%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO057^2 : 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 : n015.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 09:11:54 AM UTC 2026 % Result : Theorem 0.45s 0.67s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO057^2 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n015.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 23:53:04 EDT 2026 % 0.16/0.35 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.45/0.67 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.67 % SZS status Theorem % 0.45/0.67 % SZS output start Proof % 0.45/0.67 ( % 0.45/0.67 (declare-sort $$unsorted 0) % 0.45/0.67 (declare-sort tptp.mu 0) % 0.45/0.67 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.45/0.67 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.45/0.67 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.45/0.67 (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)))))) % 0.45/0.67 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.45/0.67 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.45/0.67 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.45/0.67 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.45/0.67 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.45/0.67 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.45/0.67 (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))))))) % 0.45/0.67 (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))))))) % 0.45/0.67 (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)))))) % 0.45/0.67 (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)))))) % 0.45/0.67 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.45/0.67 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.45/0.67 (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)))))) % 0.45/0.67 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.45/0.67 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.45/0.67 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.45/0.67 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.45/0.67 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.45/0.67 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.45/0.67 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.45/0.67 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.45/0.67 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.45/0.67 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.45/0.67 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.45/0.67 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.45/0.67 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.45/0.67 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.45/0.67 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.45/0.67 (define @t2 () (@var "A" (-> $$unsorted Bool))) % 0.45/0.67 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.45/0.67 (define @t4 () (_ tptp.mbox @t3)) % 0.45/0.67 (define @t5 () (_ @t4 @t2)) % 0.45/0.67 (define @t6 () (@list @t2 @t1)) % 0.45/0.67 (define @t7 () (lambda @t6 (_ (_ (_ tptp.mimplies (_ @t4 (_ (_ tptp.mimplies @t5) @t2))) @t5) @t1))) % 0.45/0.67 (define @t8 () (not (_ tptp.mvalid (_ tptp.mforall_prop @t7)))) % 0.45/0.67 (define @t9 () (@list @t3)) % 0.45/0.67 (define @t10 () (exists @t9 @t8)) % 0.45/0.67 (define @t11 () (not @t10)) % 0.45/0.67 (define @t12 () (@var "Y" tptp.mu)) % 0.45/0.67 (define @t13 () (@var "X" tptp.mu)) % 0.45/0.67 (define @t14 () (@var "W" $$unsorted)) % 0.45/0.67 (define @t15 () (lambda (@list @t13 @t12 @t14) (= @t13 @t12))) % 0.45/0.67 (define @t16 () (@var "Y" (-> $$unsorted Bool))) % 0.45/0.67 (define @t17 () (@var "X" (-> $$unsorted Bool))) % 0.45/0.67 (define @t18 () (lambda (@list @t17 @t16 @t14) (= (_ @t17 @t14) (_ @t16 @t14)))) % 0.45/0.67 (define @t19 () (@var "Phi" (-> $$unsorted Bool))) % 0.45/0.67 (define @t20 () (_ @t19 @t14)) % 0.45/0.67 (define @t21 () (not @t20)) % 