % 0.36/0.63 (define @t83 () (lambda @t12 @t82)) % 0.36/0.63 (define @t84 () (lambda (@list @t9 @t17) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t19)) @t17))) % 0.36/0.63 (define @t85 () (@var "BOUND_VARIABLE_8625" $$unsorted)) % 0.36/0.63 (define @t86 () (@var "BOUND_VARIABLE_8621" $$unsorted)) % 0.36/0.63 (define @t87 () (@var "BOUND_VARIABLE_8543" $$unsorted)) % 0.36/0.63 (define @t88 () (tptp.q @t87)) % 0.36/0.63 (define @t89 () (@list @t87)) % 0.36/0.63 (define @t90 () (@var "BOUND_VARIABLE_8623" $$unsorted)) % 0.36/0.63 (define @t91 () (@var "BOUND_VARIABLE_8535" $$unsorted)) % 0.36/0.63 (define @t92 () (tptp.p @t91)) % 0.36/0.63 (define @t93 () (@list @t91)) % 0.36/0.63 (define @t94 () (and (or (not (forall @t93 (or (not (tptp.rel_s4 @t86 @t91)) @t92))) (not (tptp.rel_s4 @t86 @t90)) (tptp.q @t90)) (or (not (forall @t89 (or (not (tptp.rel_s4 @t86 @t87)) @t88))) (not (tptp.rel_s4 @t86 @t85)) (tptp.p @t85)))) % 0.36/0.63 (define @t95 () (not (tptp.rel_s4 @t4 @t86))) % 0.36/0.63 (define @t96 () (tptp.p @t38)) % 0.36/0.63 (define @t97 () (tptp.q @t38)) % 0.36/0.63 (define @t98 () (and (or (not @t96) @t97) (or (not @t97) @t96))) % 0.36/0.63 (define @t99 () (tptp.rel_s4 @t4 @t38)) % 0.36/0.63 (define @t100 () (not @t99)) % 0.36/0.63 (define @t101 () (forall @t41 (or @t100 @t98))) % 0.36/0.63 (define @t102 () (not @t101)) % 0.36/0.63 (define @t103 () (or @t102 @t95 @t94)) % 0.36/0.63 (define @t104 () (or @t95 @t94)) % 0.36/0.63 (define @t105 () (or @t102 @t104)) % 0.36/0.63 (define @t106 () (@list @t4 @t86 @t90 @t85)) % 0.36/0.63 (define @t107 () (forall @t106 @t105)) % 0.36/0.63 (define @t108 () (@list @t86 @t90 @t85)) % 0.36/0.63 (define @t109 () (forall @t108 @t105)) % 0.36/0.63 (define @t110 () (forall @t108 @t104)) % 0.36/0.63 (define @t111 () (@var "BOUND_VARIABLE_8589" $$unsorted)) % 0.36/0.63 (define @t112 () (@var "BOUND_VARIABLE_8582" $$unsorted)) % 0.36/0.63 (define @t113 () (or @t102 @t110)) % 0.36/0.63 (define @t114 () (tptp.p @t111)) % 0.36/0.63 (define @t115 () (not (tptp.rel_s4 @t38 @t111))) % 0.36/0.63 (define @t116 () (forall @t89 (or (not (tptp.rel_s4 @t38 @t87)) @t88))) % 0.36/0.63 (define @t117 () (not @t116)) % 0.36/0.63 (define @t118 () (or @t117 @t115 @t114)) % 0.36/0.63 (define @t119 () (tptp.q @t112)) % 0.36/0.63 (define @t120 () (not (tptp.rel_s4 @t38 @t112))) % 0.36/0.63 (define @t121 () (forall @t93 (or (not (tptp.rel_s4 @t38 @t91)) @t92))) % 0.36/0.63 (define @t122 () (not @t121)) % 0.36/0.63 (define @t123 () (or @t122 @t120 @t119)) % 0.36/0.63 (define @t124 () (and @t123 @t118)) % 0.36/0.63 (define @t125 () (@list @t38 @t112 @t111)) % 0.36/0.63 (define @t126 () (forall @t125 (or @t100 @t124))) % 0.36/0.63 (define @t127 () (or @t102 @t126)) % 0.36/0.63 (define @t128 () (not (tptp.rel_s4 @t17 @t38))) % 0.36/0.63 (define @t129 () (forall @t125 (or @t128 @t124))) % 0.36/0.63 (define @t130 () (forall @t41 (or @t128 @t98))) % 0.36/0.63 (define @t131 () (not @t130)) % 0.36/0.63 (define @t132 () (@list @t17)) % 0.36/0.63 (define @t133 () (lambda @t132 (or @t131 @t129))) % 0.36/0.63 (define @t134 () (_ @t133 @t4)) % 0.36/0.63 (define @t135 () (forall @t36 @t134)) % 0.36/0.63 (define @t136 () (_ @t9 @t4)) % 0.36/0.63 (define @t137 () (lambda @t74 (forall @t36 @t136))) % 0.36/0.63 (define @t138 () (lambda @t36 @t126)) % 0.36/0.63 (define @t139 () (_ @t138 @t17)) % 0.34/0.63 (define @t140 () (or @t131 @t139)) % 0.34/0.63 (define @t141 () (lambda @t132 @t140)) % 0.34/0.63 (define @t142 () (_ @t14 @t17)) % 0.34/0.63 (define @t143 () (@list @t14 @t17)) % 0.34/0.63 (define @t144 () (or @t115 @t114)) % 0.34/0.63 (define @t145 () (or @t117 @t144)) % 0.34/0.63 (define @t146 () (or @t120 @t119)) % 0.34/0.63 (define @t147 () (or @t122 @t146)) % 0.34/0.63 (define @t148 () (and @t147 @t145)) % 0.34/0.63 (define @t149 () (or @t100 @t148)) % 0.34/0.63 (define @t150 () (forall @t125 @t149)) % 0.34/0.63 (define @t151 () (@list @t112 @t111)) % 0.34/0.63 (define @t152 () (forall @t151 @t149)) % 0.34/0.63 (define @t153 () (@list @t111)) % 0.34/0.63 (define @t154 () (forall @t153 @t144)) % 0.34/0.63 (define @t155 () (@list @t91)) % 0.34/0.63 (define @t156 () (or @t117 @t154)) % 0.34/0.63 (define @t157 () (forall @t153 @t145)) % 0.34/0.63 (define @t158 () (forall @t151 @t145)) % 0.34/0.63 (define @t159 () (@list @t112)) % 0.34/0.63 (define @t160 () (forall @t159 @t146)) % 0.34/0.63 (define @t161 () (@list @t87)) % 0.34/0.63 (define @t162 () (or @t122 @t160)) % 0.34/0.63 (define @t163 () (forall @t159 @t147)) % 0.34/0.63 (define @t164 () (forall @t151 @t147)) % 0.34/0.63 (define @t165 () (and @t164 @t158)) % 0.34/0.63 (define @t166 () (forall @t151 @t148)) % 0.34/0.63 (define @t167 () (or @t100 @t166)) % 0.34/0.63 (define @t168 () (or @t117 @t121)) % 0.34/0.63 (define @t169 () (or @t122 @t116)) % 0.34/0.63 (define @t170 () (not @t168)) % 0.34/0.63 (define @t171 () (not @t169)) % 0.34/0.63 (define @t172 () (not (or @t171 @t170))) % 0.34/0.63 (define @t173 () (or @t100 @t172)) % 0.34/0.63 (define @t174 () (forall @t93 (or (not (tptp.rel_s4 @t17 @t91)) @t92))) % 0.34/0.63 (define @t175 () (forall @t89 (or (not (tptp.rel_s4 @t17 @t87)) @t88))) % 0.34/0.63 (define @t176 () (forall @t41 (or @t128 @t96))) % 0.34/0.63 (define @t177 () (@list @t38)) % 0.34/0.63 (define @t178 () (forall @t41 (or @t128 @t97))) % 0.34/0.63 (define @t179 () (not @t178)) % 0.34/0.63 (define @t180 () (or @t179 @t176)) % 0.34/0.63 (define @t181 () (not @t180)) % 0.34/0.63 (define @t182 () (not @t176)) % 0.34/0.63 (define @t183 () (or @t182 @t178)) % 0.34/0.63 (define @t184 () (not @t183)) % 0.34/0.63 (define @t185 () (or @t184 @t181)) % 0.34/0.63 (define @t186 () (not @t185)) % 0.34/0.63 (define @t187 () (lambda @t132 @t186)) % 0.34/0.63 (define @t188 () (or @t100 (_ @t187 @t38))) % 0.34/0.63 (define @t189 () (forall @t41 @t188)) % 0.34/0.63 (define @t190 () (lambda @t36 @t189)) % 0.34/0.63 (define @t191 () (_ @t9 @t38)) % 0.34/0.63 (define @t192 () (lambda @t12 (forall @t41 (or @t100 @t191)))) % 0.34/0.63 (define @t193 () (lambda @t36 (forall @t41 (or @t100 @t97)))) % 0.34/0.63 (define @t194 () (_ @t193 @t17)) % 0.34/0.63 (define @t195 () (not @t194)) % 0.34/0.63 (define @t196 () (or @t195 @t176)) % 0.34/0.63 (define @t197 () (not @t196)) % 0.34/0.63 (define @t198 () (or @t182 @t194)) % 0.34/0.63 (define @t199 () (not @t198)) % 0.34/0.63 (define @t200 () (or @t199 @t197)) % 0.34/0.63 (define @t201 () (not @t200)) % 0.34/0.63 (define @t202 () (lambda @t132 @t201)) % 0.34/0.63 (define @t203 () (not @t142)) % 0.34/0.63 (define @t204 () (_ @t192 tptp.q)) % 0.34/0.63 (define @t205 () (lambda @t36 (forall @t41 (or @t100 @t96)))) % 0.34/0.63 (define @t206 () (_ @t205 @t17)) % 0.34/0.63 (define @t207 () (or @t203 @t206)) % 0.34/0.63 (define @t208 () (not @t207)) % 0.34/0.63 (define @t209 () (not @t206)) % 0.34/0.63 (define @t210 () (or @t209 @t142)) % 0.34/0.63 (define @t211 () (not @t210)) % 0.34/0.63 (define @t212 () (or @t211 @t208)) % 0.34/0.63 (define @t213 () (not @t212)) % 0.34/0.63 (define @t214 () (lambda @t143 @t213)) % 0.34/0.63 (define @t215 () (_ @t9 @t17)) % 0.34/0.63 (define @t216 () (or @t203 @t215)) % 0.34/0.63 (define @t217 () (not @t215)) % 0.34/0.63 (define @t218 () (or @t217 @t142)) % 0.34/0.63 (define @t219 () (not @t218)) % 0.34/0.63 (define @t220 () (not (or @t219 (not @t216)))) % 0.34/0.63 (define @t221 () (lambda @t21 @t220)) % 0.34/0.63 (define @t222 () (_ @t192 tptp.p)) % 0.34/0.63 (define @t223 () (lambda @t36 @t101)) % 0.34/0.63 (define @t224 () (_ @t223 @t17)) % 0.34/0.63 (define @t225 () (not @t224)) % 0.34/0.63 (define @t226 () (or @t225 @t142)) % 0.34/0.63 (define @t227 () (lambda @t143 @t226)) % 0.34/0.63 (define @t228 () (lambda @t21 @t218)) % 0.34/0.63 (define @t229 () (_ tptp.p @t38)) % 0.34/0.63 (define @t230 () (_ tptp.q @t38)) % 0.34/0.63 (define @t231 () (not @t230)) % 0.34/0.63 (define @t232 () (or @t231 @t229)) % 0.34/0.63 (define @t233 () (not @t229)) % 0.34/0.63 (define @t234 () (or @t233 @t230)) % 0.34/0.63 (define @t235 () (and @t234 @t232)) % 0.34/0.63 (define @t236 () (or @t100 @t235)) % 0.34/0.63 (define @t237 () (not @t232)) % 0.34/0.63 (define @t238 () (not @t234)) % 0.34/0.63 (define @t239 () (not (or @t238 @t237))) % 0.34/0.63 (define @t240 () (or @t100 @t239)) % 0.34/0.63 (define @t241 () (_ tptp.p @t17)) % 0.34/0.63 (define @t242 () (_ tptp.q @t17)) % 0.34/0.63 (define @t243 () (not @t241)) % 0.34/0.63 (define @t244 () (lambda @t132 (not (or (not (or @t243 @t242)) (not (or (not @t242) @t241)))))) % 0.34/0.63 (define @t245 () (_ @t244 @t38)) % 0.34/0.63 (define @t246 () (or @t100 @t245)) % 0.34/0.63 (define @t247 () (forall @t41 @t246)) % 0.34/0.63 (define @t248 () (lambda @t36 @t247)) % 0.34/0.63 (define @t249 () (lambda @t143 (not (or (not (or @t243 @t142)) (not (or @t203 @t241)))))) % 0.34/0.63 (define @t250 () (_ @t221 tptp.p)) % 0.34/0.63 (define @t251 () (lambda @t132 @t216)) % 0.34/0.63 (define @t252 () (_ @t251 @t17)) % 0.34/0.63 (define @t253 () (not @t252)) % 0.34/0.63 (define @t254 () (or @t219 @t253)) % 0.34/0.63 (define @t255 () (not @t254)) % 0.34/0.63 (define @t256 () (lambda @t132 @t255)) % 0.34/0.63 (define @t257 () (@var "BOUND_VARIABLE_7581" (-> $$unsorted Bool))) % 0.34/0.63 (define @t258 () (not (_ @t257 @t17))) % 0.34/0.63 (define @t259 () (@list @t257 @t17)) % 0.34/0.63 (define @t260 () (@var "BOUND_VARIABLE_7601" (-> $$unsorted Bool))) % 0.34/0.63 (define @t261 () (_ @t260 @t17)) % 0.34/0.63 (define @t262 () (lambda (@list @t260 @t17) (or @t203 @t261))) % 0.34/0.63 (define @t263 () (@list @t14)) % 0.34/0.63 (define @t264 () (lambda @t132 @t218)) % 0.34/0.63 (define @t265 () (_ @t264 @t17)) % 0.34/0.63 (define @t266 () (not @t265)) % 0.34/0.63 (define @t267 () (or @t266 @t258)) % 0.34/0.63 (define @t268 () (not @t267)) % 0.34/0.63 (define @t269 () (lambda @t259 @t268)) % 0.34/0.63 (define @t270 () (not (or @t217 @t203))) % 0.34/0.63 (define @t271 () (lambda @t21 @t270)) % 0.34/0.63 (define @t272 () (lambda @t143 @t218)) % 0.34/0.63 (define @t273 () (or @t11 @t15)) % 0.34/0.63 (define @t274 () (lambda @t36 @t273)) % 0.34/0.63 (define @t275 () (@list @t14 @t4)) % 0.34/0.63 (define @t276 () (lambda @t275 @t273)) % 0.34/0.63 (define @t277 () (lambda @t36 @t11)) % 0.34/0.63 (define @t278 () (_ @t277 @t4)) % 0.34/0.63 (define @t279 () (or @t278 @t15)) % 0.34/0.63 (define @t280 () (lambda @t275 @t279)) % 0.34/0.63 (define @t281 () (not @t15)) % 0.34/0.63 (define @t282 () (or @t11 @t281)) % 0.34/0.63 (define @t283 () (lambda @t36 @t282)) % 0.34/0.63 (define @t284 () (_ @t283 @t4)) % 0.34/0.63 (define @t285 () (not @t284)) % 0.34/0.63 (define @t286 () (lambda @t36 @t285)) % 0.34/0.63 (define @t287 () (lambda @t36 @t281)) % 0.34/0.63 (define @t288 () (_ @t287 @t4)) % 0.34/0.63 (define @t289 () (or @t11 @t288)) % 0.34/0.63 (define @t290 () (lambda @t36 @t289)) % 0.34/0.63 (define @t291 () (forall @t106 @t103)) % 0.34/0.63 (define @t292 () (@quantifiers_skolemize @t291 0)) % 0.34/0.63 (define @t293 () (forall @t41 (or (not (tptp.rel_s4 @t292 @t38)) @t98))) % 0.34/0.63 (define @t294 () (@quantifiers_skolemize @t291 3)) % 0.34/0.63 (define @t295 () (tptp.p @t294)) % 0.34/0.63 (define @t296 () (@quantifiers_skolemize @t291 1)) % 0.34/0.63 (define @t297 () (tptp.rel_s4 @t296 @t294)) % 0.34/0.63 (define @t298 () (not @t297)) % 0.34/0.63 (define @t299 () (forall @t89 (or (not (tptp.rel_s4 @t296 @t87)) @t88))) % 0.34/0.63 (define @t300 () (not @t299)) % 0.34/0.63 (define @t301 () (or @t300 @t298 @t295)) % 0.34/0.63 (define @t302 () (@quantifiers_skolemize @t291 2)) % 0.34/0.63 (define @t303 () (tptp.q @t302)) % 0.34/0.63 (define @t304 () (tptp.rel_s4 @t296 @t302)) % 0.34/0.63 (define @t305 () (not @t304)) % 0.34/0.63 (define @t306 () (forall @t93 (or (not (tptp.rel_s4 @t296 @t91)) @t92))) % 0.34/0.63 (define @t307 () (not @t306)) % 0.34/0.63 (define @t308 () (or @t307 @t305 @t303)) % 0.34/0.63 (define @t309 () (and @t308 @t301)) % 0.34/0.63 (define @t310 () (tptp.rel_s4 @t292 @t296)) % 0.34/0.63 (define @t311 () (not @t310)) % 0.34/0.63 (define @t312 () (not @t293)) % 0.34/0.63 (define @t313 () (or @t312 @t311 @t309)) % 0.34/0.63 (define @t314 () (@list true)) % 0.34/0.63 (define @t315 () (@list @t313)) % 0.34/0.63 (define @t316 () (@list @t294)) % 0.34/0.63 (define @t317 () (_ @t40 @t44 @t55)) % 0.34/0.63 (define @t318 () (_ @t40 @t49 @t55)) % 0.34/0.63 (define @t319 () (_ @t40 @t44 @t49)) % 0.34/0.63 (define @t320 () (not @t57)) % 0.34/0.63 (define @t321 () (not @t51)) % 0.34/0.63 (define @t322 () (or @t321 @t320 @t56)) % 0.34/0.63 (define @t323 () (@list @t302)) % 0.34/0.63 (define @t324 () (tptp.p @t302)) % 0.34/0.63 (define @t325 () (or @t305 @t324)) % 0.34/0.63 (define @t326 () (or @t298 @t295)) % 0.34/0.63 (define @t327 () (not @t326)) % 0.34/0.63 (define @t328 () (@list true false)) % 0.34/0.63 (define @t329 () (tptp.rel_s4 @t292 @t302)) % 0.34/0.63 (define @t330 () (or @t311 @t305 @t329)) % 0.34/0.63 (define @t331 () (not @t324)) % 0.34/0.63 (define @t332 () (or @t331 @t303)) % 0.34/0.63 (define @t333 () (and @t332 (or (not @t303) @t324))) % 0.34/0.63 (define @t334 () (not @t329)) % 0.34/0.63 (define @t335 () (or @t334 @t333)) % 0.34/0.63 (define @t336 () (@list @t301)) % 0.34/0.63 (define @t337 () (tptp.rel_s4 @t292 @t294)) % 0.34/0.63 (define @t338 () (or @t311 @t298 @t337)) % 0.34/0.63 (define @t339 () (tptp.q @t294)) % 0.34/0.63 (define @t340 () (not @t339)) % 0.34/0.63 (define @t341 () (or @t340 @t295)) % 0.34/0.63 (define @t342 () (not @t295)) % 0.34/0.63 (define @t343 () (and (or @t342 @t339) @t341)) % 0.34/0.63 (define @t344 () (not @t337)) % 0.34/0.63 (define @t345 () (or @t344 @t343)) % 0.34/0.63 (define @t346 () (@list false false)) % 0.34/0.63 (define @t347 () (or @t298 @t339)) % 0.34/0.63 (define @t348 () (not @t341)) % 0.34/0.63 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.34/0.63 (assume @p2 (_ tptp.mreflexive tptp.rel_s4)) % 0.34/0.63 (assume @p3 (_ tptp.mtransitive tptp.rel_s4)) % 0.34/0.63 (assume @p4 @t1) % 0.34/0.63 (assume @p5 true) % 0.34/0.63 (step @p6 (= tptp.meq_ind @t5) :rule refl :args (@t5)) % 0.34/0.63 (step @p7 (= tptp.meq_prop @t8) :rule refl :args (@t8)) % 0.34/0.63 (step @p8 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.34/0.63 (step @p9 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.34/0.63 (step @p10 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.34/0.63 (step @p11 (= tptp.mimplies @t23) :rule refl :args (@t23)) % 0.34/0.63 (step @p12 (= tptp.mimplied @t24) :rule refl :args (@t24)) % 0.34/0.63 (step @p13 (= tptp.mequiv @t25) :rule refl :args (@t25)) % 0.34/0.63 (step @p14 (= tptp.mxor @t26) :rule refl :args (@t26)) % 0.34/0.63 (step @p15 (= tptp.mforall_ind @t29) :rule refl :args (@t29)) % 0.34/0.63 (step @p16 (= tptp.mforall_prop @t33) :rule refl :args (@t33)) % 0.34/0.63 (step @p17 (= tptp.mexists_ind @t34) :rule refl :args (@t34)) % 0.34/0.63 (step @p18 (= tptp.mexists_prop @t35) :rule refl :args (@t35)) % 0.34/0.63 (step @p19 (= tptp.mtrue @t37) :rule refl :args (@t37)) % 0.34/0.63 (step @p20 (= tptp.mbox @t42) :rule refl :args (@t42)) % 0.34/0.63 (step @p21 (= tptp.mdia @t43) :rule refl :args (@t43)) % 0.34/0.63 (step @p22 (= tptp.mreflexive @t48) :rule refl :args (@t48)) % 0.34/0.63 (step @p23 (= tptp.msymmetric @t52) :rule refl :args (@t52)) % 0.34/0.63 (step @p24 (= tptp.mserial @t54) :rule refl :args (@t54)) % 0.34/0.63 (step @p25 (= tptp.mtransitive @t61) :rule refl :args (@t61)) % 0.34/0.63 (step @p26 (= tptp.meuclidean @t63) :rule refl :args (@t63)) % 0.34/0.63 (step @p27 (= tptp.mpartially_functional @t65) :rule refl :args (@t65)) % 0.34/0.63 (step @p28 (= tptp.mfunctional @t67) :rule refl :args (@t67)) % 0.34/0.63 (step @p29 (= tptp.mweakly_dense @t70) :rule refl :args (@t70)) % 0.34/0.63 (step @p30 (= tptp.mweakly_connected @t71) :rule refl :args (@t71)) % 0.34/0.63 (step @p31 (= tptp.mweakly_directed @t72) :rule refl :args (@t72)) % 0.34/0.63 (step @p32 (= tptp.mvalid @t75) :rule refl :args (@t75)) % 0.34/0.63 (step @p33 (= tptp.minvalid @t76) :rule refl :args (@t76)) % 0.34/0.63 (step @p34 (= tptp.msatisfiable @t77) :rule refl :args (@t77)) % 0.34/0.63 (step @p35 (= tptp.mcountersatisfiable @t78) :rule refl :args (@t78)) % 0.34/0.63 (step @p36 (= tptp.mbox_s4 @t83) :rule refl :args (@t83)) % 0.34/0.63 (step @p37 (= tptp.mdia_s4 @t84) :rule refl :args (@t84)) % 0.34/0.63 (step @p38 :rule aci_norm :args ((= @t105 @t103))) % 0.34/0.63 (step @p39 :rule cong :premises (@p38) :args (@t107)) % 0.34/0.63 (step @p40 :rule quant-merge-prenex :args ((= (forall @t36 @t109) @t107))) % 0.34/0.63 (step @p41 :rule alpha_equiv :args (@t110 (@list @t86 @t90 @t85) (@list @t38 @t112 @t111))) % 0.34/0.63 (step @p42 :rule refl :args (@t102)) % 0.34/0.63 