0.45/0.67 (define @t22 () (@list @t19 @t14)) % 0.45/0.67 (define @t23 () (lambda @t22 @t21)) % 0.45/0.67 (define @t24 () (@var "Psi" (-> $$unsorted Bool))) % 0.45/0.67 (define @t25 () (_ @t24 @t14)) % 0.45/0.67 (define @t26 () (lambda (@list @t19 @t24 @t14) (or @t20 @t25))) % 0.45/0.67 (define @t27 () (_ tptp.mnot @t24)) % 0.45/0.67 (define @t28 () (_ tptp.mnot @t19)) % 0.45/0.67 (define @t29 () (_ tptp.mor @t28)) % 0.45/0.67 (define @t30 () (@list @t19 @t24 @t1)) % 0.45/0.67 (define @t31 () (lambda @t30 (_ (_ tptp.mnot (_ @t29 @t27)) @t1))) % 0.45/0.67 (define @t32 () (lambda @t30 (_ (_ @t29 @t24) @t1))) % 0.45/0.67 (define @t33 () (lambda @t30 (_ (_ (_ tptp.mor @t27) @t19) @t1))) % 0.45/0.67 (define @t34 () (lambda @t30 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t19) @t24)) (_ (_ tptp.mimplies @t24) @t19)) @t1))) % 0.45/0.67 (define @t35 () (lambda @t30 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t19) @t24)) @t1))) % 0.45/0.67 (define @t36 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.45/0.67 (define @t37 () (_ @t36 @t13)) % 0.45/0.67 (define @t38 () (lambda (@list @t36 @t14) (forall (@list @t13) (_ @t37 @t14)))) % 0.45/0.67 (define @t39 () (@var "P" (-> $$unsorted Bool))) % 0.45/0.67 (define @t40 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.45/0.67 (define @t41 () (_ @t40 @t39)) % 0.45/0.67 (define @t42 () (_ @t41 @t14)) % 0.45/0.67 (define @t43 () (@list @t39)) % 0.45/0.67 (define @t44 () (forall @t43 @t42)) % 0.45/0.67 (define @t45 () (@list @t40 @t14)) % 0.45/0.67 (define @t46 () (lambda @t45 @t44)) % 0.45/0.67 (define @t47 () (lambda (@list @t36 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t13 @t1) (_ (_ tptp.mnot @t37) @t1)))) @t1))) % 0.45/0.67 (define @t48 () (lambda (@list @t40 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t39 @t1) (_ (_ tptp.mnot @t41) @t1)))) @t1))) % 0.45/0.68 (define @t49 () (@list @t14)) % 0.45/0.68 (define @t50 () (lambda @t49 true)) % 0.45/0.68 (define @t51 () (@var "V" $$unsorted)) % 0.45/0.68 (define @t52 () (_ @t19 @t51)) % 0.45/0.68 (define @t53 () (_ (_ @t3 @t14) @t51)) % 0.45/0.68 (define @t54 () (not @t53)) % 0.45/0.68 (define @t55 () (or @t54 @t52)) % 0.45/0.68 (define @t56 () (@list @t51)) % 0.45/0.68 (define @t57 () (forall @t56 @t55)) % 0.45/0.68 (define @t58 () (@list @t3 @t19 @t14)) % 0.45/0.68 (define @t59 () (lambda @t58 @t57)) % 0.45/0.68 (define @t60 () (lambda (@list @t3 @t19 @t1) (_ (_ tptp.mnot (_ @t4 @t28)) @t1))) % 0.45/0.68 (define @t61 () (@var "S" $$unsorted)) % 0.45/0.68 (define @t62 () (_ @t3 @t61)) % 0.45/0.68 (define @t63 () (@list @t61)) % 0.45/0.68 (define @t64 () (lambda @t9 (forall @t63 (_ @t62 @t61)))) % 0.45/0.68 (define @t65 () (@var "T" $$unsorted)) % 0.45/0.68 (define @t66 () (_ @t3 @t65)) % 0.45/0.68 (define @t67 () (_ @t62 @t65)) % 0.45/0.68 (define @t68 () (lambda @t9 (forall (@list @t61 @t65) (=> @t67 (_ @t66 @t61))))) % 0.45/0.68 (define @t69 () (@list @t65)) % 0.45/0.68 (define @t70 () (lambda @t9 (forall @t63 (exists @t69 @t67)))) % 0.45/0.68 (define @t71 () (@var "U" $$unsorted)) % 0.45/0.68 (define @t72 () (_ @t62 @t71)) % 0.45/0.68 (define @t73 () (_ @t66 @t71)) % 0.45/0.68 (define @t74 () (@list @t61 @t65 @t71)) % 0.45/0.68 (define @t75 () (lambda @t9 (forall @t74 (=> (and @t67 @t73) @t72)))) % 0.45/0.68 (define @t76 () (and @t67 @t72)) % 0.45/0.68 (define @t77 () (lambda @t9 (forall @t74 (=> @t76 @t73)))) % 0.45/0.68 (define @t78 () (= @t65 @t71)) % 0.45/0.68 (define @t79 () (lambda @t9 (forall @t74 (=> @t76 @t78)))) % 0.45/0.68 (define @t80 () (@list @t71)) % 0.45/0.68 (define @t81 () (lambda @t9 (forall @t63 (exists @t69 (and @t67 (forall @t80 (=> @t72 @t78))))))) % 0.45/0.68 (define @t82 () (_ @t3 @t71)) % 0.45/0.68 (define @t83 () (_ @t82 @t65)) % 0.45/0.68 (define @t84 () (lambda @t9 (forall @t74 (=> @t67 (exists @t80 (and @t72 @t83)))))) % 0.45/0.68 (define @t85 () (lambda @t9 (forall @t74 (=> @t76 (or @t73 @t78 @t83))))) % 0.45/0.68 (define @t86 () (lambda @t9 (forall @t74 (=> @t76 (exists @t56 (and (_ @t66 @t51) (_ @t82 @t51))))))) % 0.45/0.68 (define @t87 () (forall @t49 @t20)) % 0.45/0.68 (define @t88 () (@list @t19)) % 0.45/0.68 (define @t89 () (lambda @t88 @t87)) % 0.45/0.68 (define @t90 () (lambda @t88 (forall @t49 @t21))) % 0.45/0.68 (define @t91 () (lambda @t88 (exists @t49 @t20))) % 0.45/0.68 (define @t92 () (lambda @t88 (exists @t49 @t21))) % 0.45/0.68 (define @t93 () (@var "BOUND_VARIABLE_8428" $$unsorted)) % 0.45/0.68 (define @t94 () (_ @t39 @t93)) % 0.45/0.68 (define @t95 () (not (_ @t3 @t14 @t93))) % 0.45/0.68 (define @t96 () (_ @t39 @t51)) % 0.45/0.68 (define @t97 () (@var "BOUND_VARIABLE_8369" $$unsorted)) % 0.45/0.68 (define @t98 () (not (_ @t3 @t51 @t97))) % 0.45/0.68 (define @t99 () (@list @t97)) % 0.45/0.68 (define @t100 () (_ @t3 @t14 @t51)) % 0.45/0.68 (define @t101 () (not @t100)) % 0.45/0.68 (define @t102 () (not (forall @t56 (or @t101 (not (forall @t99 (or @t98 (_ @t39 @t97)))) @t96)))) % 0.45/0.68 (define @t103 () (or @t102 @t95 @t94)) % 0.45/0.68 (define @t104 () (forall (@list @t3 @t14 @t39 @t93) @t103)) % 0.45/0.68 (define @t105 () (forall (@list @t14 @t39 @t93) @t103)) % 0.45/0.68 (define @t106 () (not @t105)) % 0.45/0.68 (define @t107 () (forall @t9 (not @t106))) % 0.45/0.68 (define @t108 () (not @t107)) % 0.45/0.68 (define @t109 () (@list @t39 @t93)) % 0.45/0.68 (define @t110 () (forall @t109 @t103)) % 0.45/0.68 (define @t111 () (lambda @t49 @t110)) % 0.45/0.68 (define @t112 () (_ @t111 @t14)) % 0.45/0.68 (define @t113 () (forall @t49 @t112)) % 0.45/0.68 (define @t114 () (_ @t19 @t14)) % 0.45/0.68 (define @t115 () (lambda @t88 (forall @t49 @t114))) % 0.45/0.68 (define @t116 () (or @t95 @t94)) % 0.45/0.68 (define @t117 () (or @t102 @t116)) % 0.45/0.68 (define @t118 () (forall @t109 @t117)) % 0.45/0.68 (define @t119 () (@list @t93)) % 0.45/0.68 (define @t120 () (forall @t119 @t117)) % 0.45/0.68 (define @t121 () (forall @t119 @t116)) % 0.45/0.68 (define @t122 () (@list @t51)) % 0.45/0.68 (define @t123 () (or @t102 @t121)) % 0.45/0.68 (define @t124 () (or @t102 (forall @t56 (or @t101 @t96)))) % 0.45/0.68 (define @t125 () (_ @t2 @t51)) % 0.45/0.68 (define @t126 () (not (_ @t3 @t1 @t51))) % 0.45/0.68 (define @t127 () (forall @t56 (or @t126 @t125))) % 0.45/0.68 (define @t128 () (_ @t2 @t97)) % 0.45/0.68 (define @t129 () (not (forall @t99 (or @t98 @t128)))) % 0.45/0.68 (define @t130 () (forall @t56 (or @t126 @t129 @t125))) % 0.45/0.68 (define @t131 () (not @t130)) % 0.45/0.68 (define @t132 () (or @t131 @t127)) % 0.45/0.68 (define @t133 () (lambda @t6 @t132)) % 0.45/0.68 (define @t134 () (_ @t133 @t39 @t14)) % 0.45/0.68 (define @t135 () (forall @t43 @t134)) % 0.45/0.68 (define @t136 () (lambda @t49 @t135)) % 0.45/0.68 (define @t137 () (_ @t40 @t39 @t14)) % 0.45/0.68 (define @t138 () (lambda @t45 (forall @t43 @t137))) % 0.45/0.68 (define @t139 () (@list @t1)) % 0.45/0.68 (define @t140 () (lambda @t49 (forall @t56 (or @t101 @t125)))) % 0.45/0.68 (define @t141 () (_ @t140 @t1)) % 0.45/0.68 (define @t142 () (or @t131 @t141)) % 0.45/0.68 (define @t143 () (lambda @t139 @t142)) % 0.45/0.68 (define @t144 () (_ @t24 @t1)) % 0.45/0.68 (define @t145 () (@list @t24 @t1)) % 0.45/0.68 (define @t146 () (_ @t19 @t51)) % 0.45/0.68 (define @t147 () (forall @t56 (or @t101 @t146))) % 0.45/0.68 (define @t148 () (lambda @t22 @t147)) % 0.45/0.68 (define @t149 () (_ (lambda @t58 @t147) @t3)) % 0.45/0.68 (define @t150 () (lambda @t49 (forall @t56 (or @t101 @t129 @t125)))) % 0.45/0.68 (define @t151 () (_ @t150 @t1)) % 0.45/0.68 (define @t152 () (not @t151)) % 0.45/0.68 (define @t153 () (or @t152 @t144)) % 0.45/0.68 (define @t154 () (lambda @t145 @t153)) % 0.45/0.68 (define @t155 () (or (not (_ @t19 @t1)) @t144)) % 0.45/0.68 (define @t156 () (lambda @t30 @t155)) % 0.45/0.68 (define @t157 () (_ @t2 @t51)) % 