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t113)) % 0.34/0.63 (step @p44 :rule quant-miniscope-or :args ((= @t109 @t113))) % 0.34/0.63 (step @p45 :rule trans :premises (@p44 @p43)) % 0.34/0.63 (step @p46 :rule symm :premises (@p45)) % 0.34/0.63 (step @p47 :rule cong :premises (@p46) :args ((forall @t36 @t127))) % 0.34/0.63 (step @p48 :rule trans :premises (@p47 @p40)) % 0.34/0.63 (step @p49 :rule trans :premises (@p48 @p39)) % 0.34/0.63 (step @p50 :rule beta-reduce :args ((= @t134 @t127))) % 0.34/0.63 (step @p51 :rule cong :premises (@p50) :args (@t135)) % 0.34/0.63 (step @p52 :rule trans :premises (@p51 @p49)) % 0.34/0.63 (step @p53 :rule beta-reduce :args ((= (_ @t137 @t133) @t135))) % 0.34/0.63 (step @p54 :rule trans :premises (@p53 @p52)) % 0.34/0.63 (step @p55 :rule beta-reduce :args ((= @t139 @t129))) % 0.34/0.63 (step @p56 :rule refl :args (@t131)) % 0.34/0.63 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t140)) % 0.34/0.63 (step @p58 :rule cong :premises (@p57) :args (@t141)) % 0.34/0.63 (step @p59 :rule beta-reduce :args ((= (_ (lambda @t143 (or @t131 @t142)) @t138) @t141))) % 0.34/0.63 (step @p60 :rule trans :premises (@p59 @p58)) % 0.34/0.63 (step @p61 :rule aci_norm :args ((= @t145 @t118))) % 0.34/0.63 (step @p62 :rule aci_norm :args ((= @t147 @t123))) % 0.34/0.63 (step @p63 :rule nary_cong :premises (@p62 @p61) :args (@t148)) % 0.34/0.63 (step @p64 :rule refl :args (@t100)) % 0.34/0.63 (step @p65 :rule nary_cong :premises (@p64 @p63) :args (@t149)) % 0.34/0.63 (step @p66 :rule cong :premises (@p65) :args (@t150)) % 0.34/0.63 (step @p67 :rule quant-merge-prenex :args ((= (forall @t41 @t152) @t150))) % 0.34/0.63 (step @p68 :rule alpha_equiv :args (@t154 (@list @t111) @t155)) % 0.34/0.63 (step @p69 :rule refl :args (@t117)) % 0.34/0.63 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t156)) % 0.34/0.63 (step @p71 :rule quant-miniscope-or :args ((= @t157 @t156))) % 0.34/0.63 (step @p72 :rule quant-unused-vars :args ((= @t158 @t157))) % 0.34/0.63 (step @p73 :rule trans :premises (@p72 @p71)) % 0.34/0.63 (step @p74 :rule trans :premises (@p73 @p70)) % 0.34/0.63 (step @p75 :rule alpha_equiv :args (@t160 (@list @t112) @t161)) % 0.34/0.63 (step @p76 :rule refl :args (@t122)) % 0.34/0.63 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t162)) % 0.34/0.63 (step @p78 :rule quant-miniscope-or :args ((= @t163 @t162))) % 0.34/0.63 (step @p79 :rule quant-unused-vars :args ((= @t164 @t163))) % 0.34/0.63 (step @p80 :rule trans :premises (@p79 @p78)) % 0.34/0.63 (step @p81 :rule trans :premises (@p80 @p77)) % 0.34/0.63 (step @p82 :rule nary_cong :premises (@p81 @p74) :args (@t165)) % 0.34/0.63 (step @p83 :rule quant-miniscope-and :args ((= @t166 @t165))) % 0.34/0.63 (step @p84 :rule trans :premises (@p83 @p82)) % 0.34/0.63 (step @p85 :rule refl :args (@t100)) % 0.34/0.63 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t167)) % 0.34/0.63 (step @p87 :rule quant-miniscope-or :args ((= @t152 @t167))) % 0.34/0.63 (step @p88 :rule trans :premises (@p87 @p86)) % 0.34/0.63 (step @p89 :rule symm :premises (@p88)) % 0.34/0.63 (step @p90 :rule cong :premises (@p89) :args ((forall @t41 (or @t100 (and @t169 @t168))))) % 0.34/0.63 (step @p91 :rule trans :premises (@p90 @p67)) % 0.34/0.63 (step @p92 :rule trans :premises (@p91 @p66)) % 0.34/0.63 (step @p93 :rule bool-double-not-elim :args (@t168)) % 0.34/0.63 (step @p94 :rule bool-double-not-elim :args (@t169)) % 0.34/0.63 (step @p95 :rule nary_cong :premises (@p94 @p93) :args ((and (not @t171) (not @t170)))) % 0.34/0.63 (step @p96 :rule bool-or-de-morgan :args (@t171 @t170 false)) % 0.34/0.63 (step @p97 :rule trans :premises (@p96 @p95)) % 0.34/0.63 (step @p98 :rule nary_cong :premises (@p85 @p97) :args (@t173)) % 0.34/0.63 (step @p99 :rule cong :premises (@p98) :args ((forall @t41 @t173))) % 0.34/0.63 (step @p100 :rule trans :premises (@p99 @p92)) % 0.34/0.63 (step @p101 :rule beta-reduce :args ((= (_ (lambda @t132 (not (or (not (or (not @t174) @t175)) (not (or (not @t175) @t174))))) @t38) @t172))) % 0.34/0.63 (step @p102 :rule refl :args (@t38)) % 0.34/0.63 (step @p103 :rule alpha_equiv :args (@t176 @t177 @t155)) % 0.34/0.63 (step @p104 :rule alpha_equiv :args (@t178 @t177 @t161)) % 0.34/0.63 (step @p105 :rule cong :premises (@p104) :args (@t179)) % 0.34/0.63 (step @p106 :rule nary_cong :premises (@p105 @p103) :args (@t180)) % 0.34/0.63 (step @p107 :rule cong :premises (@p106) :args (@t181)) % 0.34/0.63 (step @p108 :rule cong 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@p193)) % 0.34/0.63 (step @p196 :rule beta-reduce :args ((= (_ @t249 tptp.q) @t244))) % 0.34/0.63 (step @p197 :rule refl :args (tptp.q)) % 0.34/0.63 (step @p198 :rule beta-reduce :args ((= @t250 @t249))) % 0.34/0.63 (step @p199 :rule ho_cong :premises (@p198 @p197)) % 0.34/0.63 (step @p200 :rule trans :premises (@p199 @p196)) % 0.34/0.63 (step @p201 :rule ho_cong :premises (@p155 @p200)) % 0.34/0.63 (step @p202 :rule trans :premises (@p201 @p195)) % 0.34/0.63 (step @p203 :rule refl :args (@t228)) % 0.34/0.63 (step @p204 :rule ho_cong :premises (@p203 @p202)) % 0.34/0.63 (step @p205 :rule trans :premises (@p204 @p163)) % 0.34/0.63 (step @p206 :rule ho_cong :premises (@p205 @p157)) % 0.34/0.63 (step @p207 :rule trans :premises (@p206 @p60)) % 0.34/0.63 (step @p208 :rule refl :args (@t137)) % 0.34/0.63 (step @p209 :rule ho_cong :premises (@p208 @p207)) % 0.34/0.63 (step @p210 :rule trans :premises (@p209 @p54)) % 0.34/0.63 (step @p211 :rule cong :premises (@p210) :args ((not (_ @t137 (_ 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