0.45/0.68 (define @t158 () (or @t101 @t129 @t157)) % 0.45/0.68 (define @t159 () (or @t129 @t157)) % 0.45/0.68 (define @t160 () (_ @t2 @t1)) % 0.45/0.68 (define @t161 () (not @t127)) % 0.45/0.68 (define @t162 () (or @t161 @t160)) % 0.45/0.68 (define @t163 () (lambda @t139 @t162)) % 0.45/0.68 (define @t164 () (or @t101 (_ @t163 @t51))) % 0.45/0.68 (define @t165 () (forall @t56 @t164)) % 0.45/0.68 (define @t166 () (lambda @t49 @t165)) % 0.45/0.68 (define @t167 () (not @t141)) % 0.45/0.68 (define @t168 () (or @t167 @t144)) % 0.45/0.68 (define @t169 () (lambda @t145 @t168)) % 0.45/0.68 (define @t170 () (_ @t149 @t2)) % 0.45/0.68 (define @t171 () (lambda @t6 (_ (_ (_ @t156 (_ @t149 (_ (_ @t156 @t170) @t2))) @t170) @t1))) % 0.45/0.68 (define @t172 () (not (_ @t115 (_ @t138 @t171)))) % 0.45/0.68 (define @t173 () (exists @t9 @t172)) % 0.45/0.68 (define @t174 () (or @t21 @t25)) % 0.45/0.68 (define @t175 () (lambda @t49 @t174)) % 0.45/0.68 (define @t176 () (@list @t24 @t14)) % 0.45/0.68 (define @t177 () (lambda @t49 @t21)) % 0.45/0.68 (define @t178 () (_ @t177 @t14)) % 0.45/0.68 (define @t179 () (or @t178 @t25)) % 0.45/0.68 (define @t180 () (lambda @t176 @t179)) % 0.45/0.68 (define @t181 () (@purify (as @$$unsorted_1 $$unsorted))) % 0.45/0.68 (define @t182 () (lambda (@list (@var "BOUND_VARIABLE_30691" $$unsorted)) false)) % 0.45/0.68 (define @t183 () (_ @t182 @t181)) % 0.45/0.68 (define @t184 () (@purify (as @$$unsorted_0 $$unsorted))) % 0.45/0.68 (define @t185 () (lambda (@list (@var "BOUND_VARIABLE_30537" $$unsorted) (@var "BOUND_VARIABLE_30538" $$unsorted)) true)) % 0.45/0.68 (define @t186 () (_ @t185 @t184 @t181)) % 0.45/0.68 (define @t187 () (not @t186)) % 0.45/0.68 (define @t188 () (_ @t182 @t51)) % 0.45/0.68 (define @t189 () (_ @t182 @t97)) % 0.45/0.68 (define @t190 () (_ @t185 @t51 @t97)) % 0.45/0.68 (define @t191 () (not @t190)) % 0.45/0.68 (define @t192 () (or @t191 @t189)) % 0.45/0.68 (define @t193 () (forall @t99 @t192)) % 0.45/0.68 (define @t194 () (not @t193)) % 0.45/0.68 (define @t195 () (_ @t185 @t184 @t51)) % 0.45/0.68 (define @t196 () (not @t195)) % 0.45/0.68 (define @t197 () (or @t196 @t194 @t188)) % 0.45/0.68 (define @t198 () (forall @t56 @t197)) % 0.45/0.68 (define @t199 () (not @t198)) % 0.45/0.68 (define @t200 () (or @t199 @t187 @t183)) % 0.45/0.68 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.45/0.68 (assume @p2 @t11) % 0.45/0.68 (assume @p3 true) % 0.45/0.68 (step @p4 (= tptp.meq_ind @t15) :rule refl :args (@t15)) % 0.45/0.68 (step @p5 (= tptp.meq_prop @t18) :rule refl :args (@t18)) % 0.45/0.68 (step @p6 (= tptp.mnot @t23) :rule refl :args (@t23)) % 0.45/0.68 (step @p7 (= tptp.mor @t26) :rule refl :args (@t26)) % 0.45/0.68 (step @p8 (= tptp.mand @t31) :rule refl :args (@t31)) % 0.45/0.68 (step @p9 (= tptp.mimplies @t32) :rule refl :args (@t32)) % 0.45/0.68 (step @p10 (= tptp.mimplied @t33) :rule refl :args (@t33)) % 0.45/0.68 (step @p11 (= tptp.mequiv @t34) :rule refl :args (@t34)) % 0.45/0.68 (step @p12 (= tptp.mxor @t35) :rule refl :args (@t35)) % 0.45/0.68 (step @p13 (= tptp.mforall_ind @t38) :rule refl :args (@t38)) % 0.45/0.68 (step @p14 (= tptp.mforall_prop @t46) :rule refl :args (@t46)) % 0.45/0.68 (step @p15 (= tptp.mexists_ind @t47) :rule refl :args (@t47)) % 0.45/0.68 (step @p16 (= tptp.mexists_prop @t48) :rule refl :args (@t48)) % 0.45/0.68 (step @p17 (= tptp.mtrue @t50) :rule refl :args (@t50)) % 0.45/0.68 (step @p18 (= tptp.mbox @t59) :rule refl :args (@t59)) % 0.45/0.68 (step @p19 (= tptp.mdia @t60) :rule refl :args (@t60)) % 0.45/0.68 (step @p20 (= tptp.mreflexive @t64) :rule refl :args (@t64)) % 0.45/0.68 (step @p21 (= tptp.msymmetric @t68) :rule refl :args (@t68)) % 0.45/0.68 (step @p22 (= tptp.mserial @t70) :rule refl :args (@t70)) % 0.45/0.68 (step @p23 (= tptp.mtransitive @t75) :rule refl :args (@t75)) % 0.45/0.68 (step @p24 (= tptp.meuclidean @t77) :rule refl :args (@t77)) % 0.45/0.68 (step @p25 (= tptp.mpartially_functional @t79) :rule refl :args (@t79)) % 0.45/0.68 (step @p26 (= tptp.mfunctional @t81) :rule refl :args (@t81)) % 0.45/0.68 (step @p27 (= tptp.mweakly_dense @t84) :rule refl :args (@t84)) % 0.45/0.68 (step @p28 (= tptp.mweakly_connected @t85) :rule refl :args (@t85)) % 0.45/0.68 (step @p29 (= tptp.mweakly_directed @t86) :rule refl :args (@t86)) % 0.45/0.68 (step @p30 (= tptp.mvalid @t89) :rule refl :args (@t89)) % 0.45/0.68 (step @p31 (= tptp.minvalid @t90) :rule refl :args (@t90)) % 0.45/0.68 (step @p32 (= tptp.msatisfiable @t91) :rule refl :args (@t91)) % 0.45/0.68 (step @p33 (= tptp.mcountersatisfiable @t92) :rule refl :args (@t92)) % 0.45/0.68 (step @p34 :rule bool-double-not-elim :args (@t104)) % 0.45/0.68 (step @p35 :rule quant-merge-prenex :args ((= (forall @t9 @t105) @t104))) % 0.45/0.68 (step @p36 :rule bool-double-not-elim :args (@t105)) % 0.45/0.68 (step @p37 :rule cong :premises (@p36) :args (@t107)) % 0.45/0.68 (step @p38 :rule trans :premises (@p37 @p35)) % 0.45/0.68 (step @p39 :rule cong :premises (@p38) :args (@t108)) % 0.45/0.68 (step @p40 :rule exists-elim :args ((= (exists @t9 @t106) @t108))) % 0.45/0.68 (step @p41 :rule trans :premises (@p40 @p39)) % 0.45/0.68 (step @p42 :rule quant-merge-prenex :args ((= (forall @t49 @t110) @t105))) % 0.45/0.68 (step @p43 :rule beta-reduce :args ((= @t112 @t110))) % 0.45/0.68 (step @p44 :rule cong :premises (@p43) :args (@t113)) % 0.45/0.68 (step @p45 :rule trans :premises (@p44 @p42)) % 0.45/0.68 (step @p46 :rule beta-reduce :args ((= (_ @t115 @t111) @t113))) % 0.45/0.68 (step @p47 :rule trans :premises (@p46 @p45)) % 0.45/0.68 (step @p48 :rule aci_norm :args ((= @t117 @t103))) % 0.45/0.68 (step @p49 :rule cong :premises (@p48) :args (@t118)) % 0.45/0.68 (step @p50 :rule quant-merge-prenex :args ((= (forall @t43 @t120) @t118))) % 0.45/0.68 (step @p51 :rule alpha_equiv :args (@t121 (@list @t93) @t122)) % 0.45/0.68 (step @p52 :rule refl :args (@t102)) % 0.45/0.68 (step @p53 :rule nary_cong :premises (@p52 @p51) :args (@t123)) % 0.45/0.68 (step @p54 :rule quant-miniscope-or :args ((= @t120 @t123))) % 0.45/0.68 (step @p55 :rule trans :premises (@p54 @p53)) % 0.45/0.68 (step @p56 :rule symm :premises (@p55)) % 0.45/0.68 (step @p57 :rule cong :premises (@p56) :args ((forall @t43 @t124))) % 0.45/0.68 (step @p58 :rule trans :premises (@p57 @p50)) % 0.45/0.68 (step @p59 :rule trans :premises (@p58 @p49)) % 0.45/0.68 (step @p60 :rule beta-reduce :args ((= @t134 @t124))) % 0.45/0.68 (step @p61 :rule cong :premises (@p60) :args (@t135)) % 0.45/0.68 (step @p62 :rule trans :premises (@p61 @p59)) % 0.45/0.68 (step @p63 :rule cong :premises (@p62) :args (@t136)) % 0.45/0.68 (step @p64 :rule beta-reduce :args ((= (_ @t138 @t133) @t136))) % 0.45/0.68 (step @p65 :rule trans :premises (@p64 @p63)) % 0.45/0.68 (step @p66 :rule beta-reduce :args ((= (_ (lambda @t139 @t132) @t1) @t132))) % 0.45/0.68 (step @p67 :rule refl :args (@t1)) % 0.45/0.68 (step @p68 :rule beta-reduce :args ((= @t141 @t127))) % 0.45/0.68 (step @p69 :rule refl :args (@t131)) % 0.45/0.68 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t142)) % 0.45/0.68 (step @p71 :rule cong :premises (@p70) :args (@t143)) % 0.45/0.68 (step @p72 :rule beta-reduce :args ((= (_ (lambda @t145 (or @t131 @t144)) @t140) @t143))) % 0.45/0.68 (step @p73 :rule trans :premises (@p72 @p71)) % 0.45/0.68 (step @p74 :rule beta-reduce :args ((= (_ @t148 @t2) @t140))) % 0.45/0.68 (step @p75 :rule refl :args (@t2)) % 0.45/0.68 (step @p76 :rule beta-reduce :args ((= @t149 @t148))) % 0.45/0.68 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 0.45/0.68 (step @p78 :rule trans :premises (@p77 @p74)) % 0.45/0.68 (step @p79 :rule refl :args (@t144)) % 0.45/0.68 (step @p80 :rule beta-reduce :args ((= @t151 @t130))) % 0.45/0.68 (step @p81 :rule cong :premises (@p80) :args (@t152)) % 0.45/0.68 (step @p82 :rule nary_cong :premises (@p81 @p79) :args (@t153)) % 0.45/0.68 (step @p83 :rule cong :premises (@p82) :args (@t154)) % 0.45/0.68 (step @p84 :rule beta-reduce :args ((= (_ @t156 @t150) @t154))) % 0.45/0.68 (step @p85 :rule trans :premises (@p84 @p83)) % 0.45/0.68 (step @p86 :rule refl :args (@t125)) % 0.45/0.68 (step @p87 :rule refl :args (@t157)) % 0.45/0.68 (step @p88 :rule cong :premises (@p87 @p86) :args ((= @t157 @t125))) % 0.45/0.68 (step @p89 :rule symm :premises (@p88)) % 0.45/0.68 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 0.45/0.68 (step @p91 :rule refl :args (@t129)) % 0.45/0.68 (step @p92 :rule refl :args (@t101)) % 0.45/0.68 (step @p93 :rule nary_cong :premises (@p92 @p91 @p90) :args (@t158)) % 0.45/0.68 (step @p94 :rule cong :premises (@p93) :args ((forall @t56 @t158))) % 0.45/0.68 (step @p95 :rule aci_norm :args ((= (or @t101 @t159) @t158))) % 0.45/0.68 (step @p96 :rule beta-reduce :args ((= (_ (lambda @t139 (or (not (forall @t99 (or (not (_ @t3 @t1 @t97)) @t128))) @t160)) @t51) @t159))) % 0.45/0.68 (step @p97 :rule refl :args (@t51)) % 0.45/0.68 (step @p98 :rule refl :args (@t160)) % 0.45/0.68 (step @p99 :rule alpha_equiv :args (@t127 @t122 (@list @t97))) % 0.45/0.68 (step @p100 :rule cong :premises (@p99) :args (@t161)) % 0.45/0.68 (step @p101 :rule nary_cong :premises (@p100 @p98) :args (@t162)) % 0.45/0.68 (step @p102 :rule cong :premises (@p101) :args (@t163)) % 0.45/0.68 (step @p103 :rule ho_cong :premises (@p102 @p97)) % 0.45/0.68 (step @p104 :rule trans :premises (@p103 @p96)) % 0.45/0.68 (step @p105 :rule refl :args (@t101)) % 0.45/0.68 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t164)) % 0.45/0.68 (step @p107 :rule trans :premises (@p106 @p95)) % 0.45/0.68 (step @p108 :rule cong :premises (@p107) :args (@t165)) % 0.45/0.68 (step @p109 :rule trans :premises (@p108 @p94)) % 0.45/0.68 (step @p110 :rule cong :premises (@p109) :args (@t166)) % 0.45/0.68 (step @p111 :rule beta-reduce :args ((= (_ @t148 @t163) @t166))) % 0.45/0.68 (step @p112 :rule trans :premises (@p111 @p110)) % 0.45/0.68 (step @p113 :rule beta-reduce :args ((= (_ (lambda @t145 (or @t161 @t144)) @t2) @t163))) % 0.45/0.68 (step @p114 :rule cong :premises (@p68) :args (@t167)) % 0.45/0.68 (step @p115 :rule nary_cong :premises (@p114 @p79) :args (@t168)) % 0.45/0.68 (step @p116 :rule cong :premises (@p115) :args (@t169)) % 0.45/0.68 (step @p117 :rule beta-reduce :args ((= (_ @t156 @t140) @t169))) % 0.45/0.68 (step @p118 :rule trans :premises (@p117 @p116)) % 0.45/0.68 (step @p119 :rule refl :args (@t156)) % 0.45/0.68 (step @p120 :rule ho_cong :premises (@p119 @p78)) % 0.45/0.68 (step @p121 :rule trans :premises (@p120 @p118)) % 0.45/0.68 (step @p122 :rule ho_cong :premises (@p121 @p75)) % 0.45/0.68 (step @p123 :rule trans :premises (@p122 @p113)) % 0.45/0.68 (step @p124 :rule ho_cong :premises (@p76 @p123)) % 0.45/0.68 (step @p125 :rule trans :premises (@p124 @p112)) % 0.45/0.68 (step @p126 :rule ho_cong :premises (@p119 @p125)) % 0.45/0.68 (step @p127 :rule trans :premises (@p126 @p85)) % 0.45/0.68 (step @p128 :rule ho_cong :premises (@p127 @p78)) % 0.45/0.68 (step @p129 :rule trans :premises (@p128 @p73)) % 0.45/0.68 (step @p130 :rule ho_cong :premises (@p129 @p67)) % 0.45/0.68 (step @p131 :rule trans :premises (@p130 @p66)) % 0.45/0.68 (step @p132 :rule cong :premises (@p131) :args (@t171)) % 0.45/0.68 (step @p133 :rule refl :args (@t138)) % 0.45/0.68 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.45/0.68 (step @p135 :rule trans :premises (@p134 @p65)) % 0.45/0.68 (step @p136 :rule refl :args (@t115)) % 0.45/0.68 (step @p137 :rule ho_cong :premises (@p136 @p135)) % 0.45/0.68 (step @p138 :rule trans :premises (@p137 @p47)) % 0.45/0.68 (step @p139 :rule cong :premises (@p138) :args (@t172)) % 0.45/0.68 (step @p140 :rule cong :premises (@p139) :args (@t173)) % 0.45/0.68 (step @p141 :rule trans :premises (@p140 @p41)) % 0.45/0.68 (step @p142 :rule cong :premises (@p141) :args ((not @t173))) % 0.45/0.68 (step @p143 :rule trans :premises (@p142 @p34)) % 0.45/0.68 (step @p144 :rule refl :args (@t3)) % 0.45/0.68 (step @p145 :rule refl :args (@t146)) % 0.45/0.68 (step @p146 :rule refl :args (@t52)) % 0.45/0.68 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t52 @t146))) % 0.45/0.68 (step @p148 :rule symm :premises (@p147)) % 0.45/0.68 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.45/0.68 (step @p150 :rule refl :args (@t100)) % 0.45/0.68 (step @p151 :rule refl :args (@t53)) % 0.45/0.68 (step @p152 :rule cong :premises (@p151 @p150) :args ((= @t53 @t100))) % 0.45/0.68 (step @p153 :rule symm :premises (@p152)) % 0.45/0.68 (step @p154 :rule eq_resolve :premises (@p151 @p153)) % 0.45/0.68 (step @p155 :rule cong :premises (@p154) :args (@t54)) % 0.45/0.68 (step @p156 :rule nary_cong :premises (@p155 @p149) :args (@t55)) % 0.45/0.68 (step @p157 :rule cong :premises (@p156) :args (@t57)) % 0.45/0.68 (step @p158 :rule cong :premises (@p157) :args (@t59)) % 0.45/0.68 (step @p159 :rule trans :premises (@p18 @p158)) % 0.45/0.68 (step @p160 :rule ho_cong :premises (@p159 @p144)) % 0.45/0.68 (step @p161 :rule ho_cong :premises (@p160 @p75)) % 0.45/0.68 (step @p162 :rule beta-reduce :args ((= (_ @t175 @t1) @t155))) % 0.45/0.68 (step @p163 :rule beta-reduce :args ((= (_ (lambda @t176 @t174) @t24) @t175))) % 0.45/0.68 (step @p164 :rule refl :args (@t24)) % 0.45/0.68 (step @p165 :rule refl :args (@t25)) % 0.45/0.68 (step @p166 :rule beta-reduce :args ((= @t178 @t21))) % 0.45/0.68 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t179)) % 0.45/0.68 (step @p168 :rule cong :premises (@p167) :args (@t180)) % 0.45/0.68 (step @p169 :rule beta-reduce :args ((= (_ @t26 @t177) @t180))) % 0.45/0.68 (step @p170 :rule trans :premises (@p169 @p168)) % 0.45/0.68 (step @p171 :rule beta-reduce :args ((= (_ @t23 @t19) @t177))) % 0.45/0.68 (step @p172 :rule refl :args (@t26)) % 0.45/0.68 (step @p173 :rule ho_cong :premises (@p172 @p171)) % 0.45/0.68 (step @p174 :rule trans :premises (@p173 @p170)) % 0.45/0.68 (step @p175 :rule ho_cong :premises (@p174 @p164)) % 0.45/0.68 (step @p176 :rule trans :premises (@p175 @p163)) % 0.45/0.68 (step @p177 :rule ho_cong :premises (@p176 @p67)) % 0.45/0.68 (step @p178 :rule trans :premises (@p177 @p162)) % 0.45/0.68 (step @p179 :rule refl :args (@t19)) % 0.45/0.68 (step @p180 :rule ho_cong :premises (@p6 @p179)) % 0.45/0.68 (step @p181 :rule ho_cong :premises (@p7 @p180)) % 0.45/0.68 (step @p182 :rule ho_cong :premises (@p181 @p164)) % 0.45/0.68 (step @p183 :rule ho_cong :premises (@p182 @p67)) % 0.45/0.68 (step @p184 :rule trans :premises (@p183 @p178)) % 0.45/0.68 (step @p185 :rule cong :premises (@p184) :args (@t32)) % 0.45/0.68 (step @p186 :rule trans :premises (@p9 @p185)) % 0.45/0.68 (step @p187 :rule ho_cong :premises (@p186 @p161)) % 0.45/0.68 (step @p188 :rule ho_cong :premises (@p187 @p75)) % 0.45/0.68 (step @p189 :rule ho_cong :premises (@p160 @p188)) % 0.45/0.68 (step @p190 :rule ho_cong :premises (@p186 @p189)) % 0.45/0.68 (step @p191 :rule ho_cong :premises (@p190 @p161)) % 0.45/0.68 (step @p192 :rule ho_cong :premises (@p191 @p67)) % 0.45/0.68 (step @p193 :rule cong :premises (@p192) :args (@t7)) % 0.45/0.68 (step @p194 :rule refl :args (@t137)) % 0.45/0.68 (step @p195 :rule refl :args (@t42)) % 0.45/0.68 (step @p196 :rule cong :premises (@p195 @p194) :args ((= @t42 @t137))) % 0.45/0.68 (step @p197 :rule symm :premises (@p196)) % 0.45/0.68 (step @p198 :rule eq_resolve :premises (@p195 @p197)) % 0.45/0.68 (step @p199 :rule cong :premises (@p198) :args (@t44)) % 0.45/0.68 (step @p200 :rule cong :premises (@p199) :args (@t46)) % 0.45/0.68 (step @p201 :rule trans :premises (@p14 @p200)) % 0.45/0.68 (step @p202 :rule ho_cong :premises (@p201 @p193)) % 0.45/0.68 (step @p203 :rule refl :args (@t114)) % 0.45/0.68 (step @p204 :rule refl :args (@t20)) % 0.45/0.68 (step @p205 :rule cong :premises (@p204 @p203) :args ((= @t20 @t114))) % 0.45/0.68 (step @p206 :rule symm :premises (@p205)) % 0.45/0.68 (step @p207 :rule eq_resolve :premises (@p204 @p206)) % 0.45/0.68 (step @p208 :rule cong :premises (@p207) :args (@t87)) % 0.45/0.68 (step @p209 :rule cong :premises (@p208) :args (@t89)) % 0.45/0.68 (step @p210 :rule trans :premises (@p30 @p209)) % 0.45/0.68 (step @p211 :rule ho_cong :premises (@p210 @p202)) % 0.45/0.68 (step @p212 :rule cong :premises (@p211) :args (@t8)) % 0.45/0.68 (step @p213 :rule cong :premises (@p212) :args (@t10)) % 0.45/0.68 (step @p214 :rule cong :premises (@p213) :args (@t11)) % 0.45/0.68 (step @p215 :rule trans :premises (@p214 @p143)) % 0.45/0.68 (step @p216 :rule eq_resolve :premises (@p2 @p215)) % 0.45/0.68 (step @p217 :rule bool-impl-false1 :args (@t104)) % 0.45/0.68 (step @p218 :rule evaluate :args ((or false false false))) % 0.45/0.68 (step @p219 :rule beta-reduce :args ((= @t183 false))) % 0.45/0.68 (step @p220 :rule evaluate :args ((not true))) % 0.45/0.68 (step @p221 :rule beta-reduce :args ((= @t186 true))) % 0.45/0.68 (step @p222 :rule cong :premises (@p221) :args (@t187)) % 0.45/0.68 (step @p223 :rule trans :premises (@p222 @p220)) % 0.45/0.68 (step @p224 :rule quant-unused-vars :args ((= (forall @t56 true) true))) % 0.45/0.68 (step @p225 :rule evaluate :args ((or false true false))) % 0.45/0.68 (step @p226 :rule beta-reduce :args ((= @t188 false))) % 0.45/0.68 (step @p227 :rule evaluate :args ((not false))) % 0.45/0.68 (step @p228 :rule quant-unused-vars :args ((= (forall @t99 false) false))) % 0.45/0.68 (step @p229 :rule evaluate :args ((or false false))) % 0.45/0.68 (step @p230 :rule beta-reduce :args ((= @t189 false))) % 0.45/0.68 (step @p231 :rule beta-reduce :args ((= @t190 true))) % 0.45/0.68 (step @p232 :rule cong :premises (@p231) :args (@t191)) % 0.45/0.68 (step @p233 :rule trans :premises (@p232 @p220)) % 0.45/0.68 (step @p234 :rule nary_cong :premises (@p233 @p230) :args (@t192)) % 0.45/0.68 (step @p235 :rule trans :premises (@p234 @p229)) % 0.45/0.68 (step @p236 :rule cong :premises (@p235) :args (@t193)) % 0.45/0.68 (step @p237 :rule trans :premises (@p236 @p228)) % 0.45/0.68 (step @p238 :rule cong :premises (@p237) :args (@t194)) % 0.45/0.68 (step @p239 :rule trans :premises (@p238 @p227)) % 0.45/0.68 (step @p240 :rule beta-reduce :args ((= @t195 true))) % 0.45/0.68 (step @p241 :rule cong :premises (@p240) :args (@t196)) % 0.45/0.68 (step @p242 :rule trans :premises (@p241 @p220)) % 0.45/0.68 (step @p243 :rule nary_cong :premises (@p242 @p239 @p226) :args (@t197)) % 0.45/0.68 (step @p244 :rule trans :premises (@p243 @p225)) % 0.45/0.68 (step @p245 :rule cong :premises (@p244) :args (@t198)) % 0.45/0.68 (step @p246 :rule trans :premises (@p245 @p224)) % 0.45/0.68 (step @p247 :rule cong :premises (@p246) :args (@t199)) % 0.45/0.68 (step @p248 :rule trans :premises (@p247 @p220)) % 0.45/0.68 (step @p249 :rule nary_cong :premises (@p248 @p223 @p219) :args (@t200)) % 0.45/0.68 (step @p250 :rule trans :premises (@p249 @p218)) % 0.45/0.68 (step @p251 :rule refl :args (@t104)) % 0.45/0.68 (step @p252 :rule cong :premises (@p251 @p250) :args ((=> @t104 @t200))) % 0.45/0.68 (step @p253 :rule trans :premises (@p252 @p217)) % 0.45/0.68 (assume-push @p260 @t104) % 0.45/0.68 (step @p255 :rule instantiate :premises (@p216) :args ((@list @t185 @t184 @t182 @t181))) % 0.45/0.68 (step-pop @p261 :rule scope :premises (@p255)) % 0.45/0.68 (step @p256 :rule process_scope :premises (@p261) :args (@t200)) % 0.45/0.68 (step @p258 :rule eq_resolve :premises (@p256 @p253)) % 0.45/0.68 (step @p259 false :rule chain_m_resolution :premises (@p258 @p216) :args (false (@list false) (@list @t104))) % 0.45/0.68 ) % 0.45/0.68 % SZS output end Proof % 0.45/0.68 % cvc5 exiting %------------------------------------------------------------